Measurement and Time Series Analysis of Emotion in Music
Emery Schubert
BE, BA (Hons)
In Two Volumes
Volume 1
A thesis submitted to the University of New South Wales
in partial fulfilment of the requirements for the degree
Doctor of Philosophy
1999
I hereby declare that this submission is my own work and to the best of my knowledge it contains no material previously published or written by another person, nor material which to a substantial extent has been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis.
I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.
Signed ______Date ______
Emery Schubert
- ii - Abstract
This thesis examines the relations among emotions and musical features and their changes with time, based on the assertion that there exist underlying, culturally specific, quantifiable rules which govern these relations. I designed, programmed and tested a computer controlled Two-Dimensional Emotion Space (2DES) which administered and controlled all aspects of the experimental work. The 2DES instrument consisted of two bipolar emotional response (ER) dimensions: valence
(happiness-sadness) and arousal (activeness-sleepiness). The instrument had a test- retest reliability exceeding 0.83 (p < 0.01, N = 28) when words and pictures of facial expressions were used as the test stimuli. Construct validity was quantified (r > 0.84, p < 0.01). The 2DES was developed to collect continuous responses to recordings of four movements of music (N = 67) chosen to elicit responses in all quadrants of the
2DES: “Morning” from Peer Gynt, Adagio from Rodrigo’s Concierto de Aranjuez
(Aranjuez), Dvorak’s Slavonic Dance Op 42, No. 1 and Pizzicato Polka by Strauss. Test- retest reliability was 0.74 (p < 0.001, N = 14). Five salient and objectively quantifiable features of the musical signal (MFs) were scaled and used for time series analysis of the stimuli: melodic pitch, tempo, loudness, frequency spectrum centroid (timbral sharpness) and texture (number of different instruments playing). A quantitative analysis consisted of: (1) first order differencing to remove trends, (2) determination of suitable, lagged MFs to keep as regressors via stepwise regression, and (3) regression
- iii - of each ER onto selected MFs with first order autoregressive adjustment for serial correlation.
Regression coefficients indicated that first order differenced (∆) loudness and
∆tempo had the largest correlations with ∆arousal across all pieces, and ∆melodic pitch correlated with ∆valence for Aranjuez (p < 0.01 for all coefficients). The models were able to explain up to 73% of mean response variance. Additional variation was explained qualitatively as being due to interruptions, interactions and collinearity:
The minor key and dissonances in a tonal context moved valence toward the negative direction; Short duration and perfect cadences moved valence in the positive direction. The 2DES measure and serial correlation adjusted regression models were, together, shown to be powerful tools for understanding relations among musical features and emotional response.
- iv - Acknowledgements
During the course of my doctoral work it was necessary to venture into several academic disciplines. I am delighted and honoured to acknowledge the various people from these areas who have contributed to making my study a most enriching experience. In the discipline of psychology I am grateful to Dr. Kate Stevens, Prof.
Denis Burnham and Peter Keller. I am further appreciative of the establishment of
AMPS (Australian Music and Psychology Seminars) by Dr. Stevens, for this provided me with a listening space and testing ground among old and new-found colleagues to whom I am also grateful.
For expert guidance in statistics and time series modelling, and for generously sharing thoughts and precious time with me, I am indebted to Prof. William
Dunsmuir. Prof. Dunsmuir possesses the perfect blend of knowledge and clarity of explanation of which I was thrilled to be a beneficiary. Frances Lovejoy provided limitless assistance in operating SPSS and shared much information on writing dissertations with me. In acoustics I received generous assistance from Assoc. Prof.
Joe Wolfe and from Densil Cabrera. Prof. Wolfe has taken a great interest in my work and continuously provided me with invaluable feedback. Densil has generously made available to me his software in order to code several psychoacoustic musical features. He also spent considerable time providing insightful comments about my drafts. My harmonic analysis of music was kindly and enthusiastically checked and aided by Colin Watts. Several librarians at the
- v - University of New South Wales were particularly helpful, among whom were Julie
Nolan and Rita Keller. For tips and tricks I acquired on computer related matters I acknowledge Paul Sluis and the staff at Professional Development, and the staff at
Vislab at the University of Sydney.
It would be difficult to name all the people who encouraged me and contributed to my work, however I must include the following people: the staff at the School of
Music and Music Education at the University of New South Wales; Dr. Carol
Richardson; Dorottya Fabian; Prof. Jane Davidson; Emeritus Prof. Robert Gregson;
Prof. Sandra Trehub; Dr. Bernice Laden; Michael Holack; Alfonso Egan; Nicola and
Rosemary Bryden; Stephanie Wilson and Jennifer Christianson. Special mention is due to Assoc. Prof. Eric Sowey for the time he spent in making perceptive comments and helpful suggestions about my drafts. I also thank my amazingly patient and encouraging friends: Christina Mimmocchi; Jan Howe; Belinda Lawson; my mother,
Agnes; and Puss (Motchko), whose versatile keyboard skills aided me with the challenge of minimising typographical errors. Nicole Cooper has supported me immensely and provided me with the benefit of her literary intellect, including the translation of an article from French. I am deeply grateful to Nicole and her family
— Martin, Lois and Sooty — for their kindness, friendliness and words (and barks) of wisdom.
It is an understatement to say that working with my supervisor, Assoc. Prof. Gary
McPherson, has been an inspiring experience. I express my most genuine thanks for his tireless support, direction, encouragement and belief in my work. I cannot conceive how I might have completed this dissertation
- vi - without him. Thanks are also due to Gary’s family for allowing me to take so much of his time and for allowing me to keep their phone engaged.
Over 100 people took part in various pilots, preliminary investigations and main experiments as participants. Many of these people gave comments and advice freely and beyond my expectations, and most people gave over an hour of their time voluntarily. To all these people, I am grateful and regret the impracticality of listing all their names and contributions here.
With the benefit of all these people, the job of making significant contributions to the research community has been an enlightening and most pleasurable experience. I hope that the readers of this dissertation are able to share in the depth of these experiences above and beyond the requirements of this dissertation as much as I did.
Finally, I gratefully acknowledge the financial assistance of the Australian
Postgraduate Award and the Faculty Resources Allocation Centre of the Faculty of
Arts and Social Sciences at the University of New South Wales.
- vii - Table of Contents
Volume 1
Volume 1 i
Abstract iii
Acknowledgements v
List of Figures xvii
List of Tables xix
Chapter 1 Introduction 1
Historical Overview...... 2 Musical Features...... 10 The Nature of Emotion...... 11 The Structure of Emotion...... 16 Purpose of the Study...... 22 Plan of Methodology...... 23 Limitations of the Study...... 24 Limitation 1: Romantic, Western Tonal Music...... 24 Limitation 2: Valence and Arousal of Emotion...... 26 Limitation 3: Level of Explanation...... 26 Limitation 4: Cognitivist Response...... 27 Limitation 5: Self-Report Measures...... 27 Limitation 6: Musicological Investigation...... 30
Chapter 2 Measuring Emotions 32
Philosophical Preamble...... 33 Structure of the Review...... 33 A Comment on Terminology: “Verbal” and “Non-Verbal”...... 35 Open-Ended Measures...... 35 Non-Continuous...... 36 Gilman and Downey...... 36
- viii - Weld...... 37 Lee...... 38 Valentine...... 39 Washburn and Dickinson...... 41 Sherman...... 42 Nelson...... 43 Gabrielsson and Lindström...... 44 Continuous ...... 46 Watson...... 46 Flowers...... 46 Evaluation of Open-Ended Measures...... 47 Checklist Measures...... 50 Non-Continuous...... 50 Heinlein...... 50 Hampton...... 51 Gundlach...... 52 Capurso...... 52 Sopchak ...... 53 Hevner...... 54 Farnsworth and McMullen...... 56 Continuous ...... 56 Hevner...... 56 Clynes...... 58 Namba, Kuwano, Hatoh and Kato...... 59 Mull...... 60 Sloboda...... 61 Evaluation of Checklist Measures...... 63 Ranking and Matching Measures...... 66 Campbell...... 66 Watson...... 67 Gabriel...... 68 Terwogt and Grinsven...... 68 Evaluation of Ranking and Matching...... 70 Rating Scale Measures...... 70 Non-Continuous Unipolar...... 71 Wedin ...... 72 Asmus...... 73 Collins...... 74 Thayer...... 75 Continuous Unipolar...... 76 Goldstein...... 76 Panksepp...... 77 Nielsen...... 77 Madsen and the CRDI...... 78 Waterman...... 81 Non-Continuous Bipolar...... 82 Gray and Wheeler...... 83 Giomo and the Diagrammatic Differential...... 84 - ix - Gregory, Worral and Sarge...... 85 Cohen...... 85 Nielzén and Cesarec...... 86 Continuous Bipolar...... 87 Schubert and Madsen...... 87 Evaluation of Unipolar and Bipolar Rating Scales...... 87 Summary...... 89
Chapter 3 Development of the Two-Dimensional Emotion Space 93
Instrument Design - Developing a Prototype...... 95 Layout of the Instrument...... 97 Axis and Pole Labels for Feedback and Training...... 99 Position Feedback and Recording...... 102 The Computer Program...... 104 Experiment I: Checklist Revision...... 107 Aim...... 107 Method ...... 107 Material...... 107 Participants...... 107 Procedure...... 108 Results and Discussion ...... 108 Music Checklist...... 112 Experiment II: Two-Dimensional Emotion Space Validity and Reliability113 Aims...... 113 Method ...... 114 Stimuli...... 114 Selection of Words...... 114 Selection of Faces...... 121 Material...... 122 Participants...... 123 Design and Procedure...... 123 Tutorial Phase...... 124 Plain Phase...... 126 Rest Period...... 127 Anchor Phase...... 127 Final Questionnaire...... 128 Results ...... 128 Intuitiveness ...... 129 Range of Mean Responses...... 132 Internal Consistency and Resolution...... 133 Test-Retest Reliability...... 137 Validity...... 138 Cross-Domain Generalisability...... 140 Mapping New Words onto the Emotion Space...... 141 Outliers...... 143 Summary...... 146
- x - Chapter 4 Musical Features and Emotional Response 149
Literature Review...... 149 Isolated, Non-Musical Sounds...... 152 Nielzén and Olsson...... 152 Scherer...... 154 Isolated, Musical Sounds...... 155 Heinlein...... 155 Gabriel...... 156 Specially Composed Melodies...... 158 Levi...... 158 Sherman...... 160 Scherer and Oshinsky...... 161 Cohen...... 163 Dolgin and Adelson...... 164 Thompson and Robitaille...... 165 Behrens and Green...... 167 Pre-Existing Melodies...... 168 Gabrielsson and Juslin...... 168 Kotlyar and Morozov...... 171 Baroni and Finarelli...... 172 Specially Composed Pieces...... 172 Rigg...... 173 Nielzén and Cesarec...... 176 Collier...... 177 Pre-Existing Pieces with modification...... 177 Gerardi and Gerken...... 177 Gregory, Worrall and Sarge...... 178 Hevner...... 179 Pre-Existing Pieces...... 188 Gundlach...... 188 Watson...... 190 Mull...... 191 Nielzén and Cesarec...... 191 Nielsen...... 193 Thayer...... 194 Flowers...... 194 Collins...... 195 Namba, Kuwano, Hatoh and Kato...... 196 Sloboda...... 197 Kratus ...... 199 Panksepp...... 200 Introspective Inquiry...... 201 Cooke and Makeig...... 202 Peterson and Sorantin...... 204 Meyer...... 205 Philosophers and Critics on Key Characteristics...... 210 Musicologists on Harmonic Structure...... 211 Film and Theatre Writers...... 214 - xi - 2DES Transformation Summary...... 218 Dynamics...... 221 Mean Pitch ...... 222 Pitch Range...... 223 Variation in Pitch...... 224 Melodic Direction/Contour...... 225 Register...... 226 Mode...... 227 Timbre...... 228 Harmony...... 230 Tempo...... 232 Articulation/Duration...... 233 Note Onset...... 234 Vibrato...... 235 Rhythm...... 236 Metre...... 238
Chapter 5 Continuous Response to Music 239
Experiment III: Continuous Two-Dimensional Emotion Space...... 239 Aims...... 239 Method ...... 240 Modification of 2DES ...... 240 Stimuli...... 243 Selection of Musical Features...... 246 Texture...... 249 Loudness ...... 252 Centroid...... 256 Melodic Pitch...... 260 Tempo...... 263 Material...... 267 Participants...... 267 Procedure...... 272 Instantaneous Results...... 273 Validity Check 1: Content Validity — Range of Responses...... 274 Validity Check 2: Internal Consistency - Averaged versus Overall Response ...... 275 Validity Check 3: External (Construct) Validity - Comparison with Checklist...... 278 Experiment IV: Test-Retest Reliability...... 280 Aim...... 280 Method ...... 280 Material...... 280 Pretest - Stimuli...... 281 Participants...... 281 Procedure...... 281 Results ...... 282 Summary...... 283
- xii - Chapter 6 Theory of Time Series Analysis 285
OLS Linear Regression Model...... 288 Goodness of Fit and Residual...... 289 Lagging and Cross-Correlation...... 291 Selecting Lags...... 296 Selecting Regressors...... 298 Collinearity...... 299 Stepwise Regression...... 300 Serial Correlation...... 301 Diagnosis of Serial Correlation...... 305 Trends...... 305 Autocorrelation Function (ACF) Diagnostics...... 307 Durbin-Watson Test...... 308 Box-Ljung Statistic...... 311 First Order Differencing...... 312 First Order Differenced, Fourth Order Lagged OLS Linear Regression...315 Autoregressive Adjustment...... 318 More Sophisticated Diagnostics: The PACF and the ACF Revisited...... 319 Further Maximising Goodness of Fit: Interrupted Time Series Analysis..322 Analysis Sequence Summary...... 323
Chapter 7 Time Series Analysis 326
Piecewise Analysis...... 327 Slavonic Dance Arousal...... 327 Slavonic Dance Valence...... 336 Aranjuez Arousal...... 339 Aranjuez Valence...... 343 Pizzicato Arousal...... 345 Pizzicato Valence...... 346 Morning Arousal...... 348 Morning Valence...... 351 The Perfect Cadence as an Interrupting Time Series...... 352 Summary of Outlier Types...... 355 Summary of Quantitative Analyses...... 357 Analysis of Emotional Response with Each Musical Feature...... 359 Tempo...... 360 Centroid...... 361 Loudness ...... 363 Melody...... 364 Texture...... 366
- xiii - Chapter 8 Overview, Conclusions and Recommendations 368
Overview of the Dissertation...... 368 Conclusions...... 374 Recommendations...... 379
References 383
- xiv -
Volume 2
Glossary and Appendices
Glossary of Terms and Abbreviations 406
Appendices for Chapter 3 418
Appendix A: Word Usage Survey...... 419 Appendix B: Displays used in Experiments II, III and IV...... 421 Opening Display and Opening Questionnaire...... 423 Valence Training...... 433 Arousal Training...... 444 2DES Training ...... 451 Plain Phase...... 458 Closing Questionnaire...... 461 Appendix C: Additional Displays used in Experiment II Only (Anchor Phase)...... 467 Anchor Preparation...... 468 Anchor Phase...... 470
Appendices for Chapter 5 472
Appendix D: Additional Displays used in Experiments III and IV Only (Music Phase) ...... 473 Appendix E: Musical Feature Time Plots...... 482 Appendix F: First Order Differenced Time Plots...... 507 Appendix G: Arousal and Valence Time Plots...... 532 Appendix H: Scatterplots ...... 543 Appendix I: Checklist Histograms, Pareto Charts and Tables...... 546 Slavonic Dance Words...... 547 Aranjuez Words...... 548 Pizzicato Words ...... 549 Morning Words...... 550 Appendix J: Additional Displays used in Experiment IV Only (Pretest).551
Appendices for Chapter 6 554
Appendix K: SPSS Output for Lagged Loudness Regression Model of Arousal ...... 555 Appendix L: Diagnosing Autocorrelation in (a) Loudness and (b) Arousal for Original Series and Differenced Transformations...... 558 Appendix M: OLS Regression Using Differenced Variables...... 565 - xv - Appendices for Chapter 7 568
Appendix N: Time Series Analysis SPSS Output...... 569 SPSS conventions...... 569 Steps of Analysis...... 570 Appendix O: Slavonic Dance Arousal Model...... 571 Appendix P: Slavonic Dance Valence Model...... 582 Appendix Q: Aranjuez Arousal Model...... 593 Appendix R: Aranjuez Valence Model...... 606 Appendix S: Pizzicato Arousal Model...... 617 Appendix T: Pizzicato Valence Model...... 627 Appendix U: Morning Arousal Model...... 637 Appendix V: Morning Valence Model...... 648
- xvi - List of Figures
Figure 1-1 Hypothetical Network Theory Configuration of an Emotion...16 Figure 1-2 Circumplex Model of Emotion-Related Categories...... 20 Figure 2-1 Taxonomy of Self-Report Measures of Emotional Response to Music ...... 34 Figure 2-2 Emotion Words for Describing Instrumental Art Music Superimposed on a Two-Dimensional Emotion Space...... 43 Figure 2-3 Hevner Adjective Circle Superimposed on a Two-Dimensional Emotion Space ...... 55 Figure 2-4 Hevner Adjective Checklist Responses to Debussy’s Reflections on the Water for Whole Piece and in Sections...... 58 Figure 3-1 Layout of Two-Dimensional Emotion Space (2DES) Computer Screen...... 99 Figure 3-2 Venn Diagram of Verbal Stimulus Sources...... 119 Figure 3-3 Dendrogram of Cluster Analysis of 24 Verbal Stimuli using Arousal and Valence Scores...... 136 Figure 3-4 Emotion Spaces Showing Mean and One Unit Standard Deviation Either Side for Each of a Selection of Stimuli...... 137 Figure 3-5 Russell, Whissell and Experimental Data on the Emotion Space139 Figure 3-6 Mean 2DES Coordinates for Facial Stimuli...... 141 Figure 3-7 Hevner Words Mapped onto the 2DES ...... 142 Figure 3-8 Physical Emotion Words used by Sloboda, Mapped onto the 2DES ...... 143 Figure 3-9 Scatterplot of Responses to the Selected Stimuli...... 146 Figure 4-1 Emotion Space Representation of Vocal Features...... 155 Figure 4-2 Suggested Mapping of Hevner Adjective Clusters onto the Two- Dimensional Emotion Space...... 184 Figure 4-3 Opening Bars of Vocal Part from “Liebstod” in Wagner’s Tristan and Isolde ...... 208 Figure 4-4 Dynamics Transformed onto the 2DES...... 221 Figure 4-5 Mean Pitch Transformed onto the 2DES ...... 222 Figure 4-6 Pitch Range Transformed onto the 2DES ...... 223 Figure 4-7 Variation in Pitch Transformed onto the 2DES ...... 224 Figure 4-8 Melodic Direction/Contour Transformed onto the 2DES ...... 225 Figure 4-9 Register Transformed onto the 2DES...... 226 Figure 4-10 Mode Transformed onto the 2DES...... 227 Figure 4-11 Timbre Transformed onto the 2DES...... 229 Figure 4-12 Harmony Transformed onto the 2DES ...... 231 Figure 4-13 Tempo Transformed onto the 2DES...... 232 Figure 4-14 Articulation/Duration Transformed onto the 2DES ...... 233 Figure 4-15 Note Onset Transformed onto the 2DES ...... 234 Figure 4-16 Vibrato Transformed onto the 2DES...... 235 Figure 4-17 Rhythm Transformed onto the 2DES...... 237 Figure 4-18 Metre Transformed onto the 2DES...... 238 Figure 5-1 A-Weighting Curve...... 256 - xvii - Figure 5-2 Analogy of Centroid with Centre of Gravity...... 258 Figure 5-3 Pitch Coding Sample: Opening Melody in Morning...... 262 Figure 5-4 Sample Waveforms and Spectra of Slavonic Dance...... 266 Figure 5-5 Participant Characteristics...... 269 Figure 5-6 Composite Response Distribution on 2DES...... 275 Figure 5-7 Scatterplot Showing Inward Trend of Averaged Response with Respect to Overall Response...... 278 Figure 6-1 Loudness and Arousal Time Series and Cross-Correlogram for mm. 25 to 47 of Morning...... 293 Figure 6-2 Comparison of Hypothetical Non-Autocorrelated and Autocorrelated Response...... 304 Figure 6-3 Examples of Trends...... 306 Figure 6-4 Residual and its ACF for Lagged Loudness Regression Model of Arousal...... 309 Figure 6-5 Typical ACF Profile for Integrated Process...... 320 Figure 6-6 Theoretical ACF and PACF Profiles for a Typical First-Order Autoregressive Process...... 322 Figure 6-7 Sequence of Steps Used in Time Series Data Analysis...... 325 Figure 7-1 Slavonic Dance MF∅Arousal at t60-68 (mm. 84-90)...... 332 Figure 7-2 Slavonic Dance MF∅Arousal at t137-146 (mm. 166-180)...... 333 Figure 7-3 Slavonic Dance MF∅Arousal at t155-164 (mm. 181-194)...... 335 Figure 7-4 Slavonic Dance MF∅Arousal at t217-228 (mm. 266-272)...... 337 Figure 7-5 Aranjuez MF∅Arousal at t210-235 (mm. 31-34)...... 341 Figure 7-6 Aranjuez MF∅Arousal at t360-370 (mm. 52-54)...... 343 Figure 7-7 Aranjuez MF∅Valence at t340-365 (mm. 46-51)...... 345 Figure 7-8 Pizzicato MF∅Arousal at t68-81 (mm. 47-69)...... 346 Figure 7-9 Pizzicato MF∅Valence at t1- 8 (mm. 1-4)...... 348 Figure 7-10 Morning MF∅Arousal at t45-50 (mm. 19-21)...... 350 Figure 7-11 Morning MF∅Arousal at t207-213 (mm. 83-87)...... 350 Figure 7-12 Valence Response Gradient for Morning...... 353 Figure 7-13 Tempo Profile for Arousal...... 361 Figure 7-14 Tempo Profile for Valence...... 361 Figure 7-15 Centroid Profile for Arousal...... 362 Figure 7-16 Loudness Profile for Arousal...... 363 Figure 7-17 Loudness Profile for Valence...... 364 Figure 7-18 Melody Profile for Arousal...... 365 Figure 7-19 Melody Profile for Valence...... 365 Figure 7-20 Texture Profile for Arousal...... 367 Figure 7-21 Texture Profile for Valence...... 367 Figure A - 1 Pareto Chart for Slavonic Dance Words...... 547 Figure A - 2 Word Cluster Histogram for Slavonic Dance ...... 547 Figure A - 3 Pareto Chart for Aranjuez Words...... 548 Figure A - 4 Word Cluster Histogram for Aranjuez...... 548 Figure A - 5 Pareto Chart for Pizzicato Words...... 549 Figure A - 6 Word Cluster Histogram for Pizzicato...... 549 Figure A - 7 Pareto Chart for Morning Words...... 550 Figure A - 8 Word Cluster Histogram for Morning...... 550
- xviii - List of Tables
Table 3-1 Feedback and Percentage Range Used for Each of the Seven Regions of the Emotion Space Dimensions...... 103 Table 3-2 Word Usage Summary Table...... 110 Table 3-3 Revised Music Checklist...... 112 Table 3-4 Valence and Arousal Values for Fifteen Words Common to Russell and Whissell Lists...... 115 Table 3-5 Correlation Matrix for the 15 Words Common to Both Whissell and Russell, Shown in Table 3-4...... 117 Table 3-6 Twenty-Four Verbal Stimuli...... 125 Table 3-7 Non-Verbal Stimuli...... 122 Table 3-8 Results for Emotion Space Training and Plain Phase Responses130 Table 3-9 Test-Retest Correlation Coefficients...... 138 Table 3-10 Correlation Coefficients of Experimentally Determined Valence and Arousal with Russell and Whissell Data...... 139 Table 4-1 Categories of Stimuli Used in Investigations of Emotional Response to Music ...... 152 Table 4-2 Vocal Indicators of Emotional States...... 154 Table 4-3 Seven Two-Level Factors Manipulated by Scherer and Oshinsky (1977)...... 162 Table 4-4 Acoustic Parameters of Tone Sequences Significantly Contributing to Variance in Attributions of Emotional States...... 163 Table 4-5 Musical Features and Emotion Expressed by Dolgin and Adelson’s Melodies...... 165 Table 4-6 Hevner’s Findings Mapped onto the Two-Dimensional Emotion Space ...... 185 Table 4-7 Characterisation by Rhythm, Interval, Pitch and Tempo...... 190 Table 4-8 Characterisation by Instrument or Family...... 190 Table 4-9 Consistent and Reliable Findings in Relationship between Musical Characteristics and Meaning as Reported by Watson...... 190 Table 4-10 Musical Stimuli used by Flowers, with Associated Emotion Words ...... 195 Table 4-11 Summary of Musical Features and Emotional Responses by Collins...... 196 Table 4-12 Basic Terms and Their Associated Descriptions Abstracted from Cooke...... 202 Table 4-13 Associations Expressed by 24 Keys...... 211 Table 4-14 Mood Categories and Associated Instruments...... 217 Table 5-1 Flow of Music Phase Module used in Experiment III as Controlled by EmotionSpace Lab ...... 243 Table 5-2 Stimuli Used in Experiment III ...... 246
- xix - Table 5-3 Dichotomised and Cross Tabulated Participant Characteristics271 Table 5-4 Averaged Versus Overall Response...... 277 Table 5-5 Comparison of Two Checklist Quadrant Mappings with Three 2DES Quadrant Measures...... 280 Table 6-1 OLS Regression Model Summary...... 296 Table 7-1 Summary of Slavonic Dance Arousal Model Coefficients...... 329 Table 7-2 Events Surrounding V7-I Cadences in Morning...... 355 Table 7-3 First Order Autoregression Models Summary...... 358 Table A - 1 Quadrant Mapping of Word Clusters Used in Experiment III546 Table A - 2 Word Cluster Frequency for Slavonic Dance...... 547 Table A - 3 Word Cluster Frequency for Aranjuez...... 548 Table A - 4 Word Cluster Frequency for Pizzicato...... 549 Table A - 5 Word Cluster Frequency for Morning...... 550 Table A - 6 Steps of Analysis...... 570
- xx -
My soul is a hidden orchestra; I know not what instruments, what fiddlestrings and harps, drums and tambours I sound and clash inside myself. All I hear is the symphony. (Fernando Pessoa)
… when an area is as uncharted as the psychology of musical emotion, imaginative and unconventional approaches are cautiously to be welcomed. At this stage, a variety of viable new methodological routes should be followed. It will be the task of researchers five or ten years from now to start drawing up a definitive map, and to decide which routes lead somewhere. (Royal, 1994, p. 76)
- xxi -
Chapter 1 Introduction
Few who have experienced the thrill of emotional interactions with music would deny that such experiences are important and enriching. These intoxicating episodes can be superior to any heightening or soothing drug because they occur without unpleasant side-effects. The fact that music can express such emotions, move people to tears of lament and to teeth-clenching ecstasy is, for many, a wondrous mystery.
How is it that by manipulating combinations of innocuous acoustic parameters composers and performers can produce such potent effects? The question has occupied scholars and practitioners for over twenty centuries. One of the many problems which face researchers is the lack of objective data available for comparing music and emotion. In this thesis, I address this problem by producing and analysing data comprising the continuous, objective measurement of musical features and emotional response. As a preface to the present research it is informative to take a historical perspective of attitudes, issues and existing research undertaken in this area.
- 1 - Historical Overview Among the ancient philosophers, Plato, Aristotle and Heraclides believed that particular musical modes such as the dorian and mixolydian had emotional effects upon the mind, or they reflected states of the soul (cited in Francés, 1958/1988, p.
316). For example the mixolydian mode was said to evoke a mournful and solemn mood while the phrygian “puts men into a frenzy of excitement” (Aristotle, Politics
1340a-b). These thinkers provided an explanation of how musical mode affected the listener. But mode is just one aspect of musical structure. Even if these ancients’ views of the effects of musical mode were correct, one could still ask what contribution was made by other elements of music. Aristotle himself posed the question “How is it that rhythms and melodies, although only sound, resemble states of the soul although they [rhythms and melodies] are only tone” (Problems c. 19, cited in Schopenhauer, 1819/1969, p. 260, square brackets are from the secondary source). Today, this question remains only partially answered.
In the seventeenth and early eighteenth centuries, Western scholars tended to view music as being subservient to words (Fubini, 1987/1990). The primary (though not exclusive) role of instrumental art music was to support and enhance the meaning of text. In this respect music served as a rhetorical device and from it grew the conventions and figures in music which are sometimes referred to as the Doctrine of
Affections (Buelow, 1980). Composers and performers moved the passions of the listener through music in such a way as to enhance or support the meaning of the orator’s words. The Renaissance and the Baroque eras saw the production of several treatises on musical figures suitable for expressing particular affections or emotions.
- 2 - For example, in his work on the art of singing, Benigne de Bacilly (1668, cited by
Sloan, 1990) documents the styles and inflections of production appropriate to the expression of emotions such as sadness and joy (Sloan, p. 38). Johann Mattheson
(1713) provided a detailed examination of the “particular characteristics of musical scales and their power to affect the passions” (cited by Collins, 1989, p. 3).
In Western Europe during the late eighteenth century, political and social change led to the rise of instrumental music as an independent art form separate from song. The growth of instrumental music demonstrated that music had expressive power in its own right. It did not need to play a subservient role to words. Consequently, music could break free of its place as an expresser of specific human emotions through social convention. Not restricted by the word nor even the imitation of nature, instrumental music became free to express the inexpressible emotions, the mystical and the irrational (Lippman, 1988, p. ix). This aesthetic movement is commonly referred to as expressionism. Expressionism was subsequently opposed by the formalists who asserted that the value in music comes not from what it expresses but from within its structure and form. The origins of formalism can be traced back to
Immanuel Kant (1724-1804) but the thesis would blossom through the work of
Eduard Hanslick (1854/1957).
Both expressionism and formalism had negative effects on the understanding of how music can express emotion: (1) According to the expressionists, emotion was expressed at a higher plane, beyond our comprehension, and (2) according to the formalists, emotional expression was a contamination of
- 3 - the purity of the structure and form of music, providing a pretext for its neglect.1
These perspectives indicate a futility in attempting to study emotions in terms of the concomitant, dynamic features of music. Many writers have opined that a particular instrument was appropriate for expressing a particular emotion, but a parallel to the so called Doctrine of the Affections was not to be found. As knowledge of musical conventions filtered down from the upper class to the powerful, emerging middle class, the principles of the doctrine were essentially lost.
It is perhaps ironic that the century of emotional expression in Western music saw the decay in the study of its underlying nature, for the legacy of the expressionist- formalist debate was to stunt the development of understanding of how music can express emotion. A notable exception was Herman Kretzschmar (1902/1990) who proposed a return to the ideals of the Baroque theories of the affections (p. 25), based on a belief that people should be educated to understand the inner meanings which music could express. He encouraged thoughtful interpretation of music through the study of the emotional function of musical elements such as pitch intervals, rhythm and harmony. For example, he proposed that rising pitch intervals express excitement while falling intervals express appeasement, and then asserted the importance of applying this knowledge in making a credible musical interpretation
(p. 20).
Although Kretzschmar’s work would not gain long term acceptance, it marked a transition from nineteenth century thinking of expressionism and
1 Francés (1958/1988, pp. 258-9) has demonstrated that even ardent formalists can have expressionist - 4 - formalism to the twentieth century. The new era was marked by what Leonard
Meyer (1956) referred to as absolute expressionism, where the nature of emotional expression could be studied in terms of musical structure and form. Meyer’s category fell between the formalist and the expressionist perspectives. However,
Meyer believed that music could only express generalised arousal. He ignored or rebuffed the growing literature of empirical aesthetics which supported the view that people were able to agree on fairly specific emotions at well above chance levels (see
Chapter 2).
The study of the nature of emotion in music has historically included two contrasting modes of investigation. The musicological mode of investigation pursued by inquirers who, if inclined to believe in a systematic relationship between music and emotion, rarely associated specific emotions with musical features for fear of criticism about the subjective nature of emotion. The empirical psychological mode of investigation was in some ways diametrically opposed to the musicological mode, enabling consensus on the expression of specific emotion, but frequently lacking insightful knowledge about the music.
The pioneer of American music psychology research, Carl Seashore, believed that emotion in music is communicated by the sound waves of the music. Seashore
(1938/1967) postulated that these soundwaves embody emotion in their structure, namely frequency (pitch), amplitude (loudness), duration (tempo and rhythm) and form (combination of the others). Further, empirical demonstrations in the 1920s and
1930s, that agreement in emotion
experiences or make cognitivist judgements. - 5 - expressed by music was possible, removed a barrier that had hindered research on the question of how music could express emotion. If music could express an emotion with reasonable predictability and stability in a given culture, it should be possible to ask the question: What is it about music that transmits these effects?
It is this question that is the concern of this study. Inspired by the work of the empiricists, my thesis is that there are underlying rules which govern the relationship between music and emotion within a given culture.2
The strength of the empirical approach was summarised by Pike (1972), who indicated the benefit of collecting responses from several people instead of the introspections of the lone expert. However, the empirical approach, stemming from the turn of the century, was often hindered by methodological flaws and technological deficiencies. Such studies provided fuel for the formalists and expressionists who believed in the strongly subjective nature of musical experience.
For example, Heinlein (1928) found that the widely accepted relationship between happy-major and sad-minor was without foundation, but some fifty years later the same data were reanalysed and found to be misinterpreted (Crowder, 1984). In the meantime, several empirical investigations upheld the thesis of a relationship
2 My thesis implies both a reductionist and behaviourist approach. While the approach of the reductionist is present, I rebuff the claim of a behaviourist approach. Behaviourists study input and output and their correlation and then contend that nothing else is worthy of study (Skinner, 1974). Those who believe that this correlation is interesting (including this author) must still study input (music), output (emotion) and their correlations. In other words, I support the notion that there is a necessary cognitive mediation between music and emotion. As John Sloboda put it: “Seen with the cold eye of physics a musical event is just a collection of sounds with various pitches, durations, and other measurable qualities. Somehow the human mind endows these sounds with significance. They become symbols for something other than pure sound, something which enables us to laugh or cry, like or dislike, be moved or be indifferent.” (1985, p. 1) - 6 - between emotions and musical features, even though this view received no serious attention from introspectionists such as Meyer (1956) and Langer (1957). In his influential book, Emotion and Meaning in Music (1956), Meyer referred to the Heinlein study, but not to the work of Hevner, Gundlach, Sherman and several others who, in the 1920s and 30s, had found more positive relationships between specific emotions and musical features.
The methodological problems that faced empirical researchers were numerous.
“Real” pieces of music usually have a large number of interacting musical features making the investigation of possible causal connections between musical features and emotional response more difficult to unravel. Further, some researchers required listeners to select a word from a list to describe the emotion in a piece of music (see Chapter 2), even though the piece typically expressed more than one emotion. This methodology made it impossible to distinguish whether the listener was making an overall reflection about the piece or responding to a salient part of the music.
One solution was to select isolated samples of sound so that a single musical structure or feature could be manipulated and tested for emotional expressivity.
Such research is often criticised because it is too far removed from naturalistic music.
While this may be true, it was one of the few practical ways of investigating the problem, and it could supply convergent evidence, or otherwise, with investigations that used “real” music.
- 7 - Until quite recently empirical researchers had to contend with static, asynchronous measurements of the dynamic process of music and emotional response. It is easy to see why this type of approach can be criticised: How could measured responses made at the end of a piece possibly cover the subtle and abrupt changes which music expresses during a performance? However, recent advancements in computer technology now facilitate improvements in methodology which were not available to these early pioneers. Modern technology offers new opportunities to develop methods of obtaining responses often enough during a performance to capture the dynamic flow of expressions in the music.
Measurement of continuous response to music is a growing area of research, but such research has not been supported with quantitative analyses. Many previous music-emotion studies fail to use analytic techniques for relating continuous responses with the components of the continuous stimulus. Sophisticated time series analytic techniques have been available in the fields of statistics and econometrics for more than twenty years, yet these procedures have not yet spread to the study of emotion in music. An innovative feature of this study is that it employed elementary time series analytic techniques in order to understand continuous data on emotion in music.
Another problem in measuring emotional response was whether the emotion was expressed by the music, giving rise to a cognitivist experience, or experienced by the listener, giving rise to an emotivist experience. Although aestheticians have theorised about the superiority of one type of experience
- 8 - over another (e.g., see Scruton, 1983 and Kivy, 1990; see also Francés, 1958/1988, pp. 243-245), there can be no doubt that both kinds of experiences are possible
(Collins, 1989; Robinson, 1994).3 It is possible to feel sadness or grief in response to a funeral march as much as it is possible to observe that the same piece can express sadness or grief. As several researchers suggest (Campbell, 1942; Francés, 1958/1988, pp. 244-5; Hampton, 1945; Swanwick, 1973), it is easier to agree on the emotion music expresses than the feelings it evokes. The latter, emotivist experience is likely to vary according to subjective states of the individual such as mood or familiarity with the piece in question. A listener may find the Chopin funeral march quite boring but still be able to indicate that the piece expressed sadness or grief. Therefore, taking the cognitivist view (as suggested by Swanwick, 1973) alleviates the problem of investigating the objective emotional content encoded in music. For this reason I have adopted a cognitivist approach for the present study.
The ambience of current research indicates that the relationship between emotion and music has become an area of concern. Rita Aiello (1994) points out that
“productive research in the psychology of music will need to address not only how the mind perceives the sounds, but the aesthetic and emotional meaning that the sounds give rise to.” (p. 51).
Scherer (1991) is even more emphatic:
While the important role of affect expression is often forcefully asserted …
systematic, and methodologically sophisticated studies are rare.
3 Sylvie Collins and Jenefer Robinson were both interested in the relationship between emotivist and cognitivist experience. Collins used an experimental-psychology methodology, while Robinson took a - 9 - What is, to my knowledge, virtually absent … is the attempt to compare the
expression of emotion in music and in speech, in order to determine similarities
and differences between underlying production mechanisms (including the
brain structures that are involved), the acoustic manifestations, and the nature
of listener inferences. (p. 148)
I have described my position with regard to the relationship between emotion and music: I believe that there is a relationship between emotion and music, and further, that there is an underlying, culturally dependent, quantifiable relationship between musical features and emotional response. Before formulating a specific purpose and approach for testing this assertion, it is necessary to define concepts associated with emotion and musical features.
Musical Features Musical features are the separable elements of music or the perceptually distinguishable combinations of elements which, when combined, form a musical object. They can be defined at various levels: a low, psycho-acoustic level, or a high, formal-structural level. Low level musical elements consist of pitch, loudness, timbre and duration. These elements are the universal constituents of musical sound. This makes them necessary, though not sufficient, elements in the construction of music.
High level elements comprise such features as harmony, voicing, phrasing, texture, form and style. These higher level elements, although specifically related to music, are often culturally specific and contain an element of subjectivity. In fact, these higher level features are in some cases peculiar to
philosophical approach. - 10 - Western music. For example, classical Western music systems of harmony are quite different from Eastern systems (e.g., Castellano, Bharucha, & Krumhansl, 1984).
Nevertheless, within a cultural context these musical features are meaningful, perceptually valid components of music.
Somewhere in between these two extremes lie rhythm, contour, envelope, and articulation. The levels of musical features which I have proposed here are not always clear, nor are they always necessary. It is, however, important to note that all of the higher level musical elements can be expressed in terms of the lowest, sound defining elements. Specific definitions of relevant musical features are reported in
Chapters 4 and 5. The other pertinent, and more difficult issue is in understanding and defining emotion.
The Nature of Emotion In order to operationalise emotion for the purpose of empirical testing, it is useful to examine what is meant by emotion. By briefly reviewing some of the influential theories of emotion in psychology a better understanding of emotion will be achieved, setting the groundwork for an informed method of operationalising the complex, multidimensional construct. Near the beginning of modern psychology a controversial theory of emotion was posited by two psychologists independently:
William James in 1884 and Carl Lange in 1885. The theory was controversial because of the order in which events and emotions occurred. The generally accepted belief was that perception led to emotion which in turn led to action. For example, the sight of a large, ravenous bear might make a person scared, and so the person would run away. In contrast, the James-Lange theory proposes that
- 11 - perceiving the bear makes a person run away, and it is physiological preparation for running and the skeletal response of running away that causes that person to feel scared. Similarly, sadness does not lead to crying. Instead, we are sad because we cry. Emotions are evoked by physiological response, and physiological response is generally evoked by stimulus perception. Although the James-Lange theory has received a mixed response from modern psychologists, it raised an important issue:
There is a closely interconnected relationship between physiology and emotion.
In 1927 Walter Cannon provided an alternative to the James-Lange theory by proposing that the subjective experience of emotion and the physiological changes associated with the emotion occur together, and that the control of these responses occurs within the brain. This theory brought to the fore another important issue:
Emotion is connected with cognition.
The relationship between cognition, physiology and emotion was crystallised in the cognitive-arousal theory developed through the work of George Marañón in 1924 and formulated by Stanley Schachter and Jerome Singer in 1962. The cognitive- arousal theory explained how generalised arousal may be interpreted as being positive or negative depending on the situational interpretation of the individual.
For example, suppose you are waiting to meet a long absent, very dear friend at the airport. Suppose also that you are feeling quite aroused. (Marañón and Schachter &
Singer produced this state of high arousal by injecting their participants with adrenalin.) If the friend appears, the individual is likely to attribute the aroused feeling to a sensation of euphoria — a positive emotion. However, if there is an announcement
- 12 - that the flight has been cancelled and that the friend is not arriving after all, the same person may attribute the arousal to a sensation of anger or distress. The theory suggests that humans have a general desire to interpret their state as a reasonably specific emotion and will therefore look for cues in the environment to help make sense of their current level of general physiological arousal. In other words, the cognitive-arousal theory suggests that emotion is determined by two factors: the cognitive evaluation of a situation and the antecedent physiological state of the individual.
Another critical issue in understanding emotion is that of communication. Charles
Darwin’s The Expression of the Emotions in Man and Animals (1872/1965) is often cited as a landmark in research on emotional communication. Darwin observed the importance of vocal, facial and postural expressions in the communication of emotion. Ekman, Friesen and associates (Ekman & Friesen, 1975, 1976; Ekman,
Friesen & Ellsworth, 1972; Ekman, Friesen & Tomkins, 1971) devised techniques for evaluating facial expressions according to a series of muscular-skeletal codings.
Vocal communication of emotion has also received attention, largely through the work of Scherer (1991). Often, humans will use a combination of channels to strengthen the communication of emotion.
Among the more recent developments in understanding emotion is the use of associative networks, or network theory. Network theory has come to mean the linking of cognitive units of information to other units by association. Bower’s (1981) influential network theory rests on the proposition that each
- 13 - emotion can be represented by a memory unit or node which is able to link to other nodes representing concepts, states or events:
… each distinct emotion such as joy, depression or fear has a specific node or
unit in memory that collects together many other aspects of the emotion that are
connected to it by associative pointers … . [Around each] emotion node are its
associated autonomic reactions, standard role and expressive behaviours … and
descriptions of standard evocative situations which when appraised lead to
sadness … . [Each] emotion unit is also linked with propositions describing
events from one’s life during which that emotion was aroused … . These
emotion nodes can be activated by many stimuli—by physiological or symbolic
verbal means. When activated above a threshold, the emotion unit transmits
excitation to those nodes that produce the pattern of autonomic arousal and
expressive behaviour commonly assigned to that emotion … . Activation of an
emotion node also spreads activation throughout the memory structures to
which it is connected, creating subthreshold excitation at those event nodes.
(Bower, 1981, p. 135)
Bower’s formulation is appealing because it integrates a variety of aspects of emotion into a unifying, cognitive framework. An emotion can be defined as either the node which is an index of the actual associated connections, or as a cluster of behaviours and reactions to which that emotion node is connected. Figure Chapter 1 -1 provides an example of how this may be visualised. Happy may
- 14 - be defined as the happy node itself, or as the links which are associated with the activation of the happy node.4
The same model can be used for music.5 In the example shown in Figure Chapter 1 -
1 happiness was activated by seeing a friend. Similarly, the perception of music may activate an emotion. However, for the recognition of emotion expressed by music, the network requires a different set up. The individual is not actually experiencing the emotion, but observing the presence of the emotion as being contained within the music. The process is somewhat analogous to recognising emotion in a facial expression (Allen, 1990; Kivy, 1990), in that the emotion does not need to be experienced. One possible network explanation is to have a repertoire of musical schemata associated with various, dissociated emotions (Schubert, 1996b). Just as the physiognomic properties of a face can be associated with a particular emotion, so too can the combinations of musical features be linked to an emotion. The actual linking process is a reflection of the individual’s disposition, acculturation and of his or her innate network of connections.
4 In the next section of this chapter I support the notion of a dimensional paradigm of emotion. This may appear at odds with the present discussion, for the emotion node suggests discrete emotions. The problem lies in the level of explanation used. Emotion nodes, while discrete, are likely to be systematically organised with respect to one another, and at this higher level, the dimensional nature of emotion emerges. This is discussed in more detail by Fischer, Shaver and Carnochan (1990) and Oatley (1996). 5 Cohen (1993) and Collins (1989), for example, have used Bower’s theory of emotion for music research. - 15 - Figure Chapter 1 -1 Hypothetical Network Theory Configuration of an Emotion Ellipses indicate nodes. Arrows indicate connections between nodes and flow of activation.
physiology perception skeletal nodes nodes node
sight of a heart rate friend jump rise emotion node
blood flow smile to face happy
dilated hug pupils
Speak: “I’m memory of a memory of memory of happy!” happy event a friend a place
cognitive nodes
The Structure of Emotion There are two broad systems of classifying emotions: categories and dimensions.
Categorical classification of emotion assumes that emotions carrying different meanings, such as happy and sad, are distinct and independent entities. Checklists imply a categorical classification of emotions. For example, Tomkins’s (1962) research on facial expressions suggested that emotions could be grouped into one of eight categories:
1. interest/excitement
2. enjoyment/joy
3. surprise/startle
4. distress/anguish
- 16 - 5. fear/terror
6. shame/humiliation
8. anger/rage.
In contrast, the dimensional classification of emotion holds that all emotions are in some way related within an n-dimensional semantic space (or, more correctly, emotion space). For example, the dimensional structure suggests that happy and sad are opposite emotions along the valence dimension of emotion. To distinguish distinct emotions having similar valence, such as sad and angry, a second dimension, arousal, may be added: Sad has low arousal and angry has high arousal.
Dimensional classification can help to visualise the interrelationships between emotions and to provide a structured framework for emotion research. Several prominent psychologists support the dimensional approach to the study of emotions
(Plutchik, 1962; Davitz, 1969; Schlosberg, 1954; Zevon & Tellegen, 1982; Russell, 1979,
1980; Niedenthal & Setterlund, 1994). However, opinions on the number of dimensions and the definitions of these dimensions do not always converge (Roberts
& Wedell, 1994). Cynthia Whissell, Michael Fournier, Rene Pelland, Deborah Weir and K. Makarec (1986) asserted that there has been considerable agreement on the validity of the dimensional paradigm of emotion consisting of two dimensions, namely valence and arousal. Whissell and her colleagues also pointed out that there has been considerable disagreement on “the role which any other dimensions may play (attention, competence, locus of
- 17 - causation, potency, dominance, have all been suggested as additional dimensions)”
(p. 876), and that the first two dimensions of valence and arousal can explain up to
80% of response variance. Potency, a dimension believed by some researchers to be the best candidate for a third dimension, appeared to explain less than 5% of the variance according to Whissell (p. 876). Sweeney and Whissell (1984) suggested that the valence and arousal dimensions were “theoretically interpretable” (p. 695) as well as being orthogonal.
Over several publications, Cynthia Whissell and various associates reported the development of a “dictionary of affect”. In one study (Whissell, Fournier, Pelland,
Weir & Makarec, 1986), participants rated lists of words on two seven point, bipolar scales, one for “evaluation (pleasantness)” and another for “activation (arousal)” (p.
877). This methodology enabled faster responses compared with other response measures available (200 words in less than 30 minutes, or less than 9 seconds per word) within a plausible paradigm of emotions (using only the two most salient dimensions).
It is conceivable that Whissell and her associates (1986) may have thought to have responses made directly in an emotion space. That is, the arousal and valence bipolar scales could be combined at right angles enabling simultaneous response to the two dimensions. Such a response format may have aided in speeding up responses and provided a convenient visualisation of the procedure for the participant. But with large lists of words on a paper and pencil test, an emotion space may not have been practical. No studies have been cited before my work
(Schubert, 1996a;
- 18 - 1996c) in which an emotion space was used as a direct response measure. However, such a development was considered pivotal to the data gathering approach of the present study.
Russell (1989) provided potent evidence about the merit of the dimensional system of classification and in particular the circumplex realisation upon a two-dimensional emotion space consisting of valence and arousal. In such a configuration emotions line up roughly along a circle centred on the cartesian plane (Figure Chapter 1 -2).
According to the circumplex model, words geometrically close together, such as delighted and happy, indicate closeness in meaning. Other researchers have used the emotion space to represent non-verbal stimuli. Schlosberg (1952) asked participants to rate emotion expressed by faces on two scales: pleasantness and attention-rejection. Responses were then plotted on a two-dimensional emotion space.
- 19 - Figure Chapter 1 -2 Circumplex Model of Emotion-Related Categories. Source: Russell (1989, p. 86). Large numbers indicate quadrant numbering convention (see Glossary).
21
43
In recent studies dealing with emotional responses to music, the dimensional interpretation of data has pervaded the literature. Gundlach’s (1935) analytic approach pioneered the dimensional interpretation of emotional data collected in response to music, however the techniques of multidimensional clustering became firmly rooted in music-emotion research from the early 1970s (Wedin, 1969, 1972).
This development is expounded in Chapter 2. Many of the studies reported agreed or implied that the first two dimensions were those associated with valence and arousal. These findings support the use of the valence and arousal dimensions of emotion as measures of response to music in addition to other modes of stimuli.
- 20 - Also, a strong intuitive implication is that the construct of emotion by which stimuli such as words and pictures are judged is similar, if not the same, as the construct used to judge emotion expressed by music. There appears no obvious reason why the emotional conception of sadness expressed by a face would be different to the emotional conception of sadness expressed by a piece of music. To put it in another way, emotional concepts appear to be stable across various domains of perception.
Studies of multidimensional response to music have required the participant to make responses about an entire selection with several or even dozens of response items. In contrast, recent evidence has focussed on continuous response using a single dimension to measure response (Nielsen, 1983; Madsen & Fredrickson, 1993; Adams,
1994; Waterman, 1996; Goldstein, 1980). Many of these unidimensional studies have deliberately left the meaning of the dimension measured subjective and vague, however given their musical correlates (as discussed in Chapter 4), it appears possible that in all these studies a construct related to the arousal dimension was being measured. A natural progression from the work of those measuring continuous response to music is to increment the number of dimensions available for response. By allowing the participant to respond along two dimensions instead of one, the effects of cognitive loading (Norman & Bobrow, 1975) will be increased minimally, and the two important dimensions of emotion may be employed.
- 21 - Purpose of the Study Building on the music-emotion literature, I propose the thesis that there exist quantifiable, underlying principles which govern a causal relationship between musical features and emotional responses. In order to examine this proposal I investigated two central questions:
1. How can emotions expressed by music be measured?
2. What musical features determine changes in arousal and valence expressed
by music?
In answering Question 1 it was necessary to demonstrate the reliability and validity of a new research instrument. This involved the construction and testing of a computer program which could measure continuous emotional responses to music, according to the two constructs that were theorised to be relevant to the definition of emotion.
From Question 2, two specific issues were addressed:
(a) What are the musical features concomitant with changes in the arousal
dimension expressed by music?
(b) What are the musical features concomitant with changes in the valence
dimension expressed by the music.
By investigating the relationship between a selection of musical features and each dimension of emotion separately I am taking a necessarily simplifying, univariate approach to the complex assertions posited by my thesis. Since the music-emotion literature has not specifically contended with the matter of quantitatively modelling time dependent, dynamic relationships, the final
- 22 - purpose of this dissertation is to introduce and apply time series analytic techniques in order to address directly Question 2a and Question 2b.
Plan of Methodology In the first phase of the study (reported in Chapter 2), literature was examined in order to define a model of emotion which could be used to clarify the types of emotions which are encoded by musical features as expressed in tonal music. The second phase of the study (Chapter 3) involved two experiments: The first experiment (Experiment I) was required to assess and update the checklist measures used by Hevner (1936) and Farnsworth (1969). This experiment provided a resource for developing a validity checking strategy for later experiments. Experiment II involved the development and testing of a new research instrument, the Two-
Dimensional Emotion Space (2DES). The instrument’s reliability and validity were examined with respect to the measurement of valence and arousal as expressed by static stimuli — printed words and images of faces. In the next phase (Chapter 4), a second literature review was conducted to clarify current thinking on the relationship between musical features and the valence and arousal dimensions of emotion. The information in this review was used to generate hypotheses for
Experiment III. In this experiment (Chapter 5) the research instrument was modified so that it could measure continuous responses to musical stimuli. The test-retest reliability of the instrument was investigated in Experiment IV (also reported in
Chapter 5). In the final phase of the study, the results of the experimental research were used to generate exploratory, predictive models of emotional response as a
- 23 - function of predetermined musical features. For this phase, relevant principles of time series analytic techniques were introduced (Chapter 6) and applied (Chapter 7).
The final chapter (Chapter 8) consists of a summary of the study, followed by conclusions and recommendations.
This dissertation is highly interdisciplinary. It ventures into the areas of psychology, musicology, aesthetics, acoustics, semiotics, linguistics, computer science and statistics. Consequently, a Glossary of terms has been included to assist the reader.
Instead of providing a detailed list of definitions, important terms which are italicised in the main text will be found in the Glossary section. The appendices of this dissertation are numerous due to many graphical and statistical references. I have placed them in a separate volume (Volume 2) so that they may be examined conveniently in parallel with the chapter text. The final sections of this chapter document the focus of this study, itemising what this study covered and what it did not.
Limitations of the Study Due to the multidimensional nature of emotion and musical features, several restrictions were made in this study.
Limitation 1: Romantic, Western Tonal Music
Musical examples were selected from the repertoire of music which was based on the familiar tonal system of Western music. Meyer (1956) asserted that emotional responses to music require familiarity with the music of the culture from which the music is produced. For example, Rigg (1964) cited a study by Morey (1940) who found that German music expressing love and
- 24 - fear to Germans expressed no emotion to Liberians. Gregory and Varney (1996) found that there were some differences in the mood perceived to be expressed by music that were dependent on the cultural background of the listener. A group of people with Indian musical backgrounds who were not completely culturally isolated from Western culture, demonstrated some differences in response to music when compared to listeners from a Western music background. In light of such evidence, musical selections were chosen from a repertoire that was accessible to a large population of the local culture. The style of music employed in film music was an obvious contender. Gorbman (1987) argues that:
The prevailing dialect of film-music language has … been composed of the
nineteenth-century late Romantic style of Wagner and Strauss. … the core
musical lexicon has tended to remain conservatively rooted in Romantic
tonality, since its purpose is quick and efficient signification to a mass audience.
(p. 4)
Also, as Vernon stated, there is an important distinguishing feature between the intention of classicism and romanticism: “the former strives at formal perfection, the latter at the expression of emotion” (Vernon, 1930, cited in Valentine, 1962, p. 284).
Therefore, it seems reasonable to assume that the late romantic style is accessible and familiar to a large proportion of the local (Western) culture. Familiarity with the musical style in question is considered at least preferable, and probably essential, because the research presented does not intend to provide evidence of emotional responses to music not familiar to
- 25 - people from the local culture. Further, much of the previous empirical research on emotional responses to music has used music of the same style, meaning that the restriction of style is advisable to enable external validity checking with previous studies using similar pieces.
Limitation 2: Valence and Arousal of Emotion
Only two components (or dimensions) of emotion were examined: valence (the happiness or sadness) and arousal (the activeness or passiveness) components of emotion. This is justified in the review of the literature where it was found that:6
a) These two dimensions account for most of the variance in psychological
investigations of emotion expressed by various kinds of stimuli (e.g., words
and pictures of faces).
b) Studies of responses to music using a similar (dimensional) definition of
emotions often include dimensions that correspond to the same two
constructs (valence and arousal).
Limitation 3: Level of Explanation
If one accepts that music is able to express emotion, the question “What is the cause of the emotion?” may be asked at different levels:
1. The question of genesis and ontogeny: Is emotion in music determined by
innate, natural principles or is it learnt through exposure and concomitant
linking?
2. The question of morphology and semiotics: What musical features,
elements or combinations cause emotional response?
6 See discussion on The Structure of Emotion on page 16 for more details. - 26 - This dissertation is limited to explaining the relationship between emotion and music at the aetiological level only, as indicated in point 2.
Limitation 4: Cognitivist Response
The present study investigates the emotions expressed by the music, rather than those experienced by the listener. Consequently the applications of the present research may be viewed by some readers as not being applicable to the field of music therapy (see Limitation 6: Musicological Investigation on page 30). Although this view is not necessarily held here, no deliberate attempt was made to draw information from, nor to apply findings to, the field of music therapy.7
Limitation 5: Self-Report Measures
This study is only concerned with self-report measures, where data are collected from individuals who were aware of the requirement to provide data. This means that two broad classes of measures were not discussed in this study. These are physiological (or “psycho-physiological”) measures and behavioural measures.8
Physiological measures were not discussed because:
1. Research has provided conflicting evidence as to what physiological
responses occur in response to music (Dainow, 1977; Bartlett, 1996; Stratton
& Zalanowski, 1991; Rosenfeld, 1985; Taylor, 1973; Vanderark & Ely, 1994).
7 For a similar study based in a research paradigm more appropriate to applications in music therapy, see Collins (1989). 8 For a discussion of these measures see Izard and Saxton (1988). - 27 - 2. Where consistent reports were found, there is evidence that physiological
responses measure the arousal component of experienced emotion
(Nakamura, 1984; Thayer, 1986; Swanwick, 1973), with the possible
exceptions of electroencephalography and electromyography measures
(Crozier, 1974, p. 13; Panksepp, 1995; Thayer, 1986), or as Radocy and Boyle
(1988) put it: “Psychophysiological measures generally are used as
indicators of ‘arousal’ rather than as attempts to measure ‘affect’” (p. 223).
This has two ramifications: First, only one component of emotion might be
measured, and second, this component is probably linked to an experienced
emotion rather than a judged emotion.
3. Self-report measures are more congenial to many subjects than the prospect
of being “wired up”.
Behavioural measures were not discussed because:
i. Studies that used these measures in emotional responses to music were
rare, and the few works cited were usually mediated by an observer who
could then be considered as the self-reporter. For example, Francés and
Bruchon-Schweitzer (1983) studied body movement in response to
music, however, the measure used could be grouped into self-reports
from the perspective of the people who where the raters of the body
movements. The raters in this study were required to assess the
movements verbally.
- 28 - ii. The difficulty in designing and the expense and time required to code and
interpret behavioural measures were considered prohibitive.9
Some researchers warn of methodological weaknesses in using self-report measures in comparison to other kinds of measures (e.g., Panksepp, 1995, pp. 191-192). Such views are contradicted by a significant body of literature that reflects consistent, meaningful self-reports to musical experiences, whereas physiological methodologies, for example, have a propensity toward inconsistency, reflecting, at least, an equally fundamental problem in methodology. In contrast, Whissell (1989) reports the advantages of self-report, verbal measures of emotion:
Language is not the only channel suitable to the communication of emotion: it
is, however, one of the "cheapest" stimulus or response measures available
because it is easily obtained and does not require an extensive support
technology. In addition, the language response is insensitive to certain artefacts
that plague other potential measures of human emotion (muscle movements
obscure responses in both polygraphic and electroencephalographic recordings,
while angle of facial presentation is a problem for pupilography and for the
scoring of facial expression).
… Naturally, a cheap measure is only valuable if it is theoretically and
ecologically valid, as well as sufficiently reliable to satisfy the requirements of
science. Measures of emotion based on language have
9 For an example of observing and coding facial expressions, see Kring, Smith and Neale, (1994); for an
- 29 - shown evidence of reliability and validity in a number of different research
situations … (pp. 121-122)
As this study of emotion expressed by music is largely exploratory, it was considered unwise to add extra dependent variables that may or may not have some relationship to the research problem under study (Zuckerman, 1976). However, pending the outcome of the present study, adding one or several physiological or behavioural measures to the self-report measures would be areas for further research.
In sum, limiting this study to self-reports is justified because self-report methods are historically well established measures, relatively easy to implement, and probably the best methods available for the kind of research problem being investigated
(Kuhn, 1979, cited by Radocy & Boyle, 1988, p. 203).
Limitation 6: Musicological Investigation The prime interest of this study is to investigate the relationships between musical features and emotional response. Therefore, this study will be limited to analysing responses to the collative properties of the musical work, rather than the human variables associated with psychological testing. The effects of the individuals’ background, for example, will not be a prime consideration here. Although such considerations were important, they were controlled in this study through broad sampling, questionnaires and statistical techniques. Of course the relationship between emotion, music and the individual’s preparatory set is an area of research that should benefit from studies such as the one under investigation. However, there is a
example of observing and coding movement,- see30 -Sims, (1988). stronger motivation to limit the sorts of variables to be controlled for a study which is exploratory and already burdened with a high degree of multi-dimensionality.
Another way of viewing this limitation is that I am using psychological techniques as tool for investigating a musicological problem.
In summary, this thesis is limited to the investigation of the expression of emotion by musical features, as expressed by a selection of the existing Romantic Western Art music repertoire. Response data are limited to a simplified, dimensional paradigm of emotion using empirical, self-report techniques. The fundamental assertion of this investigation is that there exist underlying, quantifiable rules within a given musical culture which determine the relationships between musical features and emotional responses. As outlined in the Plan of Methodology on page 23, the investigation continues with the first literature review in which I report and evaluate the methods used for collecting self-report emotions in response to music.
- 31 -
Chapter 2 Measuring Emotions
Research on the measurement of emotion may be divided into three broad groups: physiological, behavioural and self-report (see Chapter 1; Berlyne, 1974, pp. 12-15).
The review reported in this chapter will focus on the self-report measures for reasons indicated in Limitation 5: Self-Report Measures on page 27 in Chapter 1. In general, this literature deals with emotional responses to music. Particular attention is given to those studies whose dependent variables may, or do, fit into the dimensional paradigm of emotion as outlined in my discussion of
The Structure of Emotion on page 16 in Chapter 1.
The relationship between emotions and musical features is not reported in this chapter, as the focus here is on methods of developing and using self-report measures of emotion and the methods of analysing data. These relationships are discussed in the review of musical features associated with changes in valence and arousal in Chapter 4.
For each type of self-report measure, the literature was examined with a bent toward studies that measured emotional responses continuously. A brief
- 32 - preamble on some philosophical issues related to measuring emotions prefaces this review.
Philosophical Preamble Among the more thought-provoking writers on measuring emotion is George
Mandler (1982), who questioned the ability of verbal or non-verbal means of communication in being able to convey accurately the inner, private emotional experience. Plutchik and Ax (1967) strengthen this argument by suggesting that it is naive to assume a general definition of emotion. A measured emotional response can be changed by factors not related to the independent variable under investigation. The preparatory set of the individual, the individual’s mood and demand characteristics have all been shown to have some manipulative effect on emotional response. For example, Francés (1958/1988, experiment 14) found differences in responses related to the type of measure used. Nevertheless, Mandler concedes that one way of finding out how people feel is to ask them. Although there is still some debate on whether emotion in music can be measured, numerous papers report that people can agree on emotion expressed by music.10 Therefore, the focus here will be on how emotion in music can be measured.
Structure of the Review After investigating several reviews which discussed measures of emotional response to music (Abeles & Chung, 1996; Abeles, 1980; Boyle & Radocy,
10 Those interested in these arguments should consult Izard and Saxton (1988), Mandler (1982), Oatley (1996), Frijda (1986). - 33 - 1987; Collins, 1989; Hargreaves, 1986; Levi, 1978; Lundin, 1985; Miller, 1992; Radocy
& Boyle, 1988; Thayer, 1986), it became apparent that continuous response measures had received virtually no attention.11 In order to remedy this, the present review on self-report measures of emotional responses contains a discussion of measures that have been used or could be used as continuous measures within each section (as identified in Figure Chapter 2 -1). The chosen taxonomy reflects a chronology of the introduction of the various measures in experimental aesthetics from left to right
(Edmonston, 1966). This list of measures is by no means exhaustive (see Boyle &
Radocy, 1987), rather they comprise the literature which pertains to measures of emotional response to music.12 Methods of analysing the data are also discussed with a view to determining the kinds of analytic techniques to which various measures have lent themselves.
Figure Chapter 2 -1 Taxonomy of Self-Report Measures of Emotional Response to Music
self-report measures / | \ open-ended checklists — scales \ / \ ranking rating and matching / \ unipolar bipolar
11 A review devoted to continuous response measures to music was made by Schmidt (1996). 12 For a review of non-music self report measures of emotion see Plutchik and Kellerman (1989). - 34 - A Comment on Terminology: “Verbal” and “Non-Verbal” The absence of the term “verbal” in the taxonomy shown in Figure Chapter 2 -1 is deliberate because no assumptions about a necessary linguistic mediation between the measure and the musical experience is made. For example, suppose a measure of emotional response to music entails pointing to one of a group of schematic faces, then is this a non-verbal scale? There are three possibilities: (a) The image of a face might be coded into the word ‘happy’ or whatever it expresses, or (b) it might be coded by some other means, or (c) it may have an isomorphic relationship to a measure where the actual word “happy” is used. Similarly, does a seven point scale separating the antonyms ‘happy’ and ‘sad’ constitute a verbal scale? If the respondent selects a point in between the two terms, this may be coded as a “3”. It is not clear whether the selection was mediated by a linguistic process or not, nor is it clear if a verbal response was made. Consequently, it appears to me to be hazardous and limiting to use the term “verbal” in the taxonomy. There is no necessary reason for separating measures which are presented verbally from those which are presented non-verbally (see Miller, 1992; Kessels, 1986; Knapp, 1963, for further discussions of this issue).
Open-Ended Measures Open-ended measures “allow respondents the opportunity to compose their own answers instead of being forced to choose between a fixed set of answers …”
(Windschuttle & Windschuttle, 1988, p. 209). Of all the methods discussed in this review, open-ended response measures impose the least restrictions on the individual being tested.
- 35 - Non-Continuous
Gilman and Downey Open-ended measures have a long history in modern experimental aesthetics.
Studies dating from the end of the nineteenth century have been cited which used the procedure of asking individuals to write down responses to a live performance
(Downey, 1897; Gilman, 1891, 1892). June Downey (1897), for example, collected open-ended responses from twenty-two listeners after each of six pieces performed at a piano recital. No questions were asked, and the identity of each piece was not announced. At the end of each piece the subjects wrote down their impressions. In the publication all responses for each piece of music appeared together. The author’s interpretation of the emotional content of each piece was provided along with an indication of how well responses did or did not fit into these interpretations.
Downey made some qualitative comments and concluded that there was some consistency in responses to music, though in varying degrees. Benjamin Gilman’s
(1891, 1892) earlier study was similar in design to that of Downey, except that
Gilman asked specific questions. Gilman’s data reflected disagreement in interpretation within many of the pieces played.13
Since the work of these pioneers, more systematic approaches to analysis of the content of responses have become available. A common type of content analysis was to formulate categories into which responses may be grouped. In order to ensure that each category was meaningful, labels which reflected their meaning were frequently assigned. For exploratory studies the
13 For a critical review of Gilman’s study see Valentine (1962, pp. 286-288). - 36 - categories were created by inspecting and sorting responses and then creating and labelling categories post-hoc. A summary of studies where such analyses were applied to open-ended data follows.
Weld Harry Weld (1912) conducted a study where each of eight participants had both physiological and verbal (or “introspective”) responses measured while listening to phonograph recordings of a series of four minute excerpts.14 Physiological measures were made during listening. As soon as the music stopped, the participant was asked to describe the listening experience. This open-ended response was dictated, perhaps allowing for richer information than if responses were written. Weld inspected these introspective responses with respect to types of responses and with respect to the musical selections. To examine the types of responses the following categories were used:
A. Visual Imagery,
B. Auditory Imagery,
C. Actual or Imaged Motor Reactions,
D. Reactions to Descriptive Music,
E. Emotions and Moods,
F. Individual Differences.
Of interest in the present study are the “Emotions and Moods” category of response.
Weld found that participants tended to focus such feeling responses along two dimensions:
14 The duration of the listening period was determined by the rotation of a drum used for recording physiological response (part of the kymograph apparatus). One revolution took about five minutes. - 37 - Our introspective evidence justifies the conclusion that the feelings arrange
themselves between two pairs of poles in two dimensions of space. One of
these pairs can best be described as pleasantness-unpleasantness. The other pair
is more difficult to definitize and to describe; the most appropriate terms for
this pair seem to be excitement-repose. (p. 282)
This finding marks Weld’s study as a precursor of studies of the dimensional paradigm of emotions that would come to the fore in psychology during the 1950s and in music psychology not long after.15
Lee
The largest open-ended study in the first half of the twentieth century was conducted over a period of many years by Vernon Lee (1932). In her volume Music and its
Lovers she compiled responses to a questionnaire in three languages which dated from 1907. Although several questions could be answered with a yes or no response, the questionnaire was essentially open-ended. Lee divided responses into two types based on the respondent’s musical aptitude and according to two ways of experiencing music: as “hearers” and “listeners”. “Hearers” were people who were musically unsophisticated and had expressionist experiences in response to music, while “listeners” where musically sophisticated and those who had formalist experiences. Like Hanslick before her, Lee believed that the experience of the
15 The dimensional view of emotion was not new at the time of Weld’s publication. He refers to dimensional views of emotion described by Titchener and Wundt at the turn of the century (1912, p. 282). - 38 - “listener” was of the greatest value16, and yet she found that many of her “listener” respondents preferred the “hearer experience” (see Kucsan, 1995, p. 188). Valentine
(1962, p. 255) is critical of Lee’s work with respect to her analysis and descriptive manner. As with the work of Downey and Gilman, Lee’s compilation may benefit from some modern content analysis techniques.
Valentine C. W. Valentine (1914) asked 146 adults to indicate their response to each of a series of simultaneously-played two-note chords that were played on a piano. Responses were grouped into one of four categories: objective, subjective, character and associative. These categories were found suitable for descriptions in response to music and colour. Valentine (1962) describes each category:
(1) The objective type of judgement is shown by the following comments:
perfect blending, full and round, one note competes with the other for
prominence, the notes are too wide apart, and so on.
(2) The subjective type of attitude is revealed when the subjects thought
especially of the influence of the notes upon themselves, thus: jars on the
nerves, gives a creepy feeling, makes one draw a deep breath, feeling of
lethargy produced, causes melancholy, stirring, makes me think my cares are
over for a time.
(3) The character type of judgement, as in experiments with colour, reads
something of personality into the musical sounds. They were
16 According to Burnett Gardner (1987, cited by Kucsan, 1995, p. 184), Lee saw hearers as “‘heretics’ - 39 - described as follows: decided, assertive, meek, sullen, happy, lacking joviality,
hopeful, bold and forceful. People who gave this type of judgement frequently
seemed to get more enjoyment out of the harmonious intervals than did those
of the other types. Indeed, the assumption of this mental attitude sometimes
resulted in a discord being pleasing.
(4) The associative type of judgements showed most frequently as a reason for
liking or disliking an interval the fact that it recalled either some source of a
similar sound (church bells, gong, etc.) or some piece of music. Sometimes the
association might be with an event suggested by the sound, e.g. a walk by the
sea when the church bells had been heard like the sound of the interval now
heard. Such we may label a "non-fused" association, following Bullough's use of
the term in his colour experiments. Other ideas or images roused by the hearing
of the interval seemed much more intimately bound up with the sound itself:
e.g. the very chord in which it occurred in a known piece of music. These we
may label "fused" associations. (pp. 201-202)
Valentine’s groupings are of interest because they provide a way of distinguishing between different kinds of emotional responses. The subjective and the unfused association types are emotivist, while the character type judgements are essentially cognitivist. The objective type of response corresponds to the formalist experience in the sense of Hanslick (1854/1957). Valentine does not indicate whether particular categories of response were exclusive to particular people. Rather, there was a tendency for certain people to respond in one category more regularly than they would for the
who engaged in ‘musical orgies’”. - 40 - others. For example, Valentine notes a difference between the responses of males and females or musicians and non-musicians. However, it seems reasonable to conclude that people are capable of many kinds of experiences in response to music, and that for the present study, the focus will be on the character type responses (point 3, above). The fact that such character judgement responses comprise just one category of responses is a point that should be kept in mind when dealing with forced choice measures (discussed later in this chapter from page 50).
Washburn and Dickinson In a large study on reactions to a wide range of Western instrumental art music,
Margaret Washburn and George Dickinson (1927) asked a class of music students to indicate the amount of pleasantness and the sources of this pleasure for each of 182 compositions. The sources suggested were musical features such as melody, timbre and harmony in addition to exciting and quieting effects. These prescribed effects were rated as either being present or absent and the overall pleasure was rated on a four point unipolar scale (unipolar scales are discussed later in this chapter, from page 72). Finally, Washburn and Dickinson asked their participants to write
“emotional effects not included under the heads of pleasantness, excitement, and quieting” (1927, p. 122). This open-ended task is of interest. The responses were replaced with synonyms where appropriate and categorised to provide “a very fair survey of all emotions which instrumental music suggests to ordinary listeners” (p.
127). The categories were reported in a hierarchical manner. At the top of the hierarchy two emotional states were suggested: active and passive. Each of these were further divided into pleasant and unpleasant,
- 41 - however the passive state had a third category, “involving slight fear”, added.
Although there was a further division for some categories before the actual words were presented, the interesting point is that this categorical structure bears a close relationship to the four quadrants of a two-dimensional emotion space (see
The Structure of Emotion on page 16 in Chapter 1). The details of the categorisation are superimposed on an emotion space in Figure Chapter 2 -2. Washburn and
Dickinson emphasised that the pieces evoking the negative emotions (groups B and
C in Figure Chapter 2 -2) were still enjoyed.
Sherman An interesting open-ended approach was conducted by Mandel Sherman (1928). In one part of the experiment Sherman asked participants to write down the emotion being expressed by a singer whose task it was to express each of four expressive states, namely surprise, fear-pain, sorrow and anger-hate. Before the experiment began, the participants were told that the hidden singer was going to try to convey four different emotions, but the identity of these emotions was not revealed.
According to Sherman, thirty participants made eighteen kinds of responses to the four intended emotions. Only frequency of responses were reported. This approach is interesting because it could be viewed as a precursor of the checklist measure.17
17 However, the checklist method had been employed at around the same time by Heinlein (1928). - 42 - Figure Chapter 2 -2 Emotion Words for Describing Instrumental Art Music Superimposed on a Two-Dimensional Emotion Space. Adapted from Washburn and Dickinson, 1927, pp. 128-129. Category numbers (I, II, A, B and C) are retained from the source. Category II C is included in the third quadrant for convenience.
I. Active emotional states.
B. Unpleasant (slightly) A. Pleasant Uneasiness, some conflict or inhibition Diffuse activity: happiness, joy. present: hurry, unrest, searching, struggle, Diffuse superficial activity: gaiety, tumult, wrangling, confusion, frivolous, playful, humour, fun, bewilderment. teasing, mischief, whimsical, fantastic, flirting. Concentrated forward activity: exhilaration, stimulation, confidence, courage, certainty, triumph, force, power, purpose, martial, patriotic, encouraging, dignified, majestic.
II. Passive emotional states.
B. Unpleasant (slightly) A. Pleasant Sadness, melancholy. Calm, peace, soothing, reminiscence, Slight element of activity present: contemplation, thoughtfulness, something lacking: suspense, doubt, languor, sentimentality. uncertainty, anxiety, longing, yearning, wistfulness, plaintiveness.
C. Involving slight fear: foreboding, weird, sombre, mysterious, eerie, fear.
Nelson More recently, David Nelson (1985) investigated the development of children’s aesthetic responses to music using a structured, open-ended measure referred to as the Aesthetic Responsiveness Task (ART). Forty-six Suzuki violin playing children took part in the study. They were taught two pieces of music and then asked ten questions. One of the questions was “does this song have certain feelings to it”. The responses were recorded and later coded according to the quality of the answer on a scale of 1 to 3, as based on a protocol derived from an aesthetic-developmental paradigm. The - 43 - response of “A pretty feeling, it just has it” (showing an egocentric response) was scored 1, “Yes, it has an introduction feeling to it, like a movie” was scored 2 and
“Uplifting mood because of the notes and rhythm” (showing awareness of the complexity of the aesthetic object) was scored 3. The coding was applied by three judges. Nelson found that inter-judge agreement was high (Spearman rank r >
0.912). Coded responses were then correlated with each of the independent variables investigated.
Gabrielsson and Lindström In a large scale research project initiated by Alf Gabrielsson and Siv Lindström
(Gabrielsson, 1991; Gabrielsson & Lindström, 1993; Gabrielsson & Lindström, 1995)
“strong experiences of music” (SEM) were investigated. Among other measures, open-ended responses were collected from around 800 people, many of whom were musicians. Participants were asked to write or talk about “the strongest (most intense) experience of music that they ever had” (Gabrielsson & Lindström, 1993, p.
121). The approach for analysing the responses was demanding and time consuming.
We read every description very carefully, note all experiences and responses are
reported and try to sort them into suitable categories. The two authors (and
several students) have done this, at first independently of each other, then
checking each other's classifications and discussing cases in which differences
appeared. The general principle is to stick to the words used by the persons
themselves, avoiding further interpretation. Due to the task and the nature of
language, a certain arbitrariness can hardly be avoided but is hopefully
- 44 - kept to a minimum through the independent readings. The whole procedure is
also repeated several times in order to refine the analysis. (p. 122)
Applying content analysis to the first set of 149 responses yielded an initial reduction of the data into seven categories:
General characteristics of SEM
Physical responses
Perception
Cognition
Emotion
Transcendental and existential aspects
Personal development
This important research produced a rich source of data on musical experiences, but the response format did not provide a systematic way of tapping into the musical features that contributed to the subjects’ responses. Only if the subject happened to discuss musical features, or if particular parts of the music were referenced during the SEM report could such analyses be made. Indeed, this is one of the advantages of the open-ended format, for the participant was free to mention any section of music they wished. An extension of the SEM project for the present research would be to extract data where mention was made about a specific section of music and a corresponding SEM, and then to find and analyse the cited music. Adapting such an approach to the study of the relationship between musical features and emotional response is conceivable, though potentially inefficient. Other
- 45 - studies using the open-ended format have been conducted by Flowers (1988),
Hargreaves (1982), Pike (1972), Rigg, (1937) and Waterman (1996).
Continuous
Watson As part of a preliminary study, Brantley Watson (1942) used an unstructured self- report measure to collect continuous data on musical meaning as perceived by children and adults. Children from fourth grade through to twelfth grade and a group of adults were asked to think aloud while listening to an excerpt of orchestral music played on a gramophone. The respondents were prompted with questions such as “What does this mean to you?” and “How does the music make you feel?”.
Respondents were also asked what it was about the music that made them respond the way they did. Watson then classified responses into five categories: Objective,
Imaginal, Associational, Abstract and Subjective (similar to the Valentine study, discussed above, and Francés, 1958/1988, p. 232-233). The data from these categories were used to devise an adjective list for a later part of Watson’s study.
Flowers Patricia Flowers (1983) used an alternative approach to the problem of collecting open-ended information continuously. Participants listened to a piece of music using headphones. Each time a change in the music was detected, the participant was to speak a number into a microphone. Both the participant’s speech and the music were recorded on an audio cassette. The participant then took this tape home in order to identify the points where a
- 46 - change was noted and to describe what the changes were. This procedure is like a two stage open-ended method. Instead of providing a detailed response in real time, the participant could continue listening with minimal interruptions. Flowers then collected the written versions and marked them according to the presence of a particular, pre-determined vocabulary. The number of changes signalled on the audio tape also provided a response. Flowers used both the number of changes detected and the description of the changes in her analysis.18
Evaluation of Open-Ended Measures
Open-ended measures have made an important contribution to the study of emotional responses to music. Modern techniques and technology, coupled with carefully designed and structured open-ended measures offer three advantages sought by self-report measures (1) richness of data for present and future reference,
(2) systematic control and analysis through meaningful, internally consistent coding protocols, and (3) freedom for the participant to respond in a manner relevant to the researcher’s investigation. The third point is exemplified in those open ended designs that give participants the freedom to describe particular musical moments and the associated emotional responses, as in the studies by Gabrielsson and
Lindström (1993), and Sloboda (1991). Such experimental methodologies are potentially more efficient than the method where all participants respond to a predetermined selection of pieces because an emotional response is more likely to occur if the participant is free to choose music which has emotional significance to
18 Waterman (1996) used a similar procedure, but his study is mentioned in the rating scale section of this review as from the open ended section because of the way the data was reported. - 47 - them. Studies such as those by Flowers (1988) and Sherman (1928) demonstrate how the open-ended format can be used to produce a list of words and phrases suitable for more controlled, forced-choice responses. Valentine (1962, p. 294) argues that the open-ended structure avoids the problem of biasing or focussing attention to pre- determined choices imposed by other self-report measures.
However, based on the above review, five criticisms can be leveled at open-ended measures: analytic errors, subjective expression, coding consistency, dynamic interference and research time. First, the amount of information to be analysed and the method of analysis is subject to errors through inconsistencies (Rigg, 1964).
Second, as some researchers argue (Campbell, 1942; Kratus, 1993), open-ended studies are dependent on how well the subject can express him or herself. For example, a five year old is likely to make fewer responses than a fifteen year old because the younger respondent possesses a lower level of linguistic ability. Even if all subjects have access to the same vocabulary, it is well documented in psychology that recall tasks, intrinsic to open-ended responses, are more difficult than recognition tasks (Tulving, 1983). This argument provides a response to Valentine’s support of open-ended measures, for, by restricting responses to predetermined choices, the experimenter can ensure that a required variety of responses can be made. Such control cannot be afforded to the open-ended regime.
- 48 - Third, coding methods can be difficult to administer and apply consistently to the varied responses that the open-ended format can attract (Boyle & Radocy, 1987, p.
209; Russell, Suzuki & Ishida, 1993), as in the case of large scale research works such as Gabrielsson and Lindström (1993). Fourth, in the context of the present research problem, direct open-ended regimes do not lend themselves to the measurement of continuous response. The listening task becomes more difficult because attentional resources are required to make responses simultaneously, and even more seriously, the response may interfere with the listening task. Although Watson (1942) has attempted such a method, its success may have been possible due to the brevity of the excerpts. It appears that in this study participants may have responded at the conclusion of the piece as well as while the piece was unfolding. One solution to the problem of interference was demonstrated by Flowers and Waterman, where the stimulus response is measured in two phases. In the first phase an important event is simply indicated, and in the second phase the indicator is used as a cue to provide a more detailed response. The final problem related to open-ended methodology is that such studies are more time consuming to run compared with other methods.
Although response times will vary, they will usually take longer than for other methods. Furthermore, the coding process can be time consuming.
The above studies demonstrate that to be interpretable and testable, open-ended responses need to be coded. Coding enables the meaningful reduction of large amounts of data. Ironically, coding also diminishes the richness of the responses, and the expense and complexity of the open-ended methodology becomes more difficult to justify for anything but the more
- 49 - exploratory studies. Open-ended research has, therefore, been primarily important in creating a pool of data from which the forced choice measures could be constructed.
Checklist Measures The most common method of empirically measuring emotional responses to music in the first half of this century was the checklist. The procedure required the participant to select a word or several words from a list that best described the emotion expressed by the music. In many cases, respondents were free to add their own terms if they wished. The list could be created by the researcher or based on a list used by past researchers.
Non-Continuous
Heinlein Christian Heinlein (1928) employed a 15 word checklist with the intention of collecting information about how subjects felt in response to isolated chord pairs
(p. 123). Each pair contrasted a major chord with a minor chord, or vice-versa, and consecutive pairs were in different keys. The checklist was intended to reflect the valence dimension (or, as Heinlein put it, the “joyful-melancholy dimension”).
Heinlein selected words that had been used in the past by investigators and musicians to describe major chords:
bright joyful cheerful soothing clear happy
- 50 - and minor chords:
melancholy mournful dark plaintive doleful sad dull gloomy yearning.
Two musically trained participants in the study suggested that just the two terms,
“dull” and “bright”, would have been sufficient to make the required distinction.
Heinlein then drew up several frequency-percentile tables to report his data.
Hampton Peter Hampton’s (1945) study comparing emotivist experiences and cognitivist expressions is interesting because he reported some of the views of participants about word lists as a method of obtaining data. Hampton supplied a list of thirty words (with definitions) for his subjects to choose from and augment. According to
Hampton, the list contained some degree of overlap so that listeners could better express themselves. However, he provides a paragraph that is not only at odds with this assertion, but exposes some of the failings of checklists in general:
Several of the listeners added additional words such as contentment, elation,
and gaiety.
Other listeners emphasised the shortcomings of the list of words chosen by such
pungent remarks as, “Very emotional, but does not express any emotion.” “No
words fit.” “The music is beyond words.” “Music
- 51 - cannot be bound by words.” And referring to specific selections, we find such
comments as, “Schubert is just divine. How can words appreciate him.” And
again, “Words of greater subtlety are needed for Berlioz’ Fantastic Symphony,
such as ironic, fanciful, macabre.”
The author realises, of course, the shortcomings that words present in gauging
such a complex emotional experience as music presents, but if music is to be
approached from an objective, experimental point of view, these limitations
have to be condoned. (p. 240)
Gundlach Ralph Gundlach (1935) studied how people characterise musical phrases. He asked subjects to write one of a list of 17 pre-selected terms on an answer sheet in response to a fragment of recorded music. As is common practice with checklist responses, the subject was allowed to use terms not supplied on the list, however only a single response was encouraged. Many other researchers allowed the selection of as many terms as the subject wished. The selection of just one term helped to simplify the data analysis which in the Gundlach study was detailed. The study is the earliest report in the music-emotion literature to use factor analysis, based on the Thurstone simplified multiple-factor technique of 1933. In his review of the Gundlach study,
Thayer (1986, pp. 25-27) suggested that of the four factors reported, the first two could be referred to as bipolar factors of activation and pleasantness.
- 52 - Capurso Alexander Capurso (1952/1970) asked 1,075 non-musical students to indicate their emotional responses to groups of stimuli selected from 105 musical excerpts. The subjects could choose one of six categories for each piece:
A: happy, gay, joyous, stimulating, triumphant;
B: agitated, restless, irritating;
C: nostalgic, sentimental, soothing, meditative, relaxing;
D: prayerful, reverent;
E: sad, melancholy, grieving, depressing, lonely;
F: eerie, weird, grotesque. (pp. 57-58).
This measure could be classified as somewhere in between a checklist and a sorting task.19 The selection of a category (A to F) instead of a word, served to increase agreement in responses. However, the task was emotivist, which might have lowered agreement.20 There were 61 out of 105 selections for which more than 50% of respondents could agree on the category.
Sopchak Andrew Sopchak (1955) used a modified version of Campbell’s system to investigate how music affected people’s mood and whether people can agree on the emotion expressed by various pieces of classical, folk and popular music. The categories were extended from Campbell’s seven to twelve:
Sorrow Joy Calm Yearning
19 Farnsworth (1969, p. 249) refers to the task as a sort, while Radocy and Boyle (1988, p. 212) class the study under checklists; Capurso is not specific in the text. 20 See discussion under Historical Overview on page 2 in Chapter 1. - 53 - Love Eroticism Jealousy Wonder Solemnity Cruelty Rage Assertion but with only four similes for each category. The 553 participants could check any or all of the words in the list. Clearly there were highly systematic responses to some of the pieces, suggesting that there was reasonable agreement to the emotion expressed.
Typical of the attitude of some researchers (e.g., Valentine, 1962), Sopchak seemed to be surprised and disappointed that there was no perfect agreement in the emotion expressed by the music.21 It is interesting to note that for certain sections of his analysis, Sopchak dichotomised the emotion words into positive and negative groups. This shows awareness of the dimensionality of emotion words and their relationship to one another.
Hevner Adjective lists have been employed by several other researchers of emotion in music.22 However, it is Kate Hevner who is often associated with this measure. In its most common form, Hevner’s checklist comprised sixty-seven words arranged into eight clusters. Each cluster was arranged such that the words within one cluster held a strong relationship to each other, and
21 Statistically it is impossible to obtain perfect agreement where there is a stochastic component in the process under investigation, as there almost always is in psychological studies. Obtaining perfect agreement is not, and should not be, an important aim of psychological research. 22 For example, Brown, Leiter and Hildum (1957), Francés and Bruchon-Schweitzer (1983), Gatewood (1927), Hart and Cogan (1973), Kenealy (1988), Levi (1979), Odbert, Karwoski and Eckerson (1942), Rigg (1937), Rigg (1937, 1940), Rogge (1952), Scherer and Oshinsky (1977); Mull (1940), Schoen and Gatewood (1927), Shatin (1970), Shimp (1940), Van Stone (1960), Winold (1963). For a tabulated summary of some of these studies see Radocy and Boyle (1988). - 54 - clusters were related to each other such that they formed a kind of continuum. In fact, the clusters could be arranged to form a circle, as shown in Figure Chapter 2 -3, giving rise to this checklist’s popular name of the Hevner adjective circle.
Figure Chapter 2 -3 Hevner Adjective Circle Superimposed on a Two-Dimensional Emotion Space Note that axes have been rotated from conventional 2DES figures. The superimposed valence and arousal axes are discussed under Farnsworth and McMullen on page 56.
6 bright cheerful 7 gay happy 5 agitated delicate dram atic joyous merry fa n ci fu l exciting gr ace fu l exhilarated humorous impetuous light passionate playful 8 restless qu a in t sensational 4 em phatic spr igh tl y leisurely exalting soaring whim sical triumphant lyrical majestic qu i et martial satisfyin g pondero us arousal seren e ro bust soothing vigorous 1 3 tr an qui l awe-inspiring dream y dignified longing lofty 2 plaintiv e pleading sacred dark sentim ental se ri ous depressing so ber doleful tender yearning so le m n fr u stra ted yielding spiritual gloom y heavy melancholy mournful pathetic sad tr agi c
- 55 - The similarity of words within a cluster enabled the measure to be used in terms of eight clusters rather than sixty-seven words. A further inference made about the circle is that clusters diametrically opposed constitute an opposing set of emotions.
Part of the reason for this form of the adjective list being so popular is because, as
Hevner puts it:
the use of the long list of adjectives divided into eight sub-groups allows the
listener to report accurately and quickly his interpretation of the music and
enables the experimenter to make quantitative comparisons both of the details
and of the more general mood effects of the music. (1937, p. 621)
Another advantage of grouping adjectives into clusters is that it enables more sophisticated analytic techniques. For example, Hevner compared the number of responses to a piece of music that came from within a cluster with those that were made across all clusters, presenting this as a ratio similar to the chi-square statistic.
Farnsworth and McMullen Paul Farnsworth (1954, 1969) modified Hevner’s list and rearranged it into ten clusters, but no longer in the circular form. Farnsworth (1969, p. 83) believed that
Hevner’s list would continue to be improved. In his study of Hevner’s adjective circle, Patrick McMullen (1976) concluded that the list contained the two underlying dimensions of activation and evaluation. McMullen (1996) affirmed that these dimensions fit the two-dimensional concept of emotion. Figure Chapter 2 -3 demonstrates how the Hevner adjective circle
- 56 - might be interpreted in the two-dimensional structure that is the theoretical basis of emotion used in the present investigation. For example, Cluster 6 in Figure Chapter
2 -3 could be viewed as containing words which express positive valence and an intermediate degree of arousal. The correspondence of the circle with the two- dimensional emotion space does not appear to be perfect, and the actual relationship will be examined empirically in the following chapter.
Continuous
Hevner The earliest example of self-report continuous measurement of emotional response to music was cited in an experiment by Hevner (1936), where the checklist, described above (Figure Chapter 2 -3), was used by the participant to record responses to various sections of music. For example, if a piece of music had several sections, the participant would place the number “1” next to the selected term or terms and when the next section of the music began (signalled by the experimenter), a “2” would be placed next to the term characterising that section. This process continued until all sections were heard. The pieces Hevner reported were divided in three sections and each example was usually an entire movement. An example was Reflections on the
Water by Claude Debussy, as shown in Figure Chapter 2 -4.
In one experiment, Hevner discovered that responses to the Debussy piece were widely distributed across the eight clusters (Figure Chapter 2 -4A). The experiment was conducted again using the continuous procedure. In the first section of the piece, the responses were made predominantly in Clusters
- 57 - 5 and 7 (“humorous…” and “exhilarated…”), whereas in the second section, responses shifted to Cluster 4 (“lyrical…”). In the final section the Clusters 4 and 5
(“lyrical…” and “humorous…”) were chosen most frequently (Figure Chapter 2 -4B).
The results demonstrated that different sections of music evoked different, but consistent responses.
Figure Chapter 2 -4 Hevner Adjective Checklist Responses to Debussy’s Reflections on the Water for Whole Piece and in Sections Adapted from Hevner (1936, p. 251 and p. 254). Numbers correspond to the cluster from the Hevner adjective circle (see Figure Chapter 2 -3). (A) shows relative frequencies of each adjective circle cluster. (B) shows responses to the same piece in a different experiment with separate responses recorded for three sections of the music.
A
B
- 58 - Clynes Manfred Clynes (1977; see also de Vries, 1991; Clynes & Walker, 1982; Gabrielsson,
1993) developed a device that he claimed could measure emotional experience. The device, referred to as a sentograph, measured emotion by translating small, repeating finger movements into two-dimensional patterns. Clynes based this measure on the theory that emotions could be tapped through such bodily movements. I considered the sentograph as a checklist measure because of Clyne’s assertion and empirical finding that particular emotions could be clearly identified by particular movement patterns, or sentographs. One pattern of finger movements will represent joy, while another pattern will indicate love and so on.
Although not explicitly used for the purpose, the device has obvious potential as a measure of continuous response in synchronicity with the stimulus since the participant responds as the music unfolds. As a reflection of inner emotions that cannot otherwise be easily communicated, the sentograph is, strictly speaking, not a self-report instrument.
Namba, Kuwano, Hatoh and Kato Seiichiro Namba, Sonoko Kuwano, Tadasu Hatoh and Mariko Kato (1991) collected data on instantaneous impressions of three performances of the Promenade movements from Mussorgsky’s Pictures at an Exhibition. Instantaneous responses were made using key strokes, where each of fifteen keys on a computer keyboard represented an adjective. The adjectives were derived from a series of preliminary experiments. First, open-ended responses to the Promenades were gathered from
130 people. From these responses a preliminary list of sixty adjectives was formulated. Four
- 59 - hundred and ninety-eight subjects listened to the same pieces of music and were asked to select adjectives that expressed their impressions of each performance.
Namba and associates put this data through several rigorous analytic techniques
(factor analysis, multidimensional scaling and cluster analysis) to shed light on the factorial structure on the data, and to reduce the number of adjectives used to fifteen.
The English equivalents of the Japanese adjectives selected were:
triumphant quiet lonely magnificent leisurely depressed stirring pastoral brilliant powerful calm delicate mild sorrowful smooth
In one of their experiments, key-strokes were recorded as each promenade was played. Before this experiment the first letter of each adjective was placed on an appropriate key. Subjects required around 30 minutes of training to become familiar with the keyboard response lay out. With this method of “continuous judgement by selected description”, multidimensional, instantaneous impressions were obtained.
As seems to be common in the few studies that investigate continuous response,
Namba, Kuwano, Hatoh and Kato only make general comments about musical features and responses made. And although the method of continuous judgement by selected descriptions may be an appropriate way of examining the question of the relationship between musical features and emotional response, the training time of thirty minutes implies that the measure is not intuitive to use.
- 60 - Mull Helen Mull (1949) used a technique that could be viewed as a simple continuous checklist measure. Mull examined humour in music and asked the participant (one tested at a time) to raise his or her hand during listening if a humorous passage was encountered. This study is grouped as a checklist measure because it calls for the indication of the absence or presence of humour. However, the method used to synchronise each participant’s response with the music was quite primitive: a stopwatch was started when the gramophone began playing. The experimenter was required to mark a response and the corresponding time elapsed on the stop watch.
Apart from the possibility of inaccuracy and missing a response while noting the previous response, synchronisation of response with the actual passage would be subject to some variation. Mull was aware of these problems and so the continuous data of the response were discarded. Although the methodology Mull adopted was innovative in its time, it highlighted the need for a more sophisticated system of synchronising stimulus and response data collection.
Sloboda John Sloboda (1991) examined the relationship between emotivist experience and musical structures. The ensuing discussion is directed toward a part of the study that is classified here as a continuous checklist measure, the reason for which will become clear shortly. The study was conducted by postal questionnaire and the format was a hybrid of unipolar (unipolar scales are discussed below from page 72) and open-ended responses. The respondents were asked to indicate the number of times they experienced particular
- 61 - physical responses (such as shivers down the spine, laughter, tears or goose pimples) to music which they could remember from the previous five years. Each experience was rated on a five point unipolar scale. Sloboda justifies the use of reporting physical responses because the experiences are:
stereotyped, memorable, distinct from one another, and shared by all humans
regardless of culture and vocabulary. They are arguably more closely connected
to the experience of emotion than verbalizations which may be infected with
rationalisations. (1992, pp. 40-41)
Participants were asked to list up to three pieces of music which evoked one or more of the physical experiences described. They were then asked to identify such things as the nature of the response, the location in the body and how often the experience occurred.
Interestingly, Sloboda asked subjects to mention the precise musical event at which the experience occurred, and, if possible, to indicate this on a musical score or with reference to a recording. This latter request was a novel approach which appears to defy obvious placement in the present taxonomy of self-report measures. Making an indication on a musical score could be related to a checklist process, where the musical score lays out a continuum of many possible choices (i.e., each pulse of music, or point along the score, is a possible choice). It is almost certain that the musically literate respondent plays through the score in his or her mind, and when an event eliciting the required response occurs, an appropriate pencil mark is made on the score or noted. The respondent may then continue her or his mental performance, or move to another location at will. Although most respondents referred to - 62 - larger sections of music as being those that elicited a response (such as a section of a piece or section of a movement), some respondents indicated specific bars, chords or movements. Sloboda argued that reliability would be enhanced by retaining only those examples with 20 or more reported reactions. This study is unique because of the way in which these pieces were structurally analysed and compared with responses (see Chapter 4).
There are two facets of the Sloboda study that are worth noting: (1) the use of physical emotion words to measure the dependent variable,23 and (2) the use of the musical score as a response sheet. The former point, even though quite perceptive, is difficult to place into the present paradigm of emotion. Consequently, some of the physical emotion words used by Sloboda were used in a study reported in the following chapter in order to determine how well these word could be mapped onto the dimensional paradigm of emotion. The second point is of particular interest given its relationship with continuous response measures. A problem with using the score as a response measure is that it restricts respondents to those who are able to read the particular score in question.24 Further, data collection so removed from conventional pen and paper formats could be a precarious task, as the coder searches for some mark, perhaps clear, perhaps esoteric, that signifies an emotional or some other event. Nevertheless, this methodology warrants further consideration.
23 While Sloboda’s approach was innovative, he was not the first to use physical emotion words as a means of collecting responses to music. Through the SEM project (see Gabrielsson and Lindström on page 44), Gabrielsson and his associates had already discovered the salience of a variety of physical emotional experiences in response to music. 24 Sloboda did allow respondents to refer to recordings, but how these data were collated is not clear. - 63 - Evaluation of Checklist Measures Henkin (1955) was critical of the checklist measure because past research has failed to show a necessary relationship between the verbal categories and the actual aesthetic judgement (p. 162; see also Valentine 1962, p. 301). Kratus (1993) cited the work of
Reimer (1989) and Swanwick (1988) when arguing that word lists cannot adequately describe “the variety, subtlety and depth of possible emotional responses to music”
(p. 17). Also, having the option of checking one or more items in a checklist leaves the measure open to large fluctuations between those who tend to mark many terms and those who tend to mark just one term (Herron, 1969). However, as a tool for systematic investigation of emotional responses, checklists have the advantages of improving consistency of responses, compared, for example, with open-ended measures (Rigg, 1937), and sharpening an experience “when one collects it into a familiar form classified by language” (Francés, 1958/1988, p. 236).
The unanimity of responses is a function of the number of words used and the spread (or density) of the words in psychological-semantic space. As an extreme example, suppose respondents were forced to make responses on a checklist that contained only two words, excited and depressed. The responses would be far more consistent (although, as Henkin points out, less meaningful) than if the respondent had the choice of sixty-seven words of the Hevner adjective circle. This is one reason why some checklists are sub-grouped into words sharing similar meanings
(Campbell, 1942; Capurso, 1952; Farnsworth, 1969; Hevner, 1936). The researcher then has the option of analysing more fine tuned responses by looking at the specific words
- 64 - selected (at the expense of lower agreement) or to examine the group in which responses were made (increasing agreement). By way of illustration, Bonny and
Savary (1990) used the eight broad groupings of Hevner’s checklist to formulate a convenient coding of a range of musical works.
However, such groupings are also prone to problems related to semantic density. To be a good measure, each group should contain adjectives of similar meaning, and the groups should encompass a large amount of semantic space (Roberts & Wedell, 1994;
Russell, 1989). For example, both Hevner’s adjective checklist and the instrument used by Namba, Kuwano, Hatoh and Kato (1991) are deficient in words that clearly distinguish high arousal, negative valence emotions such as angry, afraid and distressed. In addition, some of Hevner’s clusters include words with fairly similar meanings, whereas other groups contain words of quite varied meanings.25
Another criticism of the checklist measure is that it does not offer the flexibility of alternative inferential statistical analyses. Checklist data are essentially nominal data types, restricting them to chi-square analysis and the like, although even this level of analysis is often absent. The reason is partly historical, since statistical clustering techniques (such as Pareto charts and factor analysis) were not always accessible or available at the height of the checklist’s popularity. For example, Sören Nielzén and
Zvonimir Cesarec (1982b) reported that in 1976, Günter Batel performed a cluster analysis of a checklist measure “to define the components determining the experience of
25 Some of the problems associated with the Hevner adjective checklist are discussed in detail under Hevner on page 182 in Chapter 4. - 65 - music” (p. 10). Gundlach’s (1935) analysis is a rare early example in which factor analytic techniques were used. Therefore, there are techniques which address this criticism of checklists and which are applied regularly in more recent studies.
Although the dominance of the checklist measure has subsided in the second half of this century, it still remains of interest to researchers studying emotivist response to music, particularly through instruments such as the Multiple Affect Adjective Check
List (MAACL) (Kenealy, 1988; Lorr, 1989; Martin & Labott, 1991; Parrott, 1982;
Plutchik, 1989; Rohner, 1985; Stratton & Zalanowski, 1991, 1994; Thaut & Davis,
1993; Thaut & de l’Etoile, 1993). Regardless of the disadvantages of the checklist measure, in Hevner’s manifestation, it is probably the fastest and most informative self-report measures available (compared with the multiple ranking and multiple rating scales discussed below). Using a computer keyboard or the musical score as a response interface provides a significant broadening of the possibilities of the checklist as applied to continuous response measurement.
Ranking and Matching Measures Matching measures are similar to checklists, except that when a selection from the list is made (i.e., matched with the stimulus), the item selected is removed. The process usually continues until all options in the list have been matched (and therefore removed).
Ranking measures are those in which the subject is provided with a series of options and asked to rank them according to a predetermined criterion (e.g., highest to lowest, happiest to saddest, and so on), relative to one another.
- 66 - The ranking produced by the participant constitutes the depended variable. Q-sorts are an example of a ranked measure (Boyle & Radocy, 1987, p. 210). Q-sorting involves the placement of a series of cards (usually about 60 to 90) with statements that relate systematically to the variable of interest. The subject then has the task of reading one card at a time and placing that card into one of several (two to fifteen) categories according to the ranking criterion.
Ranking and matching measures are found in a variety of formats. However, they are not used commonly in music-emotion research, nor can they always be clearly distinguished from other kinds of measures.
Campbell Ivy Campbell (1942) conducted a cognitivist study of responses to music by four groups of ten college students. Their task was to match one of seven words with each of seven pieces played on a piano which was hidden from view by choosing either: assertion, calm, gaiety, joy, sorrow, tenderness or yearning. Campbell referred to the list as emotion categories. They were derived to reflect a broad range of emotions and this was achieved by introspection and after much listening (p. 2).
A definition of each emotion was read out to the participants. Seven musical selections were used to reflect each of these categories. Therefore, the task of the participant involved matching rather than ranking. However, the pieces were played again with the participants being supplied with a larger range of words from which to choose. These words were intended to allow a finer degree of response, with each of the original seven categories having five or six
- 67 - synonyms listed under them. This part of the method was more like a checklist measure.
Campbell found high agreement at the categorical level and less agreement
(sometimes nearly no agreement) when more terms were available. Valentine (1962, p. 300) criticised this study on the grounds that participants could change their answers in the matching phase of the experiment, and that this could falsely inflate the amount of agreement between category and music. This problem could have been alleviated by using the list of seven words as a checklist to random selections of music, rather than as a matching task to seven pieces of music.
Watson Watson (1942) applied a ranking measure in one of his preliminary studies which investigated the discrimination of meaning in music. He formulated a sixty word adjective list based on an open-ended measure. Ten musicians were asked to indicate all the words on the checklist that were appropriate to the music via a ranking scheme. The word on the list that best described the music was marked “1”, with the next best word marked “2”, and a third choice marked “3”. Any words that the subject found unsuitable were to be checked as “unclassified”. Watson scored three points for an adjective receiving a rank of one, two for a rank of two and one for a rank of three. He used this ranking technique to refine a preliminary list of adjectives (in which responses of twelve musicians to fifty-seven pieces of music were compiled), and also as a self-report measure of meaning for subsequent studies.
In the preliminary study, Watson kept adjectives which received the highest scores,
- 68 - and removed adjectives that were not used, or were selected in tandem with many differing words (inferring that the term provided little extra meaning).
Gabriel Clive Gabriel (1978) provided participants with two emotional descriptions of a tone sequence. Both descriptions were based on different hypothesised sequences which were formulated by Deryck Cooke (1959). The participant’s task was to rate how well each of the two statements described the tune.26
Terwogt and Grinsven Mark Terwogt and Flora van Grinsven (1991) asked sixty-four children and adults to link each of eight fragments of music to one of four schematic facial expressions, each expressing happiness, sadness, anger or fear.27 Such linking is akin to a sorting task
(though this study might be equally well grouped under checklist measures). The fragments were pre-selected such that pairs of excerpts were expected to be linked to each of the four faces. The main effects were reported as a percentage of agreement.
For example, 93.8% of adults agreed on happy as being expressed by the hypothesised “happy” fragments. Terwogt and Grinsven also analysed the data by indicating the average number of times subjects selected the hypothesised emotion according to age and sex. For example, 5 year old boys linked happy to the hypothesised happy pieces 1.56 times out of two.
A multivariate analysis of variance (using the variables age, sex and emotion quality in the music) was reported. The main findings were that agreement
26 Gabriel and Cooke are discussed further under Gabriel on page 159 in Chapter 4. 27 Gerardi and Gerken, 1995; Kastner and Crowder, 1990; Kratus, 1993; and Trunk, 1981 used similar methods. Kratus took a dimensional approach compatible with this dissertation. - 69 - on the emotion word linked to a selection increases with age, and that links to angry and afraid were often confused. Terwogt and Grinsven (1991) explain the discrepancy in the fear-angry responses as a confusion between cognitivist interpretation (“What is the composer trying to express?”) and the emotivist interpretation (“How does the music make me feel?”). For example, if the composer is interpreted as trying to express anger, then the respondent might have an emotivist response of fear. Terwogt and Grinsven, as with numerous studies of emotional responses to music (see Collins, 1989), do not make clear whether they were asking subjects for a cognitivist response or an emotivist response.
Another explanation of why fear and anger were confused was offered. Based on the premise that people can classify emotions primarily along the dimensions of happy- sad (or valence) and activity (or arousal), Terwogt and Grinsven argued that happy and sad can be clearly separated along the valence dimension, whereas anger and fear are difficult to distinguish along either dimension, hence the tendency for confusion (p. 107). The confusion between fear and anger, therefore, strengthens the view that a two-dimensional representation of emotion may provide sufficient representation of emotions expressed in music.
Other sorting and matching type methodologies were used by Lifton (1961) and
Wedin (1969). Lifton asked judges to sort written responses to four pieces of music into three categories of aesthetic sensitivity. The initial responses were made by college students. Wedin (1969) used checklist and
- 70 - sorting procedures. Studies using such techniques are difficult to find partly because they bear some resemblance to checklist measures. For example, the study by
Capurso (1952/1970), discussed in the review of checklist measures above (on page
53), could be classed as a matching task.
Evaluation of Ranking and Matching
Matching schemes for measuring emotional response to music share several characteristics of checklists, which were discussed above (on page 64). However, both ranking and matching measures are rarely used to collect music-emotion data.
Watson’s (1942) study is an example of how a ranked measure can be used to judge emotional responses to music using checklists. But even such an approach has not been cited elsewhere. One reason is that the weighting schemes used by Watson were arbitrary. A score of three for the highest rank and two for the next rank may be an inaccurate reflection of respondents’ cognitive processes or intentions. A respondent may actually feel that their first two choices are very close, or very far apart. Although this problem can be rectified by non-parametric statistical procedures, the method still finds little acceptance in the study of emotional responses to music. Another reason for the rarity of ranking measures is the emerging popularity of other techniques, and in particular the class of measures referred to as rating scales. Finally, the literature cited which use ranking schemes have no apparent application to continuous response measures.
- 71 - Rating Scale Measures The most common means of collecting information on self-report emotional response is through the use of rating scales. In general there are two kinds of rating scales: the unipolar rating scale and the bipolar rating scale.
Non-Continuous Unipolar A unipolar scale measures a single concept or entity per scale; it measures the absence or presence of a particular property related to that concept or entity. For example, an individual might be asked to rate how happy a piece of music was. The unipolar rating scale might indicate five ordered possibilities from “no happiness” through to
“extremely happy”. Another example is the Likert (1932) system of assessment which involves a collection of 5 point scales, each one requiring a forced choice response to a statement of either strongly agree, agree, undecided, disagree or strongly disagree. In this respect the unipolar rating scale is a kind of refined checklist.
Conversely, a checklist could be viewed as a special case of a unipolar scale, where each term is rated on an implied two point scale — presence and absence, yes and no, or true and false. The fine line between the checklist and the unipolar scale was demonstrated by Nowlis and Nowlis (1956) who studied mood using a checklist.
The participant was required to double check an item if there was strong agreement, single check it if there was slight agreement, skip it if it probably did not apply, and cross it out if it definitely did not apply. Therefore, this checklist procedure can be equated to a four point unipolar scale. So close is the relationship between the checklist and the unipolar scale that some authors include unipolar scales when
- 72 - referring to checklists (e.g., Plutchik, 1989). However, for the present review a distinction is made between the checklist and the unipolar scale for the following reasons:
1. In general, the checklist requires an all or nothing selection for each of the
terms in the list, where the rating scale enables graded responses to each
item.
2. The checklist produces nominal data. For example, the researcher may
count the number of times subjects chose the word ‘sad’ in response to
stimulus A. The rating scale produces multilevel, ranked data and provides
a means of quantifying subject responses in degree. Hence the rating scale
lends itself to various forms of clustering and comparative statistical
techniques, such as multidimensional scaling, correlation analysis and
analysis of variance.
Rating scales, therefore, provide a more subtle indication of response than checklists.
The burgeoning of statistics and computers over the last half of this century has meant that the rating scale (both bipolar and unipolar) has become a more popular tool for analysing responses to music than the checklist. When a large list of scales are used the responses are usually clustered together and parsed into related concepts or dimensions.
Wedin Lage Wedin (1969) formulated a set of 40 unipolar scales for rating emotional expression in music. The scale set was derived from an initial group of 125 words gathered from the literature on emotion in music and Wedin’s own
- 73 - research. The words were chosen to include those of a subjective nature such as glad, happy and exalted; an objective nature, such as brilliant, sparkling and grand; and other words considered suitable for describing aesthetic experiences such as romantic and religious. Two pre-experiments were conducted to help reduce the initial list of words. These experiments involved rating the suitability of the words for describing music and grouping words of similar meaning together. Wedin produced a checklist from this experiment which was compared with the checklists of Hevner, Campbell and Watson.
The final set of 40 words was based on a cluster analysis of the grouping experiment and by using two criteria: (1) frequency of usage, and (2) the need to have a wide range of responses. It is this group of words which were presented as ten-point unipolar scales in the main experiment. Wedin applied factor analytic techniques in an attempt to assert the position that there is a stable, multidimensional “cultural space” (Nordenstreng, 1969) across musical stimuli and the individuals represented by the sample. Wedin reported these dimensions as consisting of two bipolar dimensions: Tension/Energy (representing tense-relaxed, vehement-mild, and aggressive-gentle) and Gaiety-Gloom (representing light-dark, playful-doleful, and glad-sad). In terms of the study to be reported here it is relevant to note that the first two of these dimensions relate to arousal and valence. Importantly, Wedin found that arousal and valence accounted for 70% of the total variance.
- 74 - Asmus Edward Asmus (1985) developed an instrument consisting of forty-one unipolar adjectives. Asmus arrived at the terms used in the instrument by a common procedure where potential terms are collected and then refined. For the data collection process Asmus undertook a comprehensive literature review in addition to the collection of data from eighty-seven musically experienced students. This led to the generation of 165 terms used to describe affective reactions to music. The number of words was reduced to ninety-nine after again enlisting the assistance of musical experts, after which, 2,057 students used the 99 scales to respond to three pieces of music.
Asmus applied principal component factor analysis procedures to determine nine dimensions to which the adjectives could be reduced. Finally, forty-one terms that loaded highly on the nine dimensions were selected to constitute the “9 Affective
Dimensions” (or “9-AD”) instrument. Although the 9-AD is frequently used and is considered one of the more sophisticated measures available (Radocy & Boyle, 1988), studies using the 9-AD focus on experienced emotion rather than observed emotion
(e.g., see Gfeller, Asmus & Eckert, 1991; Gfeller & Coffman, 1991). Further, responding to 41 items is not practical for continuous response measurement.
Collins Sylvie Collins (1989) formulated a set of unipolar rating scales by selecting eleven terms from Izard’s Differential Emotions Scale (1972) that seemed suitable for describing cognitivist and emotivist responses. No two scales had significant correlations across musical excerpts, meaning that the scales chosen at least had the quality of not being redundant. After performing
- 75 - principal component analysis on the data, Collins represented her scales on a two- dimensional emotion space, with the dimensions “pleasantness” and “activation”.
Importantly, Collins was convinced of the suitability of the dimensional paradigm as a suitable framework for examining emotional responses to music:
The results, in combination with Osgood, Suci and Tannenbaum’s (1957)
original findings concerning the dimensional nature of semantic space and the
circumplex models of affect of Russell (1980) and Plutchik (1962), strongly
suggest that the tendency to discriminate meaning along dimensions of
evaluation and activity applies as much to musical meaning as to the
connotative aspects of linguistic stimuli. (1989, p. 199)
Thayer Other researchers who have used unipolar scales to study emotional responses to music include Banks (1981), Behrens and Green (1993), Gabrielsson and Juslin (1996),
Kamenetsky, Hill and Trehub (1997) and Thayer (1986). Julian Thayer’s theoretical framework upon which he defines emotions is also similar to the one used here. His measure consisted of twenty emotion terms (serenity, exhilaration, relaxation, interest, amusement, excitement, content, happy, surprise, restless, agitation, tension, anger, sadness, fear, disgust, pain, arousal, visual imagery, verbal thinking) each on a nine point scale. The measure was used by 33 participants to rate emotivist experience in response to 17 excerpts of music. After verifying that ordering of the adjectives did not produce a systematic error, Thayer performed principal factors analysis on the data to isolate three factors, the
- 76 - first two accounting for most of the variance. These factors were labelled
“pleasantness” and “activation”, and both were bipolar. The activation factor grouped terms that ranged from serenity and sadness to exhilaration and agitation.
The pleasantness (valence) factor distinguished terms such as happy and exhilaration from terms such as disgust and fear. Based on the low intercorrelations, these factors were assumed to be relatively independent.
An important finding of this study, which has a direct bearing on the present study is that the term “arousal” loaded positively onto both factors. This could indicate some concern in referring to Thayer’s activity dimension as “arousal”, however the term will not be changed on the strength of this finding alone. Activity suggests a physical concept, while arousal refers more to a physiological concept and therefore the latter has a stronger relationship with emotion (see The Nature of Emotion on page 11 in Chapter 1). Further, Thayer’s analysis was performed with the pooling of words describing emotions and words describing musical features (such as perceived tempo, pitch and activity). Consequently, Thayer’s research does not diminish the value of the dimensional paradigm of emotion which I am using.
Continuous Unipolar
Goldstein A problem with the unipolar scale instrument is that, like many other self-report measures, it is difficult to continuously make the ten or even thirty judgements that are required of many such instruments as a piece of music
- 77 - unfolds in time. An obvious solution is to limit the number of questions asked. This approach was used by Avram Goldstein (1980) who provided a methodology that remedies this problem. He was interested in emotivist “thrill” responses to music, and therefore used a single, unipolar scale which indicated the strength of thrills experienced while listening to music. Subjects were asked to raise from one up to three fingers, corresponding to the intensity of the thrill. The experimenter was nearby taking notes of the number of fingers raised as the music played.
The dictionary definition used by Goldstein for a “thrill” was “a subtle nervous tremor caused by intense emotion or excitement (as pleasure, fear, etc.), producing a slight shudder or tingling through the body…” (p. 126). This definition implies a strong sense of the arousal component of emotion. One finger indicated a definite thrill, but of the lowest intensity. Three fingers indicated the highest intensity of thrill, spreading widely to distant parts of the body. The thrill was experienced for as long as the fingers were held up. Since Goldstein was interested in the number of thrills rather than the location in the music at which they occurred, no attempt was made to relate the thrill responses to the musical structure. Nevertheless, the response technique of holding up fingers, or something similar, may be worth consideration for the purpose of recording continuous responses to music.
Panksepp Jaak Panksepp (1995, experiment 6) used a similar measure to Goldstein, except instead of raised fingers, Panksepp measured the frequency with
- 78 - which the subject’s hand was raised (intended to reflect a “chill” experience) in response to three pieces of popular-rock music. Panksepp presented time series data and a time series analysis that consisted of observations. No inferential statistical time series analysis was reported.
Nielsen A cornerstone in the measurement of self-report continuous emotional response appeared when Frede Nielsen (1983) developed a simultaneous, non-verbal
(“simenon”) device. The device was a set of tongs which were squeezed together in order to indicate increasing tension:
During the listening process, a pair of tongs with a spring resistance and a
potentiometer placed in the axis is compressed to varying degrees, indicating
the level of tension experienced during the music. Tension and changes of
tension are continuously registered. A special arrangement ensures precise
synchronisation of the indicated tension and the musical sequence so that the
relationship between musical structure and the experience of tension can be
subjected to a subsequent bar-by-bar analysis. (Nielsen, 1987, p. 500)
When the device was not being squeezed it reflected a state of relaxation, suggesting that the measure is bipolar. However, logically a true bipolar scale should have obvious extremes, and a non-response is reflected by a central position. With the tension tongs it would be hard to tell whether no pressure meant no tension
(relaxation), or just no response. For this reason, Nielsen’s device is considered a unipolar measure. This classification is of no great consequence. Nielsen analysed his data by visual inspection of the
- 79 - tension curves and a variety of musical features. His analysis was conducted without the benefit of inferential time series analysis techniques (see Chapter 6).
Madsen and the CRDI The Continuous Response Digital Interface (CRDI) has become a popular tool for investigating ongoing responses as music unfolds in time (see Schmidt, 1996, for a review). The device consists of a box with a rotary dial or slider at one end, and some wires at the other for connection to a data gathering computer. The dial is labelled according to the variable under investigation. This provides the CRDI with the flexibility to be used as a single item unipolar measure or as a single item bipolar measure (discussed below from page 84). An example of the former is a study by
Clifford Madsen and William Fredrickson (1993) which attempted to replicate the
Nielsen’s findings. Instead of squeezing tension tongs, Madsen and Fredrickson asked participants to turn the dial on the CRDI which was arranged to indicate less tension at one end of the dial and more tension at the other end. Subjects registered their responses while the music, the first movement of Haydn’s Symphony No. 104, was played, and each shift on the CRDI was recorded.
In another study Madsen, with Ruth Brittin and Deborah Capperella-Sheldon, (1993) examined continuous “aesthetic experience” to music. This time the CRDI was labelled “negative” at one end and “positive” at the
- 80 - other.28 The subject was asked to use his or her definition of aesthetic experience.
The music used was the last 20 minutes of the first act of Puccini’s La Boheme.
Bobby Adams (1994) used the CRDI to measure the single, unipolar variable labelled
“emotional response”, with “no emotional response” appearing at the left side of the dial with gradually increasing emotional response indicated by moving the dial gradually to the right. This unipolar scale was used to record emotional responses to the last eight minutes of Mahler’s Resurrection Symphony in one of three conditions: while watching a video of the performance with or without sound, or while hearing the music only.
All three of these studies provide potential for a closer analysis of the time variant relationship between emotional response and musical features, however, in each case only general comments were made. Madsen and Fredrickson justified this by quoting Nielsen who proposed that only structural categories should be examined.
The inference that was drawn from this was that “ascribing tension to any single parameter is very problematic because of the joint action and interrelated function in real music of such parameters” (Madsen & Fredrickson, 1993, p. 56). This implies a rather naive but common argument that if a single musical feature does not explain the mean response, then no musical features should be checked. On the contrary, there is a complex interweaving of musical features that contribute to emotional expression, and with the availability of research tools
28 Whether such a labelling places this measure into the bipolar category or a unipolar category is admittedly hazy, but, again, of no serious consequence. - 81 - like the CRDI, the challenge is open for researchers to attempt to untangle the web.
The papers cited on CRDI research report their graphs with the time axis in units of seconds or minutes, making it impractical to follow up and extend the results in the absence of the actual recordings used. An exception was made in the Madsen and
Fredrickson (1993) study, when their “tension” CRDI graph and the original Nielsen graph were aligned (p. 58); The latter plot had bar numbers on the time axis.29
These problems of reporting and analysis of CRDI data are easy enough to amend.
There is, however, a potentially more serious problem that faces the CRDI in the context of the present research paradigm of emotion. The original CRDI, which is based on the human manipulation of a single potentiometer, can only indicate one variable at a time, meaning that only a single dimension of emotion can be studied.
Given that the definition of emotion implies at least a valence and arousal dimension, each piece of music under investigation would require two passes per subject, with the CRDI’s meaning changing on each occasion. For the purpose of the present study, this was considered methodologically problematic and procedurally clumsy.
Another solution could be to use two CRDIs in parallel, with one measuring valence,30 and the other measuring arousal. Ruth Brittin, (1991) has already used such a configuration to measure style and preference
29 See also Tyler (1996) for another exception. 30 Perhaps the labels “happy” and “sad” could be posted on this device — see Madsen, Capperella- Sheldon and Johnson (1991). - 82 - simultaneously.31 More recently, modifications of the CRDI have been made which enable simultaneous responses across two dimensions (Tyler, 1996; Madsen, 1997).32
Waterman
Waterman (1996) asked subjects to press a button upon an emotivist experience while listening to music recorded on audio tape.33 Synchronicity of music and response was achieved by recording a tone (activated by pressing a button) on one of the unused tracks of the tape. This method may be interpreted as a single item, unipolar measure because the participant was asked to rate how often something happened to him or her as the music unfolded in time. That is, a single entity was being measured (“when the music causes something to happen to you”, p. 56). The measure could have a value of zero for no responses per unit time through to however many button presses can be recorded per unit of time. Waterman obtained more data by quizzing subjects as to why they made their responses at various points
(in an open-ended format), however it is the continuous measure that is of interest here.
In coding responses, Waterman reported the number of button presses made per bar of music. Such coding lends itself to analysis of musical features by comparing the responses at each bar with the musical events in that and nearby bars of a score. That is, the report is no longer necessarily dependent
31 See Continuous Bipolar on page 89. 32 By the time of these developments to the CRDI, my own, similar, instrument - the 2DES (Schubert, 1996a) - had been fully developed and applied. See under Schubert and Madsen on page 89. 33 When respondents were performing instrumentalists, they had the option of using a bite switch or a foot pedal (p. 57). - 83 - on the recording and reproducing equipment used. In analysing the data, Waterman determined the correlation between two hearings of selected examples, selecting the portions where there had occurred a “significant musical structure” (p. 60).
However, no details of the derivation of the relationship between the musical structure and the responses are revealed, except for mentioning that the findings were in agreement with Sloboda (1991) and Collins (1989). Once again, no inferential time series analytic techniques were reported.
Non-Continuous Bipolar Another form the rating scale can take is the bipolar form. A bipolar rating scale is a scale anchored at either end by terms with opposing meanings. For example, a scale may have the word ‘excited’ at one end and ‘calm’ at the other. Arbitrary, equispaced numbers may appear between the two terms such as -3, -2, -1, 0, 1, 2, 3 indicating some kind of semantic distance between the terms with a neutral point at or near the centre. Such rating scale formats have been widely used in measuring responses to music.
A common manifestation of the bipolar rating scale is the semantic differential, which was designed with the intention of objectively and indirectly measuring the connotative properties of a stimulus (Osgood, Suci & Tannenbaum, 1957; Boyle &
Radocy, 1987). Charles Osgood and his associates developed the semantic differential “to measure connotative meanings of concepts as points in what he called
‘semantic space’”
- 84 - (Kerlinger, 1964, p. 564).34 This semantic space usually consists of two or three dimensions, as will become evident from the following studies. Of importance from the outset is that the semantic differential has a strong intuitive and empirical relationship with emotions (see Coren & Russell, 1992).
Also important is that the main dimensions concerning responses to aesthetic stimuli appear to be an evaluative factor, which is akin to valence, and an arousal factor, which is akin to activity. As Crozier (1974, p. 55) pointed out: “Osgood has conjectured that, in the case of aesthetic stimuli, the ubiquitous Evaluative factor and
‘a type of activity factor’ will be the primary dimensions of aesthetic judgment
(Osgood, et al., 1957, p, 74)”. Crozier’s interpretation of these dimensions is different to my own. Crozier and Bragg (1974) treat the evaluative dimension as one of pleasingness and the activity dimension as interestingness. I treat the evaluative dimension as valence and activity as arousal. The disparity can be explained by differences in research objectives.
Gray and Wheeler Philip Gray and Gloria Wheeler (1967) provided a relatively early example of the semantic differential scale applied to the measurement of responses to music. Their scales were created from a pool of guessed items, which were refined after testing, using an intuitive analytic approach. This led to a final list of twenty-four items.
Subjects used this instrument to judge folksongs that were selected, among several other things, to represent “different moods
34 Sometimes “affective meaning” is used as a synonym for connotative meaning. For example, see
- 85 - and emotions” (p. 242). Gray and Wheeler factor analysed the responses, producing a three dimensional graph of the “value space” for some of the selections. The first two factors, labelled “evaluative” and “potency”, loaded highly, but the third factor had a fairly low loading. The bipolar scales that could be grouped into Factor 1 included: good-bad, pleasurable-not pleasurable, performance good-performance bad, meaningful-meaningless, and for Factor 2 included relaxed-tense, smooth- rough, delicate-rugged.
Giomo and the Diagrammatic Differential The use of non-verbal measures which utilise facial expressions is a young tradition of research stemming from a desire to investigate children’s responses to music
(Kratus, 1993). Pioneers of such investigations include Trunk (1981) and, of relevance here, Swanwick with his “diagrammatic differential” (1973).
Based on such research, Carla Giomo (1993) derived a three item, non-verbal, bipolar response instrument designed to enable children to make judgements about emotion expressed by music. The three items were based on Wedin’s (1972) empirically determined aesthetic paradigm that emotional responses to music can be expressed in terms of three dimension (discussed under Non-Continuous Unipolar on page 73).
Giomo decided to use three bipolar scales instead of a checklist format because of (1) an argued lack of agreement on the emotions expressed by music, (2) a lack of agreement by researchers on which emotions to select, and (3) the statistical advantage (p. 143).
Crozier (1974, p. 55). - 86 - The scale was developed over several stages. First, of 140 schematic faces, forty-nine were chosen that appeared appropriate to the researcher, then three adults selected faces that represented each of a series of adjectives. These adjectives came from six groups consisting of three sets of two adjectives: each cluster representing one of the poles of Wedin’s dimensions. Next, twenty-two children performed the same task with slightly altered instructions. The three most popular choices for each pole were then ranked by the children according to how well they represented each pole. As a reliability check, the ranking task was repeated by the children one week later. The final step was to combine each of the three faces into their dimensional sets, forming three bipolar scales of six faces each. This is an interesting bipolar scale because there is a contrast between the middle two meanings for each scale, or as Giomo puts it, each scale consists of two polar groups. In the testing phase the children listened to a piece of music before indicating which of the polar groups was the music more like, and then which of the three faces in the selected polar group is the feeling of the music most like. Giomo’s research focussed on examining the relationship between mood and age, for which analysis of variance was used.
Gregory, Worral and Sarge Andrew Gregory, Lisa Worrall and Ann Sarge (1996) produced an insightful and relevant variation of the diagrammatic differential. While the measure itself consisted of a simple dichotomous choice between a sad face and a happy face in response to nursery tunes, the scoring of responses was resourceful. The happy face response was scored as “1” and the sad face was scored “0”. These scores were them summed across each musical condition.
- 87 - Hence the dichotomous measure suitable for young children was converted into a multilevel variable facilitating the use of more sophisticated inferential statistics than frequency counts of happy versus sad faces would allow. Gregory, Worrall and
Sarge performed analysis of variance using the mean happiness score as the dependent variable. This approach implicitly supports the notion of a dimensional relationship between happy and sad.
Cohen A novel use of the bipolar scale is to rate an intermediary event in the presence of the independent variable (the music). In a cross modal study, Annabel Cohen (1989, cited by Cohen, 1990) asked participants to judge how “happy” or “sad” a bouncing ball was. In a series of studies the height and speed of the bouncing ball was varied, and musical features of the accompanying melody were also varied. For example, it was found that a low, slow melody partially cancelled the happiness rating otherwise given to a high, fast bounce of the ball. Although Cohen intended the study to demonstrate the effects of associations caused by music upon a dynamic visual display, this methodology raises some interesting points. The method enables the participant to focus their attention on a single variable, and does not appear to burden them with the complexity and possible confusions of focussing on the music itself. That is, it is an implicit measure of the emotional valence content of music.
Nielzén and Cesarec Sören Nielzén and Zvonimir Cesarec (1981, 1982b) used a 20 item bipolar instrument to measure responses to music. The instrument was based on the
- 88 - semantic differential format used by Osgood, Suci and Tannenbaum (1957). The items consisted of bipolar pairs such as active-passive, happy-sad, sweet-bitter, tense-relaxed, with each pair separated by seven units. By performing factor analytic techniques, Nielzén and Cesarec identified three factors that explained a total of 57% of the variance of responses. These factors were labelled Tension-Relaxation, Gaiety-
Gloom and Attraction-Repulsion. The Tension-Relaxation (arousal) factor was measured by the pairs tense-relaxed, violent-peaceful, hard-soft, threatening- enticing; the Gaiety-Gloom (valence) factor was measured by the pairs happy-sad, humorous-serious, impulsive-controlled, active-passive; and the Attraction-
Repulsion factor was measured by the pairs rich-poor, beautiful-disgusting, profound-superficial, clear-diffuse.
Continuous Bipolar
Schubert and Madsen The use of continuous bipolar scales was not explicitly cited before the development of the 2DES instrument for this dissertation (Schubert, 1996a). The details of its development are fully reported in Chapter 5 and Chapter 6. More recently, however,
Madsen (1997) has reported a new continuous, two-dimensional bipolar measure of emotional response. The principal difference between Madsen’s instrument and the
2DES is in the dimensions or axis labels used. Madsen used relaxing-exciting and ugly-beautiful, whereas I used aroused-sleepy and negative valence-positive valence respectively. This difference clarifies a differing research interest. Madsen expressed the intention of exploring the relationship between the two dimensions: “… specific to the present investigation, how does the
- 89 - dimension of exciting/relaxing relate to this affective dimension of ugly/beautiful or affect?” (p. 191), whereas my aim was to measure emotion in a parsimonious fashion.
I argue that ugly-beautiful is a dimension of aesthetic response, while negative valence-positive valence is a dimension of emotional response. In this respect, the two instruments serve two different purposes. In addition, Madsen was interested in emotivist response, and he did not use the data to quantify the relationship between musical features and emotional response (see Chapter 6 and Chapter 7).35
Evaluation of Unipolar and Bipolar Rating Scales
Wedin (1972, p. 15) is critical of bipolar scales because of the arbitrariness of the antonym selection, and because comparison of the measure with the same terms in the unipolar format produce conflicting responses. Bipolar pairs, posits Wedin, are also context dependent. For example, the pair fast-slow is a different psychological variable when applied to a tornado than when applied to a symphony. Wedin also argues that it is possible, particularly in music, to perceive both poles of a pair simultaneously.
However, I propose that the bipolar scale has served as a meaningful and valid scale for investigation of emotional responses to music. First, antonym pairs have successfully reflected psychological constructs that lie along some continuum. For example, there appears no obvious reason why people should not think of happy and sad as being at opposite ends of a continuum. There are certainly exceptions to some of the continua used by some
35 Tyler (1996) developed an instrument similar to my own (Schubert, 1996a). He used a unipolar
- 90 - researchers, however, this does not mean that all bipolar scales are defective.
Second, the context in which the pairs are used is the context of emotional response to music, and this context is clear and distinct from a context such as weather patterns. Therefore, it is unlikely that the context would be confused by any but the most freely-associating individuals.
Perhaps more serious are the foibles of the unipolar scale. Lorr (1989) summarises some of the undesirable response sets that can distort results collected via unipolar scales. These include “acquiescence” (demand characteristics, or the tendency to respond at the positive end of the scale to please the experimenter) and “extreme response style” (the tendency to use the outer regions of the measure more than other regions). Although Lorr reports that these effects can, to some extent, be controlled and the effects may even be negligible, the bipolar scale intrinsically alleviates these problems.
The semantic differential has become a common format of the bipolar scale that has been applied to the study of emotional response to music (other studies include
Bartel, 1988; Brown, Leiter & Hildum, 1957; Cohen, 1990; Crozier, 1974; Eagle, 1971;
Iwashita, 1972; Iwata, 1972; Keil & Keil, 1966; Nordenstreng, 1969). However, it can require responses to many scales, making it prohibitive as a measure of continuous response. There is certainly space in the literature for bipolar format investigations of continuous response, however, of the studies cited, unipolar formats dominate the small literature in which continuous emotional responses to music have been measured.
arousal dimension and a bipolar valence dimension. The instrument was referred to as the 2D-CRDI. As with all CRDI research cited, inferential time series analysis was not undertaken. - 91 - Summary This investigation of the literature on methods of measuring emotional response to music has raised several important issues. Of the three broad groups of self-report measures, the open-ended format is the least adequate for measuring continuous response to music, while unipolar scale measures appear to be the most common.
As the important study by Namba and associates (1991) implies, in the conventional format of lists of words, checklists are not the best means of obtaining continuous response data, because the procedure appears somewhat tedious and lacking in intuitiveness. Hevner’s adjective circle provides a much clearer interface for fast response, however attempts to keep the list up to date has destroyed the convenient circular, interrelated structure.
The literature on empirical studies of emotion in music is replete with findings of at least two factors or dimensions of semantic space that correspond to the constructs of emotion as defined in Chapter 1 (
The Structure of Emotion on page 16). The dimensions that may be interpreted as valence and arousal are indeed difficult to ignore, for they form a meaningful framework of the kinds of responses individuals make to not only linguistic (Russell,
1980) and pictorial (Schlosberg, 1952) stimuli but also to musical stimuli (Collier,
1996; Collins, 1989; Thayer, 1986).
The issue of semantic density has received far too little attention. Checklists studies have been prone to using an invalid semantic density. For example, checklists that do not include words such as anger, fear and terror (Quadrant
- 92 - 2) are likely to make conclusions about emotions based on information that is missing. Several important checklists, such as Hevner’s (1936) adjective circle, have neglected this important problem.
Because it cannot be denied that music is a continuous-time phenomenon, the rarity of continuous measures in the literature is at first glance surprising. Further investigation shows, however, that the number of continuous response studies has been steadily increasing over the past decade, indicating that perhaps the desire was there, but the resources were not. This implies that the next challenge in research on emotional responses to music is to go further than making general comments about musical features and to relate the time varying features of music to emotional responses. This is expressly the goal of the present study. The review of the literature indicates that the work of Sloboda (1991) has championed this kind of research since the pioneering work of Hevner (1936).
An alternative methodology for investigating the relationship between emotion and corresponding musical features is the open-ended format. Although not suited to continuous measurement, open-ended techniques may provide other means for addressing the issue of the relationship between musical features and emotional response. In some designs the participant is free to think about any strong musical experience they wish, raising the possibility that a particular piece, section or feature of music may be incidentally or intentionally mentioned in relation to that experience. Again, Sloboda (1991) has excelled in using this methodology, but the most comprehensive study since the work of Lee (1932) has been produced by
- 93 - Gabrielsson and Lindström (1993) in the SEM project. This project has provided a rich resource of music-emotion data — as an alternative to continuous response, forced choice methods — in which relationships between emotion and musical features may be found.36
Some rating scale measures use a series of indirect measures of the construct under investigation. An example of such a measure is the semantic differential (Osgood,
Suci & Tannenbaum, 1957). However the need for continuous measurement prohibits the completion of many items. The logical alternative is to use a direct measure. I have argued that the two prominent, meaningful and essentially independent dimension of emotion in music are valence and arousal, and consequently that these dimensions are the obvious choice in obtaining a direct measure of emotional response.
This review of measures of emotional response to music has shown that although there is a variety of techniques available for collecting self-report data, no instruments, apart from those devised by Madsen (1997), Schubert (1996a) and Tyler
(1996) have provided a satisfactory answer to the question of how to measure emotion both meaningfully and satisfactorily. My 1996 contribution was developed as part of this dissertation, and the development and testing of the instrument will be discussed in detail in the following chapter (Chapter 3) and in Chapter 5. The intention, then, was to develop an instrument that can measure continuous emotional response to music with a view to comparing these responses with musical structures. The next chapter provides the first stage of a two stage development process. In the
36 The literature on emotional response as a function- 94 - of musical features is reviewed in Chapter 4. first stage an instrument is developed to measure emotional response which may then be modified to measure continuous emotional response (as will be investigated in Chapter 5).
- 95 -
Chapter 3 Development of the Two-Dimensional Emotion Space
Self-report measurements of emotion expressed by music have produced a rich variety of techniques including checklists and scales. However, from the review of the literature in Chapter 2, it is clear that two fundamental criteria, considered necessary for measuring emotion in music, were lacking. First, the measuring instrument needs to measure emotion meaningfully, and second, it should be able to measure the variation in emotion as a piece of music unfolds in time. In this chapter the first criterion is addressed. Two experiments are reported, one designed to select suitable verbal stimuli for testing a new research instrument (Experiment I), and the other investigating the reliability and validity of this instrument (Experiment II).
In my first chapter I argued for a dimensional paradigm of emotion, based on a body of evidence showing that important aspects of emotion can be represented meaningfully along two or perhaps three dimensions of emotion. Russell (1979,
1980) proposed that valence and arousal explained the greatest amount of variation in response. These dimensions of emotion were determined by analysing results of empirical data and producing multidimensional emotion spaces.
- 96 - Russell’s realisation consisted of a square with two bipolar dimensions: valence and arousal. Valence referred to the happiness or sadness of the emotion, and arousal referred to the activeness or passiveness of the emotion. An example is shown in
Figure Chapter 1 -2 on page 20 in Chapter 1. This representation is meaningful, for it infers a quantifiable relationship between various emotions in terms of their semantic distance (Russell, 1989). For example, on Russell’s emotion space, the words happy and joyous are close together, but the words happy and depressed are far apart, reflecting a meaningful relationship among the words.
A number of researchers (Russell, 1980; Plutchik 1962; Roberts & Wedell, 1994;
Schlosberg 1952; Zevon & Tellegen, 1982) have analysed data collected from measures such as checklists and sorting tasks. A logical extension of the dimensional paradigm is to allow participants to respond on the emotion space directly. I followed this approach by designing and writing a computer program called
EmotionSpace Lab to control a Two-Dimensional Emotion Space (2DES)37 designed for such a purpose (Schubert, 1996c). To my knowledge, this was a new approach that had not been previously explored in research of this type.
An important advantage of devising an instrument measuring emotion in two dimensions is that it has the potential to be extended to the measure of continuous response, thus satisfying my second criterion of measuring emotion in music.
Continuous measures impose a limitation upon the
37 The abbreviation “2DES” is used to refer to the specific two dimensional emotion space used for the research instrument in contrast with the two dimensional emotion space used in previous research. - 97 - number of responses that can be made simultaneously. Until my own research
(Schubert 1996a), and that of Tyler (1996) and Madsen (1997), investigations using a continuous response approach were restricted to measuring responses along a single dimension of emotion (e.g., Madsen & Fredrickson, 1993; Nielsen, 1983; Waterman,
1996). The alternative methodology has been to measure many dimensions asynchronously. For the purpose of this study, measuring response along two dimensions was considered to be a good compromise. Two dimensions can be chosen to include important information about emotion and to potentially allow continuous measurement. Development and testing such an instrument was conducted in the following sequence:
1. Develop a prototype instrument.
2. Demonstrate that the instrument can measure emotion meaningfully.
3. Demonstrate that the instrument can measure emotion continuously.
The first two parts of the sequence are the focus of this chapter.
Instrument Design - Developing a Prototype The 2DES should be a reliable and valid instrument before it can be used to measure emotional responses to music. In order to determine its success, the instrument was tested with stimuli whose emotional content in terms of valence and arousal were already known. This empirical work is reported in Experiment II: Two-Dimensional
Emotion Space Validity and Reliability from page 117. The following subsections discuss the design of the 2DES and
- 98 - an experiment conducted to enable updating past checklist measures, which were required for examining validity in Experiment III (on page 245 in Chapter 5).
The transformation of the emotion space idea into an operational instrument was a gradual process that commenced with a pragmatic approach to layout and operation, and was followed by revisions that were made through consultation with several suitably skilled persons and through an examination of psychometric instrument development literature.38 A professional counsellor who was experienced in administering psychometric tests, a professor from the School of Psychology at the
University of New South Wales, my supervisor and an additional three people took part and made suggestions during informal, preliminary pilot work. This process helped to accelerate the progression from the drawing board to a testable instrument.
An important objective of the software was that it take over the labour intensive aspects of field research. The software was designed to be portable, and to control and administer all aspects of the experiment, removing the need for human laboratory assistants and minimising human error and experimental running costs.
However, this meant that more time was required in the program development stage. I was fully responsible for developing the program, writing the code and testing. The process took me from May 1994 to July 1995 before the program was ready to use for
38 Cohen, Swerdlik and Phillips, (1996, pp. 219-254); Gregory (1992), Murphy and Davidshofer, (1991) and in particular, Gable’s (1986) monograph on instrument development in the affective domain. - 99 - experimental work. Developments and corrections (or “bug fixes”) continued after this time as modifications to the software were required.
Strictly speaking, the instrument developed is not psychometric, for it is not intended to measure behaviours and abilities such as personality, preference and emotivist experiences. Rather, the instrument is ultimately intended to measure the emotion judged by the participant to be expressed by music. In this respect the 2DES can be thought of as a musometric instrument.39 Another way in which this instrument is different from traditional psychometric instruments is that, whereas psychometric instruments usually consist of many scales (or “items”), the present measure calls for the use of two, and only two, scales (valence and arousal).
Using a well designed human-computer interface to collect data has many advantages, the most important being that computer collected data reduces human error, thus increasing data reliability (Cohen, Swerdlik & Phillips, 1996, p. 702).
Evidence also suggests that people enjoy doing computerised tests (Cohen, Swerdlik
& Phillips, 1996, p. 712). The speed and accuracy provided by computers was crucial for the measurement of continuous response (a consideration that was exploited in
Experiments III and IV, reported in Chapter 5). Computer interfacing was developed in consultation with a freelance visual graphics artist and computer design experts from Vislab at the University of Sydney. The main literature consulted relevant to human computer interfacing was Apple Computer (1992), Kelley and
39 I am grateful to Dr. Kate Stevens for alerting me to this fact and for suggesting the terminology. - 100 - Charness (1995), Sutcliffe (1995), and Williams and Webster (1996). The discussion that follows is a report of the instrument that arose from this preliminary work.
Layout of the Instrument
Although many versions and rotations of the emotion space are possible, Larsen and
Diener (1992) suggest the use of the orientation best suited to the needs of the researcher. With some slight modifications, Russell’s square shaped layout was chosen (Figure Chapter 3 -1). The emotion space square consisted of two orthogonal axes intersecting at the origin of the cartesian plane: The valence dimension was represented by the x-axis and the arousal dimension was represented by the y-axis.
Placing the arousal component on the vertical axis, with increasing arousal corresponding to higher points on the axis, is intuitive because the physical position on the axis is analogous to the “height” of the arousal — high arousal at high points and low arousal at low points. The selection of the directions to represent valence are less intuitive. Consistent with the procedure adopted by Russell (1980) I decided to maintain the common orientation with positive emotions represented on the right and negative emotions on the left.
Any two-dimensional space, such as a piece of paper, could be used as an emotion space, but the present realisation was intended for execution on a computer screen.
A pointer or cursor controlled by the operator of the computer’s mouse could be freely moved across the square. For feedback, two information boxes were placed near the bottom left of the computer screen, indicating the position of the cursor. The stimulus, if visual, was
- 101 - presented to the participant in an area near the top left of the screen. The top of the screen had a region reserved for the provision of instructions to the participant, as shown in Figure Chapter 3 -1.
Figure Chapter 3 -1 Layout of Two-Dimensional Emotion Space (2DES) Computer Screen Stimulus Box - the location in which visual stimulus is shown (such as a word or a picture); Instruction Box - to inform and assist participant; Emotion Space - the region of the computer screen within which responses are made; Current Region Box - provides verbal feedback about the cursor position; Percentage Box - provides numerical feedback about the cursor position; Cursor - indicates actual response being made by the participant within the emotion space, and is manipulated by moving the computer’s mouse.
S t i mul us B ox Instruction Box Emotion Space
0% 0%
Current Region Box Percentage Box Cursor
Axis and Pole Labels for Feedback and Training
The 2DES contained no verbal information about the cursor position. This left the response area uncluttered. However, pilot work revealed the
- 102 - necessity of having more feedback for the user. First, a training phase was used in the experimental procedure to clarify the concepts pertinent to the emotion space.
The language used in the training phase, and the language used for providing feedback about responses followed several stages of preliminary development, the results of which are documented below.
On the emotion space itself, two perpendicular axes crossed at a “no emotion” or zero point at the centre of the square. Eight small, schematic faces were placed around the extreme points of the emotion space to reinforce emotional regions visually. The face shapes were determined after a thorough review of relevant literature concerned with facial expressions (Adelmann & Zajonc, 1989; Bruyer, 1986;
Darwin, 1872/1965; Ekman & Friesen, 1975; Ekman, Friesen & Tomkins, 1971; Faigin,
1990; Kratus, 1993; Peck, 1987; Schlosberg 1952).40 Mouth and eye opening size corresponded roughly to arousal, and degree of smiling or frowning corresponded roughly to valence.
Two sources of extra feedback were provided in boxes away from the emotion space square: verbal feedback and numerical feedback. These feedback boxes were located at the bottom left corner of the screen (Figure Chapter 3 -1). They indicated the coordinate position of the cursor as a verbal message of valence and arousal, and as a percentage away from the centre of the emotion space.
40 Darwin (1872/1965) proposed that the link between the (implied) arousal dimension of emotion and mouth shape was the requirement for sound production. For example, he writes: “When infants
- 103 - The next consideration was how to label the axes, regions and poles of the emotion space for the purposes of training and feedback. Russell (1980) referred to the poles of the valence dimension as pleasure and displeasure. Other labels used by various researchers for this dimension have been negative-positive quality, valence, hedonic tone, affect, dysphoria-euphoria, unpleasant-pleasant, ugly-beautiful. Two considerations helped me to determine the pole labels for this axis:
(1) The instrument was intended for the use of judgements about emotion
expressed rather than emotions experienced.
(2) The instrument was to measure responses to aesthetic and everyday
stimuli.
The first consideration eliminated labels that were loaded with personal, experiential connotations such as displeasure-pleasure and dysphoria-euphoria. These labels implied a description of the state of the individual responding (emotivist response), rather than a response made about the stimulus (cognitivist response). The second consideration eliminated terms that necessarily suggested something unpleasant about negative emotions such as sad, angry and depressed. For example, a piece of music may express sadness and yet not be disliked (Schubert, 1996b). Madsen (1997) used ugliness-beauty as his pole labels. Although my instrument had been designed before Madsen’s publication, I do not consider his labels suitable for a dimension of emotion because in an aesthetic context it is possible to confuse or interpret the ugly as being, at the same time, beautiful (Valentine, 1962; Langer, 1957). Therefore, the remaining candidates were hedonic tone and valence. Although there was no strong reason to choose one over the
cry they open their mouths widely and this, no doubt, is necessary for pouring forth a full volume of - 104 - other, hedonic tone was rejected because it may be associated with hedonism — a term loaded with moral connotations. On the other hand, valence was an emotionally neutral term, meaning little more than something that can be positive or negative. Based on these considerations I chose to label the poles as negative valence and positive valence.
There were several alternatives available for labelling the poles of the arousal dimension, including aroused-sleepy, activity, relaxation-tension and active-passive.
Russell (1980) used aroused-sleepy, and this labelling was retained. Labels involving the word activity were not used because of their intuitive link to movement rather than emotion. “Tension” was not used for the same reason, and also because there appeared the possibility that, in music, it may be confused with the ambiguous use of a term that describes a musical structure with the physical analogy of tension (such as the tension of an unresolved chord), or the effect of a musical structure (the unresolved chord creating tension).41 The arousal label, apart from lacking these problems, also has the advantage of being more strongly connected with emotions, having physiological connotations rather than being analogies of physical movement or physical principals.
The above argument serves not only to determine appropriate labels for each axis of the emotion space, but to provide evidence for the construct validity of the 2DES.
That is, the 2DES measures a construct which past research suggests is, at least in part, that of emotion.
sound…” (pp. 91-92). 41 The rejection of “tension” is contrary to the work of Nielsen (1983) and Madsen and Fredrickson (1993). Although I suspect that the different labels measure essentially the same construct and that therefore the label choice is not of great consequence, it is an area that requires further investigation. - 105 - Position Feedback and Recording Respondents could move the position of the cursor to any point within the emotion space square. Since Whissell and her colleagues used a seven point scale for rating valence and arousal, and in keeping with conventions of many psychometric scales
(Gable, 1986, pp. 41-45), I decided to use seven divisions demarcated by six tick marks. As the cursor moved around the emotion space a slider on each axis also moved in alignment with the cursor. In addition, verbal labels reflecting the cursor position in the emotion space were shown in the current position box which was updated as the cursor moved. The verbal labels used for each region are shown in
Table Chapter 3 -1.
The participant had even more finely tuned feedback about his or her current position. The position of the cursor was displayed on a 201 point percentage scale (-
100% to +100%, with a central zero point) in a rectangle beside the current position box — the percentage box (Figure Chapter 3 -1 on page 102). The percentage ranges corresponded to the seven categories of each axis as shown in Table Chapter 3 -1.
- 106 - Table Chapter 3 -1 Feedback and Percentage Range Used for Each of the Seven Regions of the Emotion Space Dimensions
Region Descriptions Percentage range
Valence Axis 1 very negative valence -100% to -72% 2 negative valence -71% to -43% 3 slightly negative valence -42% to -14% 4 no valence component -13% to 13% 5 slightly positive valence 14% to 42% 6 positive valence 43% to 71% 7 very positive valence 72% to 100%
Arousal Axis 1 very sleepy -100% to -72% 2 sleepy -71% to -43% 3 slightly sleepy -42% to -14% 4 no arousal component -13% to 13% 5 slightly aroused 14% to 42% 6 aroused 43% to 71% 7 highly aroused 72% to 100%
The Computer Program The 2DES is controlled by a computer program called EmotionSpace Lab. The program was written in Hypertalk, a high level, pseudo-object oriented authoring tool available within the Hypercard development environment. Hypercard and Hypertalk enabled creation and control of human-computer interfacing and computer aided interaction. The EmotionSpace Lab program was written with the intention of taking over much of the routine of testing that burdens researchers and their assistants.
The program operates over 12 modules:
Introduction
Help
Preliminary Questionnaire
- 107 - Valence Tutorial
Arousal Tutorial
Emotion Space Tutorial
Main Experiment: “Plain phase”
Enforced rest timer
Retest Preliminary: Anchor Placement
Retest: “Anchor phase”
Closing Questionnaire
Close
Each module is essentially a self contained unit of program which can, nevertheless, interact with other modules. The order of some of the modules can be changed (e.g., the valence and arousal tutorials are swapped randomly across participants), while some can be repeated. Some modules are interlinked with others. For example, the help module (with opening screen shown in Display 67 on page 462) may be called at several points during the experiment and this module has links to the tutorial modules and to the introductory screens of several other modules. Certain modules must link with others. The Anchor Placement phase, for instance, must be followed by the Anchor phase (Appendix B from page 474). Although most modules start with an introductory screen explaining what the module is about, or what is about to happen, some modules may consist of just one or several information and instruction screens (see Appendix B from 427 for a sampling of the various human-computer interfaces used).
- 108 - The main program, or to use the Hypercard metaphor, the stack, controls the order in which modules are presented and makes decisions about when and where to store responses and other information. The overall programming strategy was to provide a user-friendly environment in addition to a large degree of flexibility to the researcher. Because the EmotionSpace Lab program was used exclusively by me during its development, the participant friendliness criterion was considered to be of utmost importance in the early stages. File storage and formatting remained experimental until later versions of the EmotionSpace Lab program.
Although the 2DES was designed to measure responses to music, in the initial stages it was necessary for the instrument to be able to measure emotional judgements in general. In its initial phase of development the 2DES was an asynchronous instrument, meaning that it could measure response without time constraints. For testing and calibrating the instrument, temporally static stimuli, such as words and pictures of faces, were used.
It was necessary to have a pool of verbal stimuli to use for testing the instrument.
Specifically, I required two kinds of stimuli:
1. Words which occupied known theoretical positions on the emotion space,
and
2. Words which were suitable for describing music.
The first kind of stimuli were available from publications by Russell (1980) and
Whissell (1989). These words could be used to generate hypothesised responses on the 2DES. However, the second kind of stimuli were required
- 109 - for comparing responses to musical stimuli made on the emotion space. The words used were taken from traditional checklist measures. Probably the two most influential checklists used in music-emotion experiments are the Hevner (1936) adjective circle and the Farnsworth (1969) modification. Since checklist measures in music research have been used less frequently in the recent past, they have been left in need of revision.
Word frequency literature was considered an unsuitable way of revising the checklists because several words had inflated frequencies due to various meanings in different contexts. For example, Hofland and Johansson (1982) reported the words
“dark”, “heavy” and “serious” as having relatively high usage. “Dark” and “heavy” appeared on the Farnsworth list, while all three appeared on the Hevner List.
However, the meaning of these words change depending on the semantic context.
“Heavy” is used to describe physical weight more frequently than to describe a work of art. An alternative to word frequency investigation was to conduct an experiment in order to revise the checklists and to provide a resource for the selection of verbal stimuli for general and musical use. This experiment is reported in the following section.
Experiment I: Checklist Revision
Aim
The aim of Experiment I was to estimate frequency of usage for words in musical contexts and general contexts and to, therefore, assist in revising and formulating word lists for later experiments.
- 110 - Method
Material Ninety-one words were collected, including all of the Hevner (1936) adjective circle words, Farnsworth’s (1969) modified list, and a selection of words from other, non- musical sources (Russell, 1980; Whissell 1989). The non-musical words were chosen in order to ensure a spread of meanings across the valence and arousal dimensions of emotion and to allow the possibility of adding new words to the existing checklists.
The words were printed in two columns on a sheet of A4 paper in the format (shown in Appendix A on page 425)42. For each word there were two scales to be completed, a general usage scale and a musical usage scale. Each scale had three points (see
Appendix).
Participants Twenty-four highly trained musicians completed the survey. They consisted of six academic staff members, two administrative staff members (each holding music degrees), two Music Honours students and fourteen Masters of Music students, all from the School of Music and Music Education at the University of New South
Wales. While restricting the sample to trained musicians may appear limiting, it was considered likely that they would have given more thought about describing music with words than would a group formed by random sampling.
42 The order of the Appendices in this dissertation correspond to the order of chapters rather than the order in which the Appendices are cited. - 111 - Procedure The survey took place during a Masters of Music class (except for the two administrative staff members who completed the survey separately). All people in the class took part and they received no payment, credit or gift. The survey took approximately twenty minutes to complete. Participants were handed one of three versions of the form. One version was in alphabetical order and the other two were in different random orders. The instructions were read to the class and participants were given the opportunity to ask questions before commencing. No time limit was imposed.
Results and Discussion
Data were scored on a scale of one (for “low usage” or “not useful”) to three (for
“high usage” or “very useful”) in order to derive a simple analytic procedure. One way ANOVA was performed on the general usage and music suitability data.
Tukey’s HSD (honestly significant difference, e.g., see Howell, 1997, pp. 377-378) test was used to compare pairwise mean usage scores at p = 0.05.
The results of the analysis are summarised in Table Chapter 3 -2. The table indicates words with extreme usage scores — either significantly higher mean usage than at least one other word in the list or significantly lower mean usage than at least one other word in the list. The positive number in the High column indicates the number of words for which the target word had a statistically significant, higher mean. For example, the stimulus “sad” had a significantly higher general usage score than sixteen other words in the list, suggesting
- 112 - that the word sad is a high general usage word. Similarly, the negative number in the low column indicates the number of words for which the target word had a statistically significant, lower mean. “Droopy” had 26 words with a statistically higher music suitability score, suggesting that the word is unsuitable for describing music. Words with high and low entries indicate that they were distributed around the mid usage value and had relatively small deviation scores. For such stimuli it was possible to have words with significantly higher means and other words with significantly lower means. Words not shown in the table had statistically equivalent means, reflecting relatively large deviation scores.
- 113 - Table Chapter 3 -2 Word Usage Summary Table High and Low refer to the number of words whose usage/suitability scores were significantly different (p = 0.05) from the stimulus word. Sign indicates whether mean was lower or higher than the other words. For example, “pleased” had a mean music suitability score significantly lower than 28 other words, while “dramatic” had a mean music suitability score which was significantly higher than 27 other words. H denotes source of word as being the Hevner Adjective Circle (1936), F denotes Farnsworth’s (1969) revision, and RW denotes Russell’s (1980) circumplex model or Whissell’s (1989) dictionary of affect.
Music Suitability Stimulus General Usage Mean High Low Mean High Low 1.25 -21 afraid (RW) 2.54 11 2.42 10 agitated (HF) 1.96 1 1.38 -17 alarmed (RW) 2.08 1 1.96 1 -1 angry (RW) 2.79 19 1.22 -21 annoyed (RW) 2.71 15 1.96 1 -1 aroused (RW) 2.08 1 1.33 -19 astonished (RW) 2.13 1 1.83 -9 at ease (RW) 1.83 1.63 1 -1 awe-inspiring (H) 1.63 1.58 -10 bored (RW) 2.79 19 2.5 19 bright (HF) 2.54 11 2.75 25 calm (RW) 2.54 11 2.33 12 cheerful (HF) 2.29 5 1.5 -13 content (RW) 2.21 3 2.54 20 dark (HF) 2.42 9 1.83 delicate (HF) 1.83 1.25 -21 delighted (RW) 2.33 6 1.54 -12 depressed (RW) 2.63 13 1.88 -2 depressing (HF) 2.58 11 2.08 5 -1 dignified (H) 1.75 -6 1.38 -17 distressed (RW) 2.09 1 1.83 -3 doleful (HF) 1.13 -36 2.92 27 dramatic (HF) 2.38 8 2.54 20 dreamy (HF) 2.04 1 1.5 -26 droopy (RW) 1.5 2.08 5 -1 emphatic (HF) 1.96 1 -5 2.29 9 exalting (HF) 1.58 -11 2.38 10 excited (RW) 2.75 18 2.67 23 exciting (HF) 2.79 19 2.17 6 exhilarated (HF) 2 1 -1 1.54 -12 fanciful (HF) 1.38 -24 1.5 -13 frustrated (HF) 2.63 13 1.79 -3 gay (HF) 2.17 3 1.79 -17 glad (RW) 2.17 3 2.25 9 gloomy (HF) 1.96 1 -2 2.54 20 graceful (HF) 2.08 1 -1 2.29 9 happy (HF) 2.75 18 2.5 19 heavy (H) 2.67 14 2.21 9 humorous (H) 2.33 6 1.75 -3 impetuous (HF) 1.54 -13 2.35 9 joyous (HF) 1.91 1 -6 2.04 2 leisurely (HF) 2
- 114 - Music Suitability Stimulus General Usage Mean High Low Mean High Low 1.63 -9 light (HF) 2.29 5 1.5 -13 lofty (H) 1.5 1.92 1 -2 longing (HF) 1.71 2.63 13 lyrical (HF) 1.46 -15 2.54 20 majestic (HF) 1.88 1.96 1 martial (H) 1.38 -24 1.54 -12 melancholic (F) 1.58 2.5 10 -1 melancholy (H) 1.83 -4 2.17 5 merry (HF) 1.54 -13 1.46 -20 miserable (RW) 2.42 10 2.46 8 mournful (HF) 1.79 -6 2.71 14 passionate (H) 2.46 10 1.79 -5 pathetic (HF) 2.29 6 2.04 2 plaintive (HF) 1.33 -20 2.21 5 playful (HF) 2.29 6 1.71 -8 pleading (HF) 1.63 -10 1.13 -28 pleased (RW) 2.42 10 2.29 8 ponderous (H) 1.46 -15 1.33 -23 quaint (HF) 1.33 -20 1.71 -7 quiet (HF) 2.38 8 1.83 -5 relaxed (RW) 2.63 15 2.29 8 restless (H) 2.38 8 1.71 -8 robust (H) 1.71 -6 2.5 10 sacred (HF) 2.21 3 2.46 8 sad (HF) 2.71 16 1.13 -28 satisfied (RW) 2.42 10 1.5 -13 satisfying (H) 2.29 5 1.92 2 -2 sensational (H) 2.33 8 2.33 8 sentimental (HF) 2.21 3 2.42 8 serene (HF) 1.63 -10 2.08 2 serious (HF) 2.58 14 1.46 -20 sleepy (RW) 2.33 8 2.25 7 soaring (H) 1.71 -6 1.5 -19 sober (HF) 2.13 3 2.63 13 solemn (HF) 2.08 2.46 8 soothing (HF) 2.08 2.13 4 spiritual (HF) 2.17 3 1.79 -5 sprightly (HF) 1.33 -20 1.38 -22 surprised (RW) 2.58 14 2.42 8 tender (HF) 2.04 2.33 8 tense (RW) 2.63 15 1.33 -23 tired (RW) 2.67 15 2.54 10 tragic (HF) 2.21 3 2.63 13 tranquil (HF) 1.79 -6 2.71 14 triumphant (HF) 1.92 -1 2.38 8 vigorous (HF) 1.96 2 2 whimsical (HF) 1.5 -15 2.33 8 yearning (HF) 1.54 -13 1.25 -21 yielding (H) 2.08 1
- 115 - Music Checklist A checklist of words suitable for describing musical responses was formulated based on the findings of the experiment. Seven Hevner words were added to the
Farnsworth list because of high music suitability. These words were calm, heavy, melancholy, passionate, ponderous, restless and soaring. Twenty words were removed from Farnsworth’s list: depressing, doleful, emphatic, exhilarated, fanciful, frustrated, gloomy, impetuous, light, longing, melancholic, pathetic, plaintive, pleading, quaint, quiet, serious, sober, sprightly and whimsical.
If two words had very similar meanings, such as the same root, only the highest usage word was retained. For example, both “excited” and “exciting” had many significant differences, but since exciting had more (23 versus 16), only it was retained.
To control for inflated Type I error, and to make the analysis more conservative, a condition was set for the addition of non-music words. A word had to have a
“number of significant differences” score of more than five to be added to the list.
The choice of five was pragmatic and was based on post-hoc inspection.
Subsequently only one word from the non-musical set, “tense”, was added to the revised word list. All music words had mean usage scores greater than 2 on a scale of 1 to 3. The selected words are listed in
Table Chapter 3 -3.
- 116 -
Table Chapter 3 -3 Revised Music Checklist These words were used in Experiment III. The words were grouped according to similarity of meaning (based on Farnsworth’s 1969 grouping). The grouped by meaning version of this checklist is reproduced in Appendix J, Table A - 1 on page 552.
agitated merry bright mournful calm passionate cheerful ponderous dark restless delicate sacred dramatic sad dreamy sentimental exalting serene exciting soaring graceful solemn happy soothing heavy tender joyous tense leisurely tragic lyrical tranquil majestic triumphant melancholy vigorous yearning
Experiment II: Two-Dimensional Emotion Space Validity and Reliability
Aims
There were two broad aims in this experiment. The first was to test the validity and reliability of the 2DES as a measure of the emotion expressed by temporally static stimuli. This was achieved by testing four hypotheses:
1. The 2DES is intuitive to use (intuitiveness hypothesis).
2. Responses are made consistently on the 2DES (reliability hypothesis).
- 117 - 3. Responses are consistent with predictions of positions on the emotion space
(validity hypothesis).
4. The 2DES can be used to measure responses to cross-domain (non-verbal)
stimuli (generalisability hypothesis).
The second aim was to determine the mapping of a variety of words and pictures of faces onto the emotion space.
Method
Stimuli
Selection of Words Twenty-four words and five pictures of faces were used as stimuli as indicated in
Table Chapter 3 -7. The stimuli were chosen so as to encompass a wide variety of emotions, to enable validity and reliability checks, and to map some words (used in past literature to describe music) onto the two-dimensional space.
There was a large number of potential stimulus words available for testing. The
Russell (1980) study alone provided a list of 28 words all placed on the emotion space using hypothesised positions and positions determined though multidimensional scaling. Also, there exists a dictionary of affect which contains over 4000 words, 107 of which are reproduced in Whissell (1989). The dictionary of affect provided two numbers, one for the valence component of the word and the other for the arousal component of the word. The numbers ranged from 1 to 7, with a standard deviation of 1. For the circumplex, Russell did not provide numerical values in the publications cited (and he has not been able to procure them after a request by personal communication), however, he does imply that the emotion space figures are to scale. For example, in his 1989 paper (p. 86) Russell describes a simple method of
- 118 - reading off how well words on the circumplex are correlated by measuring angles directly from the emotion space diagram (reproduced in
Figure Chapter 1 -2 on page 20 in Chapter 1). Further, given that the points do not make up a perfect circle, it is reasonable to assume that they are a scaled representation. Therefore, the words appearing in the Russell emotion space were converted to numerical coordinates by measuring the euclidean distance of each point from the origin and transforming the reading to a scale of 1 to 7, as used by
Whissell. The formula used for the transformation was:
1 z - MIN Equation Chapter 3 -1 z’ = round (6 x ( + )) 6 MAX - MIN where z is the value read off for each dimension of the stimulus word, MIN is the minimum value of the axis for the dimension being measured, MAX is the maximum value of the axis for the dimension being measured and z’ is the transformed value, scaled to a number between one and seven (inclusive). “Round” is a rounding function that returns the value of the expression rounded to one decimal place. The transformation was applied to the Russell circumplex. The results of the fifteen words that also appear in Whissell’s list are shown in Table Chapter 3 -4. In this table the valence values of the two sources appear together as do the arousal values.
- 119 - Table Chapter 3 -4 Valence and Arousal Values for Fifteen Words Common to Russell and Whissell Lists. Data were taken from Whissell (1989, pp. 124-125) — based on a range from 1 to 7 with mean of 4 and standard deviation of 1, and Russell (1989) — based on estimates transformed from the circumplex reproduced in Figure Chapter 1 -2 on page 20 in Chapter 1. + denotes a noticeable difference between the Whissell and Russell data sets. Hypothesised quadrant is based on a simple mean.
|X X| | | - Quadrant 1; - Quadrant 2; - Quadrant 3; - Quadrant 4. | | X| |X
valence arousal hypothesised word Russell Whissell Russell Whissell quadrant afraid 2.8 3.4 6.2 4.9 X|
|
angry 3.6 2.7 6.2 4.2 X|
|
annoyed 2.7 2.5 5.9 4.4 X|
|
astonished 5.0 4.7 6.5 5.9 |X
|
bored 2.8 3.2 2.0 2.7 |
X|
calm 6.0 5.5 2.0 2.5 |
|X
content+ 6.3 5.5 2.3 4.8 |
|X
delighted 6.3 6.4 5.0 4.2 |X
|
depressed+ 1.8 3.1 2.7 4.2 |
X|
- 120 - valence arousal hypothesised word Russell Whissell Russell Whissell quadrant gloomy 1.6 3.2 2.7 2.4 |
X|
happy 6.5 5.3 4.3 5.3 |X
|
pleased+ 6.5 5.1 3.7 5.3 |X
|
sad 1.8 2.4 2.9 3.8 |
X|
satisfied+ 6.1 4.9 2.1 4.1 |
|X
serene 6.3 4.9 2.6 4.3 |
|X
Table Chapter 3 -5 Correlation Matrix for the 15 Words Common to Both Whissell and Russell, Shown in Table Chapter 3 -4
(N=15) Whissell Russell Whissell Russell Valence Valence Arousal Arousal Whissell Valence 1.0000 Russell Valence .9119** 1.0000 Whissell Arousal -.0906 -.1673 1.0000 Russell Arousal .3879 .2534 .5831* 1.0000 * p < 0.05 ** p < 0.01
Visual inspection of the column pairs in Table Chapter 3 -4 demonstrates a close relationship between the Russell data and the Whissell data. Table Chapter 3 -5 shows the Pearson correlation matrix of these data sets and verifies the relationships, with significant correlations within valence data sets and within arousal data sets and low correlations between arousal and valence data. However, the correlation between the arousal data sets, although
- 121 - significant, are fairly low (r = 0.58, p < 0.05). This is due mainly to the discrepancies between the Russell and Whissell data for the arousal values of content, depressed, pleased and satisfied (marked “+” in Table Chapter 3 -4). The arousal values for these words place them in opposite halves of the emotion space. In each case the
Whissell data places them in the upper half of the emotion space (arousal greater than 4) and the Russell data into the lower half (arousal less than 4). This systematic discrepancy implies that the error might be accounted for by the different methods used for obtaining or transforming data.43 The selection of a variety of words common to the Russell and Whissell sets, which also come from well separated regions of the circumplex, will serve to support content validity and enable a quantitative testing of construct validity.44
Words were chosen from Russell (1980), Whissell (1989) and Hevner (1936) as listed in Table Chapter 3 -7. The results of Experiment I were used to narrow the selection of words (see Table Chapter 3 -2 on page 114). Very low usage words were not used. The final two stimuli, tears and shivers, were physical emotion words, selected to explore whether the terminology, used by Sloboda (1991), could be mapped onto the present two-dimensional framework. Included among these words were a set of basic emotion words to be used for training. Some of the words selected were found in more than one source. The source of each word may be represented by a Venn diagram (see Figure Chapter 3 -2)
43 For a more detailed investigation of the kinds of errors to which such studies are susceptible, see Roberts and Wedell (1994). 44 Such a test may also be regarded as a test of convergent validity. See Gregory (1992, pp. 129-133). - 122 - Figure Chapter 3 -2 Venn Diagram of Verbal Stimulus Sources
Hevner
Whissell Russell
Basic
Sloboda
- 123 - Table Chapter 3 -7 Twenty-Four Verbal Stimuli Word Source Hypothesised Quadrant
afraid R and W(basic) 2
angry R and W (basic) 2
annoyed R and W 2
bored R and W 3
calm R and W 4
gloomy H, R and W 3
happy H, R and W 1 (basic)
sad H, R and W (basic) 3
excited R 1
frustrated R and H 2
relaxed R (basic) 4
cheerful W and H 1
surprised W 1.5
- 124 - Word Source Hypothesised Quadrant
bright H ? dreamy H ? graceful H ? humorous H ? melancholy H ? mournful H ? passionate H ? solemn H ? vigorous H ? shivers S ? tears S ?
R - from the Russell (1980) circumplex; W - from the Whissell (1989) affect dictionary; H - from the Hevner (1936) adjective circle; S - Physical emotion words used by Sloboda (1991); (basic) denotes member of the ‘basic’ emotion words used for tutorials only.
|X X| | | - Quadrant 1; - Quadrant 2; - Quadrant 3; - Quadrant 4; ? - no | | X| |X hypothesised quadrant.
Selection of Faces To test the instrument as a measure of response to cross-domain (non-verbal) stimuli,
16 pictures of facial expressions were taken from Ekman and Friesen (1975) and scanned into an Apple Macintosh computer using Hyperscan, a bit mapped scanning program operated in a Hypercard environment. Because bitmapping can affect image quality, two students and a member of staff at the School of Music, University of New South Wales were asked to judge the eight best quality images with the added restriction that the images must express a variety of emotions. This selection process was informal, with each judge sitting at the computer, and the images being displayed one at a time and scrolled back and forth as required by the judge. There was agreement on six images, and one of these was dropped because of a repetition of emotion and gender. This omitted expression was of happiness by a male.
- 125 - The final five pictures selected represented a fairly wide selection of emotions, encompassing anger, surprise, happiness and one neutral expression. Each image was of a different person. The facial expressions and codes used are shown in Table
Chapter 3 -7.
Table Chapter 3 -7 Non-Verbal Stimuli.
Facial Sex Source** Code+ Hypothesised Expression* Quadrant anger female Photo No. 29, p. 189 22fb X|
|
happiness female Photo No. 34, p. 191 42f |X
|
happiness male Photo No. 30, p. 189 44m |X
| neutral female Photo No. 54, p. 201 34f Origin
surprise male Photo No. 6, p. 177 32m X
|
|X X| | | - Quadrant 1; - Quadrant 2; - Quadrant 3; - Quadrant 4. | | X| |X * As described in Ekman and Friesen, 1975, pp. 130-134. ** All photograph citations refer to Ekman and Friesen, 1975. + Used for future reference, based on a 5x5 grid system where 11 is top left and 51 is top right of an emotion space.
Material The experiment was designed to be operational on a desktop computer. The software introduced the participant to the experiment, controlled and presented stimuli, recorded responses, provided interactive training and provided help. The program, EmotionSpace Lab, was developed on an Apple Macintosh computer using
Hypercard 2.2 development and authoring software. The program was designed so that it could be run on any of the standard Macintosh screens available at the time of the study (1994).
- 126 - Participants made nearly all responses using the mouse, with occasional responses made on the computer’s “qwerty” keyboard. The execution of the software on standard Macintosh computers enabled the experiment to be run in several locations and on several different machines. However, because the software was under development, and therefore required close monitoring, the experiments took place on either one of two computers. One was an Macintosh SE30 located in the
“Instrument Room” and the other was a Macintosh LC520 located in the “Electronic
Music Studio”, both rooms being part of the School of Music and Music Education facilities at the University of New South Wales. Neither room was soundproofed, however no disturbances were noticed or reported during the experiments (with one exception), and all tests were conducted when the rooms were not being used for other purposes.
Participants Twenty-eight participants (mean age 22.5, SD 6.21) took part in the study. The youngest participant was 12 years old and the oldest was 46. The subjects were all students, 27 undergraduates and one high school student. Twenty-five of the undergraduates were enrolled in Music or Music Education courses. In addition, one student was enrolled in Psychology and another in Science. All undergraduates were enrolled full time at the University of New South Wales.
Design and Procedure Participants were tested one at a time. Upon arrival the participant was greeted and asked to sit by the computer. The computer was initialised and
- 127 - the participant asked to follow the instructions on the screen. If possible, the experimenter would sit outside and be available for help via a telephone connection.
Otherwise, the experimenter would sit in the testing room unobtrusively and away from the participant so as not to create any disturbance.
The first task for the participant was to click the mouse to begin (Appendix B,
Display 2 on page 429). If he or she could not use the mouse the experimenter would provide help. None of the participants indicated that they had problems using the mouse. After the first mouse click a welcome screen was displayed explaining what was about to happen. The participant was then asked some housekeeping questions
(see Appendix B from Display 4 on page 430). Even though the participant’s name was requested, the option to use a pseudonym was provided. Having names associated with data is convenient for the experimenter and confidentiality of data was made clear to the participant.
The experiment was divided into a series of three sequential phases. Output samples of the cards, messages and dialogs45 are shown in Appendix B.
Tutorial Phase After housekeeping, the participant was introduced to the concepts of arousal and valence across two interactive tutorials. Because these dimensions were assumed fairly intuitive, the main focus of the tutorials was to introduce and clarify any unfamiliar terminology.
- 128 - One tutorial, the “valence training”, described and defined, in simple terms, what was meant by valence (Appendix B from page 439). Using a single horizontal axis, a few varied examples were provided (depressed, joy, aroused and no arousal/valence component), after which the participant was asked to indicate the valence expressed by a short series of stimuli. The five basic emotion words (Table Chapter 3 -7 on page 124 or Figure Chapter 3 -2 on page 123) were presented as practice stimuli.
These basic emotion words were chosen because they were likely to be understood and internalised by the participant. Basic emotion words usually include “happy”,
“sad”, “angry”, “afraid”, “surprised” and “relaxed”. However, pilot work showed that “surprised” produced large variations in response making it unsuitable for training. It was therefore used as a test stimulus (see discussion of Outliers on page
149). The participants were given on line help if they appeared to be having problems understanding the valence concept.
Another tutorial, the “arousal training” (Appendix B from page 450), followed the same format as the valence tutorial. This time the arousal terminology was introduced, and the vertical arousal axis was used. The same demonstration examples and practice stimuli were used as in the valence tutorial, but in a different random order. The tutorial order was also randomised so that approximately half the participants received the arousal tutorial first, while the other half received the valence tutorial first.
After each concept was introduced, the third and final tutorial demonstrated, interactively, how valence and arousal could be judged simultaneously on the emotion space. This was the “emotion space tutorial” (Appendix B from
45 The American spelling of dialogue is used- in129 reference - to a human-computer interface. page 457). Once again, the same stimuli were used for demonstration purposes and for practice. Because the emotion space was expected to be an intuitive instrument to use, the five practice responses made across the three stages were recorded for analysis. This meant that, in effect, a repeated measure was made for each of the five stimuli. The first two stages produced separate arousal and valence scores in what could be viewed as a disjointed pre-test, and the response on the newly introduced emotion space was the retest.
Plain Phase After training, the participants were briefed on the requirements of the main part of the experiment. They were informed that a series of words and faces would be displayed, one at a time, and that their task was to judge the emotion expressed by the stimulus and indicate this judgement as quickly and accurately as possible, on the emotion space, for each stimulus (Appendix B, Display 72 on page 465). The procedural steps for the main experiment can be summarised as:
1. Participant moves cursor to centre of 2DES when ready begin (Display 73
on page 466).
2. Participant receives instruction:
“Move the pointer to the position on the emotion space you believe to
reflect the emotion expressed by the stimulus.” (Appendix B, Display 74 on
page 466)
3. If mouse is not clicked within 15 seconds a new message appears in the
message box:
- 130 - “Click the mouse at the point [on the emotion space] that best reflects the
emotion expressed by the stimulus.”
4. Stimulus presented (at random).
5. Mouse click and cursor position recorded.
6. The response to a selection of test words were checked. For these words, if
the mouse click was more than 3/10 of a quadrant either side of the
hypothesised position (Table Chapter 3 -7 on page 124), a warning message
was displayed. This first response was, nevertheless, always accepted.
Checking was used only to encourage the participant to concentrate and not
guess responses. Participants were not told that their first response would
be accepted.
7. Repeat from step 1 until all stimuli shown.
Rest Period After the presentation of the stimuli, participants were asked to rest for three minutes before continuing. A timer on the EmotionSpace Lab program counted down until it was time to continue. After this time an alarm was sounded to draw the participant’s attention to the computer.
Anchor Phase The method of testing reliability for the 2DES was to investigate its stability in the advent of modification. The procedure was identical to the Plain phase but the 2DES was modified. A series of markers or “anchors” were placed, by the participant, around the 2DES before commencing the phase (Appendix C from page 474).
- 131 - The Anchor phase was performed in two sections: preparation and execution. In the preparation stage five dots were displayed on the emotion space. Each dot had an adjacent verbal label corresponding to the basic set (happy, sad, angry, afraid and relaxed) with the initial position of each dot corresponding to the position selected for those words in the 2DES Training Phase (Appendix C, Display 88 on page 475).
These dot/label combinations were referred to as anchors, for they would remain on the emotion space for the rest of the phase. Before continuing, the participant had the option of fine tuning the position of the anchors by dragging the dots on the screen to a preferred location (Appendix C, Display 89 on page 475). The next section of the Anchor phase was to display each of the remaining twenty three stimuli using exactly the same procedure as in the Plain phase, the only exception being that a different random order of stimuli presentation was used.
Subjects were randomly assigned to one of two orders of testing. One group did the
Plain phase followed by the Anchor phase group, as described above. The other group, consisting of approximately half the participants, completed the Anchor phase before the Plain phase.
Final Questionnaire After the 29 stimuli were judged, the participant was again asked to complete a few housekeeping questions before being thanked and allowed to leave (Appendix B from page 467). The time taken to complete the tutorials and the test phase varied depending on the amount of time participants spent exploring the help options and on the type of computer used. On average, the experiment took 8 to 12 minutes for training, 5 minutes for
- 132 - questionnaires and 15 to 20 minutes for each phase of the main experiment. For the
LC520, the average total duration was around 45 minutes. For the slower, SE30 computer, the average total duration was about 55 minutes.46
Results
All analyses were conducted on emotion space training and Plain phase data, with the exception of test-retest analysis which compared the Plain phase/Valence training/Arousal training data with the Anchor phase/2DES training data. The mean, standard deviation and 95% confidence intervals of each stimulus is shown in
Table Chapter 3 -8. These results were examined in terms of instrument resolution, internal consistency, test-retest reliability, content validity and convergent validity.
Intuitiveness Two hypotheses in this experiment were tested by analysing differences in response deviation scores. The ratio of two variances is distributed as an F distribution.
Consequently, F-ratio tests were performed between groups of variance scores as according to the procedure described by Hoel (1962).47 The distribution of the ratio may be expressed in a simplified form as:
46 On slower computers such as the Macintosh SE30, the participant had to wait a few seconds while the computer checked and stored responses. 47 As Hoel indicated, this test assumes that responses are independent and normally distributed. However, in Experiment II participants responded to all words, and therefore the F-test is, strictly speaking, inappropriate. A simple comparison of the sums of square might be a sufficient indication of the equivalence of deviation scores. Ratios close to one would support the null hypothesis of no difference. The F-ratio already gives this number, and so the F-test is unnecessary. I have included it more for the sake of completeness than correctness. It is simple, and some readers may prefer such a test than a more elaborate test or no test at all. - 133 - Table Chapter 3 -8 Results for Emotion Space Training and Plain Phase Responses N = 28 * denotes basic emotion word or “training word”, used for training. CI denotes 95% confidence interval. See Glossary for explanation of Quad. Codes used for face stimuli are shown in Table Chapter 3 -7 on page 126. Stimulus Quad Valence Arousal Lower Mn Upper CI SD Lower Mn Upper CI SD CI CI Range CI CI Range 22fbFace 2 -59.58 -49 -38.42 21.17 28.0 13.15 28 42.85 29.71 39.3 32mFace 2 -34.30 -23 -11.70 22.60 29.9 33.04 44 54.96 21.92 29.0 34fFace 2 -54.64 -41 -27.36 27.29 36.1 0.32 12 23.68 23.36 30.9 42fFace 1 51.29 59 66.71 15.42 20.4 47.91 56 64.09 16.18 21.4 44mFace 1 45.85 55 64.15 18.29 24.2 42.76 51 59.24 16.48 21.8 afraid* 2 -63.68 -50 -36.32 27.36 36.2 22.79 37 51.21 28.42 37.6 angry* 2 -71.36 -57 -42.64 28.73 38.0 49.47 63 76.53 27.06 35.8 happy* 1 63.91 72 80.09 16.18 21.4 49.93 59 68.07 18.14 24.0 relaxed* 4 29.79 42 54.21 24.42 32.3 -44.85 -30 -15.15 29.71 39.3 sad* 3 -71.90 -64 -56.10 15.80 20.9 -42.10 -24 -5.90 36.21 47.9 annoyed 2 -63.18 -56 -48.82 14.36 19.0 25.56 40 54.44 28.88 38.2 bored 3 -40.26 -31 -21.74 18.52 24.5 -59.32 -47 -34.68 24.64 32.6 bright 1 35.04 48 60.96 25.93 34.3 38.66 48 57.34 18.67 24.7 calm 4 19.64 32 44.36 24.72 32.7 -27.32 -17 -6.68 20.64 27.3 cheerful 1 54.31 61 67.69 13.38 17.7 36.59 44 51.41 14.82 19.6 dreamy 4 19.38 32 44.62 25.25 33.4 -55.12 -38 -20.88 34.24 45.3 excited 1 46.68 57 67.32 20.64 27.3 66.33 74 81.67 15.35 20.3 frustrated 2 -63.62 -55 -46.38 17.24 22.8 25.39 43 60.61 35.23 46.6 gloomy 3 -63.15 -54 -44.85 18.29 24.2 -48.59 -34 -19.41 29.18 38.6 graceful 4.5 37.53 48 58.47 20.94 27.7 -8.70 4 16.70 25.40 33.6 humorous 1 55.61 64 72.39 16.78 22.2 43.46 52 60.54 17.08 22.6 melancholy 3 -52.51 -38 -23.49 29.03 38.4 -46.51 -32 -17.49 29.03 38.4 mournful 3 -70.26 -61 -51.74 18.52 24.5 -34.01 -19 -3.99 30.01 39.7 passionate 1 43.43 55 66.57 23.13 30.6 63.31 72 80.69 17.39 23.0 shivers 2 -52.71 -43 -33.29 19.43 25.7 33.28 45 56.72 23.43 31.0 solemn 3 -24.64 -13 -1.36 23.28 30.8 -24.15 -13 -1.85 22.30 29.5 surprised 1 29.81 41 52.19 22.38 29.6 43.19 54 64.81 21.62 28.6 tears 2.5 -52.28 -42 -31.72 20.56 27.2 -16.77 3 22.77 39.54 52.3 vigorous 1 1.47 15 28.53 27.06 35.8 64.29 72 79.71 15.42 20.4 M 21.27 28.13 M 24.48 32.39 Min 17.70 Min 19.60 Max 38.40 Max 52.30
- 134 - G1 S 2 ∑ 1g1 g1 =1 G Equation Chapter 3 -2 1 Fα;G1 (N −1), G2 (N −1) ~ G2 S 2 ∑ 2g2 g2 =1 G2
Where Sxy is the standard deviation score of word y in group x and group x has Gx words. The instrument is intuitive to use if the variance scores of the basic group
(five words = G1) are not greater than the variance scores of the twenty four test words (group 2, G1 = 19). Since N = 28 (the number of responses), the degrees of freedom for the F distribution are:
5 x (28 - 1), 19 x (28 - 1) → 135, 513
and at α = 0.05 significance this gives a critical value of
F0.05; 135, 513 = 1.242
By substituting the deviation scores from Table Chapter 3 -8, the F statistic for valence becomes:
F = (19 x 4692.5)/(5 x 15264.72)
= 1.168 which is significant at p = 0.1195 and for arousal:
F = (19 x 7110.3)/(5 x 21407.27)
- 135 - = 1.262 which is significant at p = 0.0389
The valence result does not reject the null hypothesis of a difference between deviation scores for training words and test words at p = 0.05, but the arousal deviation is significantly different. The latter result provides evidence that the arousal dimension of the 2DES is not intuitive to use. This finding may be attributed to the deviation score for the training word sad, which is obtrusively large (47.9%).
However the large deviation is due to outlier responses which were found to be a result of the stimulus rather than the instrument (see Outliers on page 149) and so the intuitiveness hypothesis for the arousal dimension cannot be rejected on the basis of this analysis alone. Instead, the training stimuli should be updated to contain words with more agreed upon valence and arousal responses. For example, sad could be replaced with another Quadrant 3 word such as bored or gloomy.
Range of Mean Responses An interesting observation about the test words is that they tended to map away from the sleepy (lower) region of the emotion space. Inspection of Table Chapter 3 -8 on page 134 and Figure Chapter 3 -4 on page 142 indicate this as a general trend. The lowest mean arousal score was only -34.68% (for bored). This is in contrast with the highest arousal score of 81.67% (for excited). The problem may be of semantic density — perhaps words were not selected with a strong enough sleepy component.
However, I would posit that there may be a problem with the 2DES. It is not necessarily a psychological fact that the arousal dimension is bipolar. Perhaps it is unipolar, and that the
- 136 - lowest arousal point should be at the origin (see further, Green & Cliff, 1975). That is, the valence axis should be at the bottom of the emotion space. Using this line of reasoning, the negative arousal words that did appear could be explained by demand characteristics. Some participants may have felt that they ought to use the lower part of the emotion space even though they didn’t need to. Another possibility, which also assumes that the problem is not one of semantic density, is that the arousal dimension is scaled. Some weighting factor is required as a function of arousal in order to spread the compressed sleepy dimension words further down the emotion space. This is a problem of calibration.
To summarise, the non-uniform distribution of the range of means can be explained in three ways: (a) semantic density, (b) demand characteristics upon a unipolar construct, and (c) scaling. If explanation (b) were correct the 2DES would require direct modification of its layout. I have chosen to leave this as an area for future research, for varying the layout of the emotion space would mean losing the central point of no emotion. This point was considered necessary in order to provide the participant with a neutral starting point and a point of non-response during continuous measure (refer to Table Chapter 3 -1 on page 107), as will become apparent in the report on Experiment III on page 245 in Chapter 5.
Internal Consistency and Resolution Data were analysed in two ways in order to examine the reliability hypothesis. First, standard errors and confidence intervals were used to
- 137 - examine the instrument’s resolution. Then the relationship among words was examined via cluster analysis.
The confidence interval for each stimulus is shown in Table Chapter 3 -8 on page 134.
The range covered by the confidence interval provides an estimate of the resolution of the instrument. Narrow intervals indicate high resolution because the instrument is able to distinguish emotions closer together. For example, cheerful has a narrow confidence interval range of (13.4, 19.6)%48, while melancholy has a large confidence interval range of (29.0, 38.4)%. Although confidence intervals varied from word to word, a useful index of the resolution of the instrument is to determine the average of the 95% confidence intervals. This was found to be (21.27±4.5, 24.48±6.95)%. This interval bounds the stimulus in a square so that any response within the square is statistically equivalent. Halving the distances indicates how far out of the square a stimulus must be before it can be detected as expressing a distinct emotion. That is, the valence must differ by (21.27/2=) 10.6% and the arousal by (24.48/2=) 12.2%.
The worst acceptable resolution was considered to be one quadrant, which was 50%.
With just 28 participants, the 2DES provides a much higher resolution.
Larger variations for some stimuli, such as tears, could be due to some factor not related to the 2DES instrument, such as the context in which the word was presented.
This is discussed in the analysis of Outliers on page 149 below.
- 138 - Another way of describing the resolution of the 2DES is through hierarchical agglomerative cluster analysis. This is a kind of cluster analysis where stimuli are combined in progressive stages according to their proximity. At the first stage of analysis each stimulus forms a separate independent cluster. At the next stage of analysis the stimuli closest to each other, here in terms of arousal and valence, are merged to form a new, broader cluster. The procedure continues until all stimuli merge into one cluster. The distance between clusters of stimuli is an indication of how different groups of stimuli are. A hierarchical cluster analysis using average linking (between groups) was performed using the valence and arousal data and squared euclidean distances to determine proximities. The dendrogram of this analysis is shown in Figure Chapter 3 -3.
The stimuli cluster into four quadrants at some stage of the analysis (at a relative distance of around fifteen out of twenty-five units). Of interest here is the relative distances between old clusters (those to the left on the dendrogram) and new clusters
(those to the immediate right). A long distance from one cluster to another indicates that the former is a successful grouping of its associated stimuli. There are two clusters well separated in meaning. These clusters are clearly interpretable as negative valence and positive valence stimuli, corresponding to the right and left halves of the 2DES.
At the next level down (to the left in Figure Chapter 3 -3), each of the two major clusters divide again into two interpretable groups: high arousal and low arousal, giving rise to the four quadrants. For example, the stimuli “calm”,
48 The notation (x, y)% indicates x valence and y arousal on a -100 to +100 scale. - 139 - “graceful”, “dreamy” and “relaxed” cluster into what can be interpreted as a positive valence, low arousal cluster (Quadrant 4 on the 2DES). By ignoring the stimulus vigorous, the distance between the quadrant clusters and the valence cluster is around eight units (15 - 7).
The omission of “vigorous” calls for a note of caution. The success in clustering demonstrated in this analysis was a function of the number of stimuli and their spread of meaning (or semantic density — as discussed in Roberts & Wedell, 1994).
The stimuli chosen fitted neatly into one of four quadrants, however, selection of stimuli that fell between quadrants would obscure the cluster analysis, as would different methods of calculating proximities between stimuli (see Norusis, 1990;
Kaufman & Rousseeuw, 1990). Under such a circumstance a possible solution would be to perform two separate cluster analyses, one for valence and another for arousal data. But this problem need not concern us here. The main purpose of the cluster analysis is to verify that the 2DES groups stimuli together in a meaningful way.
- 140 - Figure Chapter 3 -3 Dendrogram of Cluster Analysis of 24 Verbal Stimuli using Arousal and Valence Scores
- 141 - Figure Chapter 3 -4 Emotion Spaces Showing Mean and One Unit Standard Deviation Either Side for Each of a Selection of Stimuli
- 142 - Test-Retest Reliability Test-retest reliability was determined by correlating the combined Plain and
Emotion-Space phase scores with the combined Arousal, Valence and Anchor phase scores. A correlation of 0.83 (p < 0.01) for arousal and 0.90 (p < 0.01) for valence was evaluated (Table Chapter 3 -9). The results support the hypothesis that the instrument exhibits temporal stability under varied conditions, and is therefore robust or resilient to some changes in appearance.
Table Chapter 3 -9 Test-Retest Correlation Coefficients Arousal 1 Arousal 2 Valence 1 Valence 2 Arousal 1 1.0000 0.8290** 0.2800** 0.2900** Arousal 2 0.8290** 1.0000 0.2431** 0.2583** Valence 1 0.2800** 0.2431** 1.0000 0.8965** Valence 2 0.2900** 0.2583** 0.8965** 1.0000
* p < .05 ** p. < .01 Two tailed N = 672
Validity Construct and criterion validity can be supported by demonstrating a relationship between the present data set and similar data gathered elsewhere. Comparing Table
Chapter 3 -7 on page 124 with Table Chapter 3 -8 on page 134 shows perfect agreement at the quadrant level between all 13 words having a hypothesised quadrant. Only “surprised” showed a slight disagreement (Quadrant 1.5 hypothesised, Quadrant 1 obtained). As a more refined comparison, the 11 words in common with the Russell set and the 10 words common with the Whissell set were each compared to the experimental data via a Pearson product-moment correlation analysis. The relevant portion of
- 143 - the correlation matrix is shown in Table Chapter 3 -10. Experimental data were highly correlated with those of both Whissell and Russell data (r > 0.8411, p < 0.01).
On a word by word basis, all but one word (happy) from the Russell and Whissell data points were within one standard deviation of the experimentally determined positions (see Figure Chapter 3 -5). This provides strong support for the criterion and construct validity of the instrument.
Table Chapter 3 -10 Correlation Coefficients of Experimentally Determined Valence and Arousal with Russell and Whissell Data.
mean arousal mean valence mean arousal 1.0000 .2663 mean valence .2663 1.0000 Russell arousal .9099** -.1911 Russell valence .2521 .9503** Whissell arousal .8411** .4489 Whissell valence .2625 .9501** ** p < 0.01 Two tailed. N = 11 for Russell data and N = 10 for Whissell data.
- 144 - Figure Chapter 3 -5 Russell, Whissell and Experimental Data on the Emotion Space Dotted rectangles indicate one standard deviation either side of the experimental mean of the stimulus. Angry is not shown here due to space constraints (see Figure Chapter 3 -4 on page 142).
Cross-Domain Generalisability The same analysis of variance technique described under Intuitiveness on page 133 was used to test whether deviation scores for face responses were different to words.
By substituting the deviation scores from Table Chapter 3 -8, the F statistic for valence becomes:49
F = (19 x 3983.02)/(5 x 15264.72)
- 145 - = 0.9915 which is significant at p = 0.5142 and for arousal:
F = (19 x 4273.5)/(5 x 21407.27)
= 0.7586 which is significant at p = 0.9736
Therefore, the null hypothesis that variation in response to faces are the same as those of words is not rejected and the ability of the 2DES to measure non-linguistic stimuli is defended. Further, the mean coordinates of each face, shown in Figure
Chapter 3 -6, fell within the hypothesised verbal label quadrant. Variations can be accounted for by the inability of a single word to express precisely the emotion of a particular facial expression. Based on this argument the 2DES might be a more concise measure of emotion expressed than a single emotion word.
49 See footnote 47 on page 133. - 146 - Figure Chapter 3 -6 Mean 2DES Coordinates for Facial Stimuli See Table Chapter 3 -7 on page 126 for a description of the facial stimuli.
Mapping New Words onto the Emotion Space Eleven stimuli were chosen for exploratory mapping onto the emotion space. For convenience, all of the Hevner words (which include nine new, unhypothesised test words) are mapped on Figure Chapter 3 -7, and the two Sloboda words are mapped on Figure Chapter 3 -8. Each stimulus mapped onto locations on the emotion space in a predictable manner. Some words mapped near the origin of the 2DES but still demonstrated a fine shade of emotional meaning (with 95% confidence as listed in
Table Chapter 3 -8 on page 134) in terms of valence and arousal. For example, solemn mapped to a point near the origin (-13, -13), but the mapping suggests a fine shade of meaning toward the sleepiness, negative valence side of the 2DES
(Quadrant 3, Figure Chapter 3 -7). For some words, above average standard deviations reflected poor mapping onto the emotion
- 147 - space. The worst mapping word was the arousal component of tears (Figure Chapter
3 -8) which had a standard deviation of 52%. Interestingly, the valence dimension for tears mapped well onto negative valence with a much smaller deviation score of
27.3%.
Figure Chapter 3 -7 Hevner Words Mapped onto the 2DES
- 148 - Figure Chapter 3 -8 Physical Emotion Words used by Sloboda, Mapped onto the 2DES
Outliers The large variation in standard deviations between stimuli and the presence of some fairly large standard deviations (see Table Chapter 3 -8 on page 134) raises the question: What are the sources of these variations? An examination of some outliers, retest scores and interview information was made. I assert that outliers were caused by two kinds of errors:
1. Within individual (“random”) error — the spread of meaning of the
stimulus.
2. Between individuals (“systematic”) error — different understanding of the
word.
Within individual error accounts for changing meanings of a stimulus due to the mood of the subject and the context in which the stimulus is presented.
- 149 - The second kind of error, among individuals, suggests that people may code or represent meaning in slightly different ways.
The analysis of systematic outliers began with an examination of responses to the stimulus “sad”. This stimulus was chosen for further analysis because a few participants mentioned that they believed it to express high arousal, contrary to the mean response (Table Chapter 3 -8) and contrary to the hypothesised response (Table
Chapter 3 -4 on page 120). The scatterplot of raw data for both Arousal/Valence and
Emotion-Space training phase in response to sad is shown in Figure Chapter 3 -9d.
Outlier responses made to the same word by the same participant in both phases are circled in the figure. Five out of twenty-eight participants made consistent outlier judgements for the word sad. Based on the corroboration of interview data with the scatterplots, participants who made consistent outlier responses for a particular stimulus made this response intentionally, and not by chance or through misunderstanding.
Further evidence of a definite intention was reflected by the fact that it was not a handful of participants who made outlier judgements for most of the stimuli, but, instead, various participants were responsible for only one or two outlier pairs. For example, participants 5, 6, 8, 26 and 34 responded with outlier pairs for the stimulus sad; participants 22, 26, 6 and 23 for dreamy; and participants 20 and 10 for frustrated. Systematic outlier responses involved nine participants (one third of the sample) for these three stimuli alone. This provided evidence that people have slightly varied mental representations of the semantic content of certain words. Put differently, this consistent contributor to variance might be attributed to misunderstanding - 150 - or misinterpreting the meaning of a stimulus relative to a cultural norm. Such an interpretation of these responses poses interesting philosophical and psychological questions about the nature and representation of meaning. In this respect the 2DES shows potential as an insightful tool in linguistics research.
The more random elements in response were explained in one of two ways: (1) the participant guessed an answer, or (2) the context in which they interpreted the stimulus changed. Variance due to guessing is an unavoidable consequence of the experimental design because in order to demonstrate that the instrument was intuitive to use, first responses were always accepted. Because stimuli were presented without overt context or priming, the variation in meaning of words could account for a degree of variation in responses. For example, words having meanings which were obviously sensitive to context, such as surprise, tended to have a greater variation in responses. I hypothesise that if a word such as surprise was presented in a context (“Mrs. Hokopesic loved the surprise of opening presents” or, in contrast,
“Romboflot was surprised by the early arrival of the debt collector”) then the responses would be less varied.
- 151 - Figure Chapter 3 -9 Scatterplot of Responses to the Selected Stimuli Responses to test (Plain phase) and retest (Anchor phase) are shown. Numbers denote participant code. The participant code numbering system is arbitrary. Each number appears twice per plot. For the basic emotion words such as sad, the test phase scores consisted of combined Arousal Training and Valence Training score and the retest score was calculated from the response made during the 2DES Training phase. Test stimulus responses consisted of Plain phase score for test and Anchor phase score for retest. Participants who made similar outlier responses in both test and retest are circled. X-axis denotes valence and y-axis denotes arousal. a) cheerful b) dreamy
c) frustrated d) sad
Summary An instrument which could directly and parsimoniously measure emotional response was designed and tested. The instrument was referred to as the 2DES and was fully computer controlled by the EmotionSpace Lab software. It consists of two axes representing the pertinent dimensions of emotion, valence and arousal, joined to form a square space. Verbal feedback and numerical feedback was provided to enable responses to be measured with high resolution. The verbal feedback scale was based on seven point bipolar
- 152 - distinctions and the numerical scale was a 201 point percentage scale ranging from -
100% to +100% for each axis.
Checklist words used to describe music were considered a useful resource for the selection of stimuli to test the instrument. However, two often-cited word lists appeared to contain outdated words, and a word usage survey, Experiment I, was conducted to help in revising the lists. The Farnsworth list was modified by the removal of twenty low usage words, the addition of seven words from the Hevner adjective circle and the addition of one new word. The revised music checklist consisted of 37 words. The data from the experiment was used for Experiment II and would be required in a later experiments (Experiment III, reported in Chapter 5).
Experiment II provided a detailed empirical examination the 2DES. Twenty-eight participants used the 2DES to judge the emotion expressed by 29 stimuli consisting of 24 words and five pictures of faces. After training, the main experiment was run twice, once using a plain emotion space and another time using an emotion space containing a series of “anchors” which identified participant chosen locations of five
“basic emotions”. The results demonstrated that the 2DES was an instrument which had a good semantic resolution (valence and arousal components approximately 12% points apart, or more, could be distinguished), was intuitive to use (training stimuli responses had the same deviation scores as test stimuli at p = 0.05) and showed high, significant reliability (test-retest r > 0.83, p < 0.01) and validity (external data r > 0.84, p = 0.01) as a measure of two pertinent dimensions of emotion. Various sources of error were identified which could be controlled.
- 153 - For example, outlier pairs (that is, similar outliers produced by the same person in both phases) were analysed separately and other outliers could be discarded on the grounds that they may have been guessed. The instrument is also capable of distinguishing emotion expressed by non-linguistic stimuli (pictures of faces) suggesting that it is suitable for the measurement of emotion expressed by music.
In order to investigate the application of the 2DES to measure response to music, some modifications were made to the instrument, as discussed in Chapter 5. Prior to this, a literature review was conducted for the purpose of assembling knowledge concerning the relationships between musical features and emotional responses and thence for generating hypotheses for their relationships. This review forms the focus of the next chapter.
- 154 -
Chapter 4 Musical Features and Emotional Response
The thrust of the previous two chapters was to examine the question of how to measure emotions. The main aim of this chapter is to generate hypotheses about how musical features relate to emotional response. To accomplish this aim, the chapter is divided into two sections. The first section comprises a literature review and the second section consists of transformations of the appropriate and relevant findings onto a series of two-dimensional (valence and arousal) emotion spaces, one for each musical feature.
Literature Review The literature review had two aims:
1. To examine how musical features have been operationalised as
independent variables; and
2. To determine the emotions, if any, that can be associated with each musical
feature in terms of valence and arousal.50
Given the complex, multidimensional nature of music and emotion, it would be naive to assume that an isolated musical feature could be sufficient to
50 Much of the literature requires some interpretation in order to transform codings of emotions into positions on the two dimensional emotion space. Readers interested in a more unadulterated review
- 155 - express emotion. In fact, many researchers acknowledge that it is often an ensemble of interacting musical features that induce emotional expression (e.g., as noted by
Hevner, 1935, 1937; Levi 1978; Nielzén & Cesarec, 1982b; Nielsen, 1987). And this too is only part of the story. The preparatory set and the mood of the listener can also affect emotional response, although these human factors are not considered here (see
Limitation 6: Musicological Investigation on page 30 in Chapter 1). Therefore, throughout the ensuing review, it should be kept in mind that composers and performers use a collection of musical features to achieve a particular emotional expression. Treating musical features in isolation is merely a simplification of a complex question. Consequently, much of the empirical domain of research lends itself to the generation of hypotheses for the relationship between musical features and emotions.
There were several ways in which this review could be structured. The two obvious choices were to group literature according to: (1) the kinds of emotions reported or investigated — for example, the musical features associated with happiness, sadness and so on; or (2) the musical features — for example, the emotional correlates of pitch, loudness, tempo, timbre and so on (see Bruner, 1990; Behrens & Green, 1993, p. 21; Collins, 1989; McMullen, 1996; Radocy & Boyle, 1988, for other alternatives).
However, both these options pose a problem because many relevant studies investigate several emotional categories or dimensions as well as several musical features. Reporting these studies in either format would lead to undue
are referred to Valentine, 1962; Bruner, 1990; Miller 1992; Radocy and Boyle, 1988; Rigg , 1964; Sloboda, 1996. - 156 - repetition. Instead, this review is organised around the kinds of stimuli used. For example, some studies used isolated tones or chord progressions, others used original compositions, and others used existing compositions.
Organising this review around the kinds of stimuli used enables the observation of similarities or differences in responses across various categories of stimuli, as well as providing an overview of the kinds of stimuli used by empirical researchers.
Although the prime interest in this research is on responses to music, literature in other areas of the audio arena are discussed briefly. The order of subheadings chosen loosely represents a progression from stimuli well removed from music, to those which examine highly complex musical forms, or to use Hargreaves’s (1986) terminology, the progression is from “experimental” to “naturalistic” (pp. 108-110; see also Valentine, 1962, p. 19, p. 196), as described in items one to seven of Table
Chapter 4 -1. Following this, the contributions of some introspective inquirers, such as philosophers, musicologists and writers on theatre and film, are also mentioned.
Perhaps it is appropriate that these “introspectionists” follow the naturalistic stimuli, as these people discuss their own experiences of real music; they can examine their own responses in great detail without having to worry about stimulus construction and experimental control and, ideally, they will do so with great insight.
- 157 - Table Chapter 4 -1 Categories of Stimuli Used in Investigations of Emotional Response to Music
Stimuli Examples 1. Isolated, Non- Synth esi sed sounds; higher lower experimental Musi ca l Sounds speech 2. Isolated, Musical Ch ord progressi ons; Sounds tone pairs 3. Specially Composed Improvisations, Mel odi es monoph oni c compositions based on theoretical premise 4. Pre-existing Melodies Well known tunes control validity stimulus 5. Specially Composed Harmonised Pieces compositions based on theoretical premise: Ri gg, Ni el zén a nd Cesarec 6. Pre-existing Pieces The Hevner studies with Modification 7. Pre-existing Pieces Western art music lower higher naturalistic 8. Introspective Inquiry Philosophical theories
Isolated, Non-Musical Sounds
This section examines the stimuli and results of studies where emotional responses to non-musical sounds have been reported. The majority of these studies come from the field of voice research. However, there are a handful of studies where non- voiced sounds are studied, such as the study by Sören Nielzén and Olle Olsson
(1993).
Nielzén and Olsson Nielzén and Olsson investigated emotional responses to seven complex tones, each at two different durations. The complex tones were generated by FM synthesis and their durations were either 0.5 or 3s. Subjects judged each of the 14 complex sounds on twelve bipolar rating scales that would fit into the three affective dimensions of
Tension-Relaxation, Lightheartedness-
- 158 - Gloom and Attraction-Repulsion. Although timbral qualities made a difference to the emotional ratings on all three dimensions, duration had a significant effect only on the Lightheartedness-Gloom factor (valence), where there was a significant difference for two of the seven sounds. The two sounds in question had, perhaps, the most “musical” and harmonic characteristics, one being the synthesis of a trumpet sound and the other of a female voice. In both cases the shorter sounds were judged as being significantly more lighthearted than their longer counterparts.
Nielzén and Olsson demonstrated that duration has little impact on emotional response under the conditions of the study. However, the increased valence for the two shorter sounds was explained in terms of the findings in the music psychology literature that shorter, staccato articulation contributed to the expression of joy in music (see Articulation/Duration on page 243).
It has been argued that the non-linguistic sounds of speech can be used to encode information and that this encoding is similar to music (Fonagy, 1981 and Sundberg,
1983, both cited in Nilsonne & Sundberg, 1985). This is also consistent with the views of scholars such as Peter Kivy, Herbert Spencer, Mary Louise Serafine and
Charles Darwin who have posited that voice has the ability to communicate emotion in speech and in song.51 Given the consistency of findings in research on emotion in voice and speech (Scherer, 1981, p. 205), I though it constructive to consult some of the non-musical,
51 For precis or source readings of the views of such scholars see Heneghan, 1990; Katz & Dahlhaus, 1987-1992; Lippman, 1986-1990. For studies in which the singing voice is compared with the spoken voice see Baroni & Finarelli, 1994; Scherer, 1991, p. 148; Sundberg (1982). - 159 - voice literature in order to broaden the scope of information available for generating hypotheses on musical features and emotional response.
Scherer Although there are several options for collecting emotional vocal stimuli, the most common forms in empirical studies have used the voices of actors simulating emotional behaviours (Scherer, 1981). Scherer summarised the findings of empirical research on emotion in voice (shown in Table Chapter 4 -2). These findings were transformed onto a two-dimensional emotion space as shown in Figure Chapter 4 -1, with the proposed results of the transformations indicated by quadrant (Quad) in
Table Chapter 4 -2.52
Table Chapter 4 -2 Vocal Indicators of Emotional States Adapted from Scherer (1981, p. 206). ? denotes “not known”. See Glossary for explanation of Quad.
Emotion Quad Pitch level Pitch range Pitch variability Loudness Tempo Happiness/joy 1 High ? Large Loud Fast Confidence ? High ? ? Loud Fast Anger 2 High Wide Large Loud Fast Fear 2 High Wide Large ? Fast Indifference 0 Low Narrow Small ? Fast Contempt ? Low Wide ? Loud Slow Boredom 3 Low Narrow ? Soft Slow Grief/sadness 3 Low Narrow Small Soft Slow Evaluation ? ? ? ? Loud ? Activation ? High Wide ? Loud Fast Potency ? ? ? ? Loud ?
52 All relevant findings in this review are transformed onto the emotion space on a feature by feature basis in the second section of this chapter. - 160 - Figure Chapter 4 -1 Emotion Space Representation of Vocal Features
high pitch loud large pitch variability fast wide pitch range
narrow pitch range small pitch variability slow low pitch soft
Isolated, Musical Sounds
Heinlein Christian Heinlein (1928) investigated the emotional effects of modality and intensity. He asked participants to make responses to chord pairs mechanically recorded on a Duo-Art piano roll. To cover all possible keys in both modalities (12 x
2) and reversing major/minor combinations (x 2), Heinlein used 48 chords per test.
Intensity was varied across four levels: (1) major and minor chords played piano, (2) major and minor chords played forte, (3) major played piano and minor played forte, and (4) major played forte and minor played piano. Each chord was sustained for five seconds with a fifteen second gap between chords. Successive chord pairs were separated by a tritone to “reduce harmonic and melodic associations” (p. 122).
Participants were asked to judge how each chord made them feel. Although
Heinlein’s interpretation of the data indicates that the “assumptions long entertained by theorists in regard to the supposed intrinsic characters of the modes must be dismissed” (p. 140), Crowder’s (1984) reanalysis of the data indicated that there is a relation between modality and valence. Heinlein
- 161 - also found that the soft chords were rated with words more soothing than the loud chords. Hence loudness appears related to the arousal dimension.
Gabriel Clive Gabriel (1978) produced 16 sine tone sequences in order to test the emotional meanings of Deryck Cooke’s (1959, discussed on page 211) basic musical terms. For example, one of the terms described was the first five notes of an ascending major scale which, according to Cooke, suggested an outgoing expression of joy. Gabriel reproduced this melodic configuration with the pitches C, D, E, F and G, with each note of 0.6 seconds duration and a 0.06 second gap between successive notes. The example was preceded, as were all examples, with a chord that was in the modality of the example, in this case a C major chord. Each example was repeated three times.
Two descriptions of the tune were provided to the participant — one being the version suggested by Cooke and the other being a randomly selected version from the subset of descriptions for the same modality (in this case another description from the major key progressions). The participant’s task was to determine the degree to which each description matched the tune. Gabriel found that the descriptions proposed by Cooke for the musical terms are no better than those randomly assigned from the corresponding modality set. Two important findings arise from the Gabriel study: Although not conclusive, the study provides evidence that melodic contour is not important in determining emotion expressed.53 In addition, Gabriel
53 Gabriel cites several researchers who do not support the existence of a relationship between emotional response and melodic contour, including Gundlach (1935), Hevner (1936), Rigg (1937) and Valentine (1931), however, some authors, for example Dolgin and Adelson (1990), Gerardi and Gerken (1995), and Scherer and Oshinsky (1977) argue that there is a relationship. - 162 - proposed that, while modality (major or minor) affects the evaluation (valence) dimension of emotion, melodic contour may effect the activity (arousal) component of emotion. Brown (1979) was critical of Gabriel’s study because: “Gabriel's experiments isolated the melodic units from any tonal or rhythmic context, whereas the inclusion of a potent tonal and rhythmic context in Gabriel's experimental melodic stimuli might have produced results more in agreement with Cooke”
(p. 29). Brown’s criticism is supported by Collins (1989), who found empirical support for the relationships predicted by Cooke’s theory when using “real” music as the stimulus.
Other researchers who used isolated, highly controlled sound combinations included
Crozier (1974), Bragg and Crozier (1974) and Vitz (1966), though such studies were more concerned with preference response rather than cognitivist emotion. Also, as
Francés (1958/1988) notes:
Experiments that involve the simplest stimuli — isolated tones — provide
useful and solid data owing to their restriction of the number of variables, and
so they can be relied on. But they are of only indirect relevance to music. (p.
276)
This remark makes it easy to see why “real” (naturalistic) musical stimuli should be used for the investigation of the research question. However, I considered it important not to disregard these studies. Rather, a variety of approaches were considered in order to provide, hopefully, some convergent evidence. The literature that used more musical contexts through which to study emotional response comprises the remainder of this review.
- 163 - Specially Composed Melodies Specially composing a melody for the purpose of empirical investigation affords the researcher a greater degree of experimental control than using a previously composed piece. Musical structure can be controlled and manipulated and, according to some researchers (e.g., Banks, 1981; Behrens & Green, 1993), the familiarity factor can be eliminated. However, some researchers use pre-existing melodies in addition to the specially composed melodies (e.g., Gabrielsson & Juslin,
1996; Scherer & Oshinsky, 1977). Under such circumstances the study is reported under the heading (“specially composed” or “pre-existing”) that is considered of greatest relevance to the current research questions.
Levi Some researchers have been interested in the Gestalt that is related to the physiognomic properties of a melody (Cort, 1960; Dor-Shav, 1976; Levi, 1979; Pike,
1972; Rosar, 1994). Their approach usually involved the creation of melodic patterns that relate to some intended expression (Levi, 1979) or visual analogy (Dor-Shav,
1976). Such approaches may provide insights to the musical features which index the relevant physiognomic properties.
David Levi (1979) used verbal descriptions of six emotions, namely agitation, calm, gaiety, joy, sorrow and triumph, in order to compose a series of melodies, each expressing one of the emotional descriptions. For example, Levi searched the literature for descriptions of triumph and then transformed these descriptions into the following musical properties:
Triumph
- 164 - …
Musical Specifications. The critical feature of this melody should be the
contrast between groups of higher and lower frequencies. Other tonal
properties should be used to make the higher notes stand out and dominate the
melody. Thus the higher notes should be louder, longer in duration, and
rhythmically simpler than the lower notes. By contrast, the lower notes should
be softer, staccato, and relatively complex. Overall the melody should be
relatively fast. (p. 80)54
In the main study, Levi used a twelve adjective checklist and found that people could successfully decode the emotion encoded by the compositions which were based on the descriptions like the one quoted above. Levi grounded this methodology on the premise that “melodic figures which are structurally similar to an emotion would be described in terms indicative of that emotion” (p. ii). The methodology was posed in contrast to the more conventional means of analysing components of music in isolation. The analysis of separate musical features of a melody, in Levi’s opinion, was misguided:
Existing studies of musical expressiveness confirm that the use of emotional
vocabulary to describe music is a reliable phenomenon. The determinants of
this expressiveness has been studied mainly by considering various musical
features independently. This approach fails to consider structures of melodic
figures and to provide a systematic framework for predicting musical
expressiveness. (p. 118)
54 Levi uses the term “frequency” to mean musical pitch. - 165 - Although Levi’s criticism is warranted, many researchers are well aware of this problem, and examine musical features independently merely in an attempt to reduce a complex problem into a series of simpler problems. Levi’s Gestalt approach is different and interesting because he attempts to produce emotionally expressive melodies based on preconceived, verbal analogies which are transformed into formulae for composing, which are intended to evoke the musical expression of the original emotion.
However, a number of questions arise from Levi’s approach. The first is concerned with reciprocity. Would the structure of music that is judged, say, as expressing triumph, produce descriptions of its musical structure that conforms to the structure of triumph (i.e., do descriptions of all “triumphant” pieces of music resemble the description of triumph quoted above)? The next question is one of specification.
Levi composed his melodies from descriptions he researched. If the descriptions were handed to a group of composers, without the provision of the intended emotion label, would the composers still be able to encode the hidden emotion, based purely on the description of the musical structure? Until these questions can be examined, it may be advisable to accept Levi’s methodology with some caution.
Sherman Mandel Sherman (1928) used monotones and two versions of a specially composed melody to investigate the effects of pitch, mode and length of melody on emotional expression. In the first part of the study a professional singer, hidden from view, sang the pitch E in groups of five notes. For each group she attempted to convey one of four different emotions, but keeping
- 166 - pitch, dynamics and note durations as constant as possible. The task was then repeated on the note A. Sherman reported no important difference in responses between the two pitches. In the next part of the study the same singer sang a melody in several ways. A tune of thirteen notes was composed and sung in two modes, A major and A minor. The number of notes in the tune could be long (13 notes) or short (the first 5 notes). After tabulating frequencies of written responses by thirty graduate psychology students, Sherman found that the use of the term sorrow was reported most often and that the longer melody produced a greater number of emotional responses. Further examination of his frequency table indicates that by summing the positive valence responses (confidence, joy, reverence and relaxation) and the negative valence responses (sorrow, fear, disagreement, anger and regret), the tally becomes,
• For melody in A major: 12 positive valence terms, and 13 negative valence
terms.
• For the melody in A minor: 3 positive valence terms and 18 negative valence
terms.
Of importance is the difference of the two score pairs and their directions. The difference of the valence score for the major key melody is (12 - 13 =) -1, whilst the difference score for the minor key version is (3 - 18 =) -15. This re-analysis raises two points: (1) The minor melody is systematically rated as more negative in valence than the major version, and (2) The high negative valence score for the major version of the melody could be due to some other factor, such as the mellowness of the singer’s voice.
- 167 - Scherer and Oshinsky Klaus Scherer and James Oshinsky (1977) used responses to a series of eight tone sequences to investigate the relationship between acoustic-musical properties and emotions. A Moog synthesiser was used to produce and aid in the manipulation of stimuli. Seven such properties were manipulated, each at two levels, as shown in
Table Chapter 4 -3, leading to the production of 128 saw-tooth tone stimuli. A further 36 tone sequences were produced by manipulating four of the original stimuli according to two three-level factors. These factors were filtration level (low, intermediate and high) and tonality (major, minor and atonal). From these melodies a third group of stimulus sets were selected and used for testing. The findings, reproduced in Table Chapter 4 -4, include the effect of interacting acoustic features, demonstrating how two or more features occurring together can strengthen response. The table also shows the emotion space quadrant mapping appropriate to the corresponding adjective. The mapping highlights the absence of Quadrant 4 emotions. Emotions engendered in words such as calm, relaxed and dreamy are absent.55
55 The issue of semantic density was discussed under Evaluation of Checklist Measures on page 64 in Chapter 2. - 168 - Table Chapter 4 -3 Seven Two-Level Factors Manipulated by Scherer and Oshinsky (1977)
Factor Values amplitude variation small, large pitch (or fundamental high, low frequency) level pitch contour up, down pitch variation small, large tempo slow, fast envelope low attack/decay ratio, equal attack/decay ratio filtration cut off level intermediate (three harmonics), high (eight harmonics)
Table Chapter 4 -4 Acoustic Parameters of Tone Sequences Significantly Contributing to Variance in Attributions of Emotional States. Source: Scherer and Oshinsky (1977, p. 340). ? denotes no quadrant hypothesised.
Rating scale Quad Single acoustic parameters (main effects) and configurations (interactions, effects) listed in order of predictive strength Pleasantness ? Fast tempo, few harmonics, large pitch variation, sharp envelope, low pitch level, pitch contour down, small amplitude variation (salient configuration: large pitch variation plus pitch contour up) Activity 1.5 Fast tempo, high pitch level, many harmonics, large pitch variation, sharp envelope, small amplitude variation Potency ? Many harmonics, fast tempo, high pitch level, round envelope, pitch contour up (salient configurations: large amplitude variation plus high pitch level, high pitch level plus many harmonics) Anger 2 Many harmonics, fast tempo. high pitch level, small pitch variation, pitch contours up (salient configuration: small pitch variation plus pitch contour up) Boredom 3 Slow tempo, low pitch level, few harmonics, pitch contour down, round envelope, small pitch variation Disgust 2 Many harmonics, small pitch variation, round envelope, slow tempo (salient configuration: small pitch variation plus pitch contour up) Fear 2 Pitch contour up, fast sequence, many harmonics, high pitch level, round envelope, small pitch variation (salient configurations: small pitch variation plus pitch contour up, fast tempo plus many harmonics) Happiness 1 Fast tempo, large pitch variation, sharp envelope, few harmonics, moderate amplitude variation (salient configurations: large pitch variation plus pitch contour up, fast tempo plus few harmonics) Sadness 3 Slow tempo, low pitch level, few harmonics, round envelope, pitch contour down (salient configuration: low pitch level plus slow tempo) Surprise 1.5 Fast tempo, high pitch level, pitch contour up, sharp envelope, many harmonics, large pitch variation (salient configuration: high pitch level plus fast tempo)
- 169 - Cohen Annabel Cohen (1990, 1993) used simple melodic fragments that were manipulated by pitch (highness and lowness), tempo and modality. The participant’s task was to judge the happiness or sadness expressed by a bouncing ball in the presence of the various versions of the melody. Cohen found that low, slow melodies were associated with the bounce being rated as sadder, and that if the melody was based on a major triad, the ball was judged to be happier. Because only the valence component was judged (no doubt, to keep the procedure simple), the findings can be used to provide evidence about the direction of valence responses to the variables of pitch, tempo and modality. Although Cohen’s findings of tempo being related positively to valence appear contrary to previous studies (see Tempo on page 242), it can be explained by the fact that happiness and sadness have distinct arousal values in addition to distinct valence. In Experiment II, Chapter 3, happy had a significantly higher arousal value than sad (59% versus -24%, from Table Chapter 3 -8 on page
134). Consequently, happy and sad are not good indicators of valence because they are confounded with arousal. Therefore, these findings could not be used to generate hypotheses about absolute positions on the emotion space, simply because the implied dimension does not correspond to the arousal or valence dimension.
Dolgin and Adelson As a preliminary stage of their investigation into the ability of children to interpret affect in music, Kim Dolgin and Edward Adelson (1990) composed 16 unaccompanied melodies which expressed pre-determined emotions as according to adult raters. Each composition, which lasted for 15 to 20
- 170 - seconds, was rated by more than 85 out of 100 adults as sounding either happy, sad, angry or frightened. Four melodies expressed each emotion. This preliminary phase of the study stands out because Dolgin and Adelson analysed the musical features of the compositions and compared them with the emotional categories. The features analysed were tonality, articulation, motion, tempo and contour. Although volume was held constant, Dolgin and Adelson indicated parenthetically that “loudness is more appropriate to anger or joy than to sadness” (pp. 89-92). Their analysis of the melodies according to the other musical features is shown in Table Chapter 4 -5. All the negative valence emotion melodies (sad, angry and frightened) had minor modalities. The low arousal term (sadness) was distinguished from the higher arousal terms (happy, angry and frightened) in that it did not use staccato articulation and its tempo was the slowest. Melodic motion and contour produced no obvious relationship that could be generalised to arousal and valence.56 The emotion space mapping in Table Chapter 4 -5 indicates that, as with the Scherer and
Oshinsky (1977) study, there is no Quadrant 4 emotion.
56 Checking and further analysis of these melodies is possible since their scores are included in the paper on pp. 90-91. The analysis summarised in Table Chapter 4 -5 does not reflect an exact control over the musical stimuli. For example, for the “angry” excerpts, the contour did change noticeably (instead of remaining flat), and for the “frightened” excerpts I remain unconvinced that the contours were systematically controlled to go down then up. In the fourth, “frightened” example, the melody moves upward and then downward instead of down then up. Such oversights give reason for concern regarding the papers where original musical examples are not included in the publication of experimental results. - 171 - Table Chapter 4 -5 Musical Features and Emotion Expressed by Dolgin and Adelson’s Melodies Source: Dolgin and Adelson, 1990. p. 89.
Emotion Quad Tonality Articulation Motion Tempo Contour Happy 1 major staccato/ step allegro /\ legato Sad 3 harmonic/ legato step largo — minor \ Angry 2 minor: accented skip allegro __ d7 chord staccato Frightened 2 minor: staccato/ step/ moderato \/ tritones legato skip
Thompson and Robitaille William Thompson and Brent Robitaille (1992) investigated the ability of the composer to communicate emotional messages to the listener. Five highly trained musicians were each asked to compose six, monophonic melodies. Three of these musicians received training in composition at a tertiary institution. The melodies were to express each of the six emotions: joy, sorrow, excitement, dullness, anger and peace. A general overview of the compositions were provided by Thompson and
Robitaille, with the music composed by one of the composers included as an example. The success of the emotion communicated was tested empirically by fourteen listeners. In the overview, the authors summarised the kinds of musical features associated with each of the emotion terms:
In communicating the emotional quality of joy, the five composers generally
wrote within a strongly tonal framework. Joyful melodies tended also to
involve a sense of movement through rhythmic variation. The primary features
of melodies intended to convey sorrowfulness were slow tempi, and implied
minor and chromatic
- 172 - harmony. Melodies intended to convey excitement generally involved fast
tempi. Three of the five melodies intended to convey excitement also involved
a progressive increase in the number of intervalic leaps and high pitches.
Melodies intended to be dull were generally very tonal, and were characterized
by stepwise motion, or simple triadic movement. In melodies intended to
convey anger, an emphasis was seen on rhythmic complexity, and implied
chromatic harmony or atonality. Melodies intended to convey peacefulness
were mostly very tonal, were slow in tempi, and often involved stepwise
motion leading to melodic leaps. Three of the five "peaceful" melodies also
involved triplets. (p. 82)
A positive relationship between arousal and tempo is supported by this analysis since joy and excitement were characterised by fast tempi, and peacefulness and sorrowfulness were characterised by slow tempi. A relationship is also apparent between harmony and valence, since sorrow and anger were expressed by more dissonances (than positive valence emotions) through the use of implied minor tonality, chromaticism and atonality.
Behrens and Green Gene Behrens and Samuel Green (1993) contended that by using improvised melodies, the potentially confounding variable of familiarity found in pre-composed music is eliminated. In response to these claims Behrens and Green recruited eight musicians to perform improvisations expressing several emotions. The performers were two violinists, two trumpet players,
- 173 - two vocalists and two timpanists. Each player was to express three emotions: sad, angry and scared, one per improvisation. After asking 58 students to determine the emotion expressed by each of the 24 improvisations, Behrens and Green found that the most accurate ratings were made when the voice expressed “sad”, the timpani expressed “angry” and the violin expressed “sad” or “scared”.
There may be a temptation to conclude that the timbres of particular instruments are suited to expressing particular emotions. Certainly this may be true, but notwithstanding Behrens and Green’s innovative method, there are some points that require closer examination. First, it appears somewhat peculiar that the emotions with similar valence scores (all negative) were selected. One would expect that, with only three emotion categories to work with, emotions more semantically distinct
(such as happy, sad and angry) would yield more distinct results, and that this might be a more advisable starting point. However, Behrens and Green claim that selecting emotions from one valence pole would maximise internal validity (p. 22).
Second, the study highlights how, just like other categories of musical stimuli, the use of improvisations also has a set of problems associated with it. An improvisation by its very nature is associated with flexibility and skill that is perhaps not compatible with the need for experimental control. This was evident when the
“more abstract improvisations performed by one of the trumpet players” (p. 29) was reported as having affected the responses of the less musically experienced judges.
- 174 - Finally, and related to the previous point, it is difficult to assign an emotion to an instrument because the concurrent manipulation of musical features with each improvisation were not controlled. A transcription of at least some of the improvisations may have been useful. The Behrens and Green (1993) study pioneered the method of using improvisation as the musical stimulus, and this method has been refined in subsequent studies where the improvisation was based on a predetermined theme and where the analysis of musical features and structures was more detailed (e.g., Gabrielsson & Juslin, 1996, discussed below).
Pre-Existing Melodies
The “pre-existing melody” is a fairly popular category of musical stimulus used in empirical research on musical features and their relationship with emotional response. The fact that these tunes were often familiar was seen as an advantage of the design (in contrast to researchers who use specially composed pieces because they wished to remove the familiarity factor). Other approaches are also mentioned in the ensuing discussion. First, a paper using instrumentally produced melodies is reported followed by literature using the singing voice.
Gabrielsson and Juslin Alf Gabrielsson and Patrik Juslin (1996) recorded musicians’ performances of four melodies, each with seven different kinds of expression. The expressions were natural, happy, sad, angry, tender, solemn and no expression. The melodies were the opening eight bars of the Eurovision signature tune (from Charpentier’s Te
Deum), a Swedish folk melody, the
- 175 - Negro spiritual Nobody Knows and a piece composed for the study. The performers were a singer, a flautist, a violinist and six electric guitarists. They were instructed to play each piece seven times, once expressing each of the seven emotions; the only restriction being that they play the notes on the score. Judges were asked to rate how well each performance matched the five expressive terms, happy, sad, angry, tender and solemn. In addition to the seven kinds of expression, the term fear was included for the guitar performances. The responses were used to determine which performances warranted further analysis.
What makes this study unusual is the level of detail of the analysis of the performances. Gabrielsson and Juslin examined the musical and acoustic properties of timing, articulation, dynamicism, tone onset and vibrato. The duration of each note was measured as the time taken between onset of successive notes, with an error of less than ±20ms. Mean tempo was obtained by dividing the length of each performance by the number of beats. Amplitude envelopes were used to compare articulations and “loudness” of different versions of the same tune. In addition, loudness, spectra, vibrato and intonation were determined through use of Swell
Soundfile Editor software. The results of this study were tentatively summarised by emotional expression in terms of musical and acoustic features:
Happiness is expressed by means of fast tempo, moderate variations in timing,
moderate to loud sound level, tendency to (relatively) sharpen contrasts
between "long" and "short" notes (as in dotted patterns),
- 176 - mostly airy articulation, rapid tone onsets, bright timbre, fast and light vibrato
(electric guitar).
Sadness: slow tempo, relatively large deviations in timing, low or moderate sound level, tendency to (relatively) soften contrasts between "long" and "short" notes, legato articulation, slow tone onsets, slow and deep vibrato, flat intonation in bending (electric guitar).
Anger: fast tempo, loud sound level, tendency to (relatively) sharpen contrasts between "long" and "short" tones, no final ritard, mostly non legato articulation, very sharp tone onsets, harsh timbre, distorted tones.
Fear: highly irregular tempo, very large deviations in timing, low sound level, large dynamic variation, mostly staccato articulation, fast and intense vibrato
(fear was used only with the electric guitar).
Tenderness: slow tempo, relatively large deviations in timing, low sound level, tendency to (relatively) soften contrasts between "long" and "short" notes, legato articulation, slow and soft tone onsets, soft timbre, intense vibrato
(electric guitar).
Solemnity: moderate to slow tempo, relatively small deviations in timing, moderate or loud sound level, mostly sharp tone onsets. (pp. 86-87)
- 177 - These results can be adequately transformed onto an emotion space because all four quadrants are represented.
Kotlyar and Morozov Emotion and singing are closely related to both music and speech research, suggesting that the number of studies in which analysing expression of emotion through song may be numerous. However, this is not the case. The reason is probably because of the associations that singing has with lyrics. This association adds a semantic channel of information that, to the experimental psychologists, could act as a confounding variable with the emotion expressed by the musical and the prosodic features. That is, it may be the words of a song indicating the emotion rather than the combination of musical features. Kotlyar and Morozov (1976) addressed this problem by using both vocal and synthesised stimuli for their investigation. They asked singers to express joy, sorrow, anger and fear in addition to a neutral performance of several vocal excerpts. The features measured were syllable duration, temporal gaps between syllables, sound pressure level and tone rise and decay time.
The average syllable durations were shortest for fear and longest for sorrow. In addition, voice onset time and decay time were also slower when sorrow was being expressed. Fear was characterised by longer inter-syllable durations or pauses.
Dynamics and tone onset time appeared to be related to arousal, with angry expressions being realised “loudly” with fast onset and fear expressions realised
“softly” with short onset. Kotlyar and Morozov tried to validate these results by electronically synthesising the musical
- 178 - features found to characterise the various emotions based on the vocal part of the study. The findings were in reasonable accord with those made in response to the vocal stimuli.
Baroni and Finarelli Mario Baroni and Luigi Finarelli (1994) asked three singers to each perform three versions of three vocal excerpts from the operatic repertoire. The three versions expressed joy, sadness and aggression for each excerpt. Baroni and Finarelli analysed the features of global dynamic levels and syllabic and global durations.
Although their interest was in comparing the singing and spoken voice, I am reporting some results pertaining to the singing voice alone. The average time taken to express sadness was longer than the time taken to express joy for the same piece, and the time taken to express aggression was quite erratic. However, these results were not consistent for one of the excerpts “Ed or fra noi parlim da buoni amici” (And now let us speak as good friends) from Puccini’s Tosca, (act 2, scene 5), possibly due to the semantic content of the words. Other studies of emotion and singing voice have been conducted by Anolli and Ciceri, (1992, cited by Baroni & Finarelli, 1994),
Sundberg (1982) and Seashore (1923).
Specially Composed Pieces
The purpose of composing fully harmonised pieces for experimental use is, as it is for composition of melodies discussed above, to allow the researcher greater control over the musical stimulus without forfeiting the musical context. The researcher has the option of combining musical features and structures as desired, and to produce a piece that is unfamiliar and playable
- 179 - in full (Behrens & Green, 1993). However, some music psychologists do not regard themselves as capable, or are not particularly talented or experienced, in the art and technique of composition. One option for such researchers was to use a mixture of specially composed pieces and pre-existing pieces (Rigg, 1937; Nielzén and Cesarec,
1982b). As was the case for melodies, such studies are reported under the section that reflects the composition type (pre-composed or specially composed) which is most salient and relevant to the present study.
Rigg Melvin Rigg (1937) conducted an empirical investigation of the theory of Erich
Sorantin (1932) by playing fourteen excerpts, each used as examples by Sorantin, in addition to six pieces composed by Rigg for the experiment. Each piece was played on the piano twice in a row to 100 subjects. Sorantin’s theory prescribed sets of musical features that each characterised joy, lamentation, longing and love. For example, the expression of joy was characterised by
Accelerated tempo
Ascending fourths in melody
Major mode
Simple harmony
Staccato notes
Forte dynamics
Iambic (short-long) or anapaestic (short-short-long) rhythm
- 180 - Rigg found that the excerpts containing most or all the musical features in this list were rated significantly more often as characterising joy than any other emotion.
There was also fairly high agreement that the musical features characterising lamentation consisted of:
Descending minor seconds in melody
Minor mode
Legato phrasing
Dissonance
Trochaic (long-short) rhythm
Low register
Slow tempo
Despite the apparent presence of all the theorised characteristics, contrary results for one of the pieces, an excerpt from Beethoven’s Fidelio, were found. After further investigation, Rigg found that the tempo at presentation was too fast, and that tempo was a factor that could “destroy the lamentation effect” (p. 448). The characterisation of longing and love each produced lower agreement between their corresponding sets of musical features than did joy and lamentation. As Rigg noted, part of the reason for the lower agreement was that a word such as longing was not unrelated to lamentation, and perhaps it was an oversimplification on the part of Sorantin that a list of musical features could be used to distinguish subtly related emotions.
A lesson from this study was that until the musical features that characterise more distinct emotions (such as joy and lamentation) are well grounded, it is
- 181 - counterproductive to investigate the musical characterisations of emotions that are in themselves difficult to distinguish. From this point of view, the two-dimensional emotion space provides a means by which distinct groups of emotions may be selected. For example, it is likely that lamentation and longing fall into the third quadrant (bottom-left) of the emotion space, whereas joy falls into the first quadrant
(top-right) (see Experiment II on page 117 in Chapter 3). So having established the relationship between the emotions, the more dissimilar, spatially distant ones can easily be distinguished and therefore selected for testing.
In another study by Rigg (1940), five pieces composed for a previous experiment were each performed at six different speeds ranging from 60 beats per minute through to 160 beats per minute. Eighty-eight college students were asked to judge whether each performance was “serious-sad” (consisting of the adjectives solemnity, sorrowful longing, melancholy, lamentation and agitation) or “pleasant-happy”
(hopeful longing, love, reverie, gaiety, joy and triumph). Rigg reported a strong relationship between the responses and the tempi based on the direction of the aggregate scores of each category. Faster tempi were judged as more pleasant-happy and slower tempi as more serious-sad. From this it was concluded that “faster speed tends to make the music happier (or more joyful), while slower speeds makes it sadder (or more of a lamentation)” (p. 570).
This finding, that tempo is related to valence, is at odds with research showing that tempo is related to the arousal dimension, and possibly valence (Gabrielsson &
Juslin, 1996; Imberty, 1975; Jackendoff, 1991; McFarland,
- 182 - 1985). The disparity can be accounted for by the measure used and the interpretation made.57 Rigg’s two categories (happy-sad) imply a valence dimension, but a closer inspection of the terms reveals that there is a confounding distinction of arousal related terms as well. A similar conflict was discussed in my review of the Cohen study, reported on page 170. The serious-sad category has only one arousal term, agitation, and upon inspection of Rigg’s data, the votes for agitation increase or are stable as tempo is increases, in contrast to the other votes in that category. In the pleasant-happy category, joy, triumph, and in some cases gaiety tended to swamp the other members of the category which were lower arousal words. The trend attributable to arousal, then, is as strong, if not stronger than that which Rigg attributes to valence. My reanalysis of Rigg’s data suggests that tempo has a positive affect on arousal, and that it may have some effect on valence as well.
Nielzén and Cesarec In their study of emotional response to music Sören Nielzén and Zvonimir Cesarec
(1981) used thirteen short, original compositions in an effort to eliminate associations with pre-existing compositions. The pieces were 12 to 35 seconds long and used a small orchestra consisting of two flutes, four violins, one oboe, two clarinets, two
French horns, two violas, two 'celli, one double bass and one bassoon. To ensure a high degree of objectivity each composition was rated by eight musically educated people (the method of
57 The anomalous finding between tempo and emotion can be traced back to the nineteenth century philosopher, Schopenhauer. Peterson (1994) remarked that Schopenhauer, along with Beardsley, “suggested that there is a relation between slow tempo and sadness, and between fast tempo and happiness”. Peterson continues “However, as even Schopenhauer and Beardsley would surely admit, slow expression is not necessarily sad, and fast expression is not necessarily happy.” (p. 67). - 183 - rating is discussed in the review of Nielzén and Cesarec, 1982b, discussed below on page 199). The findings of this study were that “‘tension’ correlated significantly with dissonant harmony, lack of melody and minor modality; ‘gaiety’ correlated significantly with fast tempo, discontinuity (staccato) and marked rhythm;
‘attraction’ correlated significantly only with unsophisticated rhythmic articulation”
(p. 21).
In another study by Nielzén and Cesarec (1982a) that used seven new compositions for small orchestra, two of the pieces were identical but their tempi were manipulated. One piece was played at 120 bpm and the other at 94 bpm. Emotional experience data were gathered from two groups of participants. One group, ten patients diagnosed with manic psychosis, indicated higher valence scores for the version with faster tempo, while 20 normal participants rated the tension (arousal) dimension as higher for the faster version.
Collier Geoffrey Collier (1996), as part of his study on affective synaesthesia, composed ten short pieces of music ranging from a few seconds to a few minutes in duration. His work is of interest here because he specifically uses the two-dimensional (valence and arousal) model of emotion. He proposed that:
The perceptual locus of an aesthetic stimulus in this two-dimensional space is
hypothesised to provide a first approximation to how the
- 184 - synesthetic qualities of a percept provide a basis for emotional responses to
such stimuli. (p. 1)
Although the details of the musical features were not provided, Collier did report that the arousal dimension of responses to the music correlated with tempo (r = 0.66, p < 0.05).
Pre-Existing Pieces with modification
Gerardi and Gerken Gina Gerardi and Louann Gerken (1995) generated four stimuli from a pre-existing melody in a cognitivist study. A 2 x 2 manipulation was used where the mode of the piece was changed (from major to minor or vice-versa) and the melodic contour was changed (up to down or down to up). Melodies in one mode and with a predominant contour were chosen for manipulation. Four melodies were selected for manipulation making a total of 16 stimulus melodies. Sixty-eight participants judged the valence expressed by the melodies on a dichotomous face scale: happy or sad. Gerardi and Gerken concluded that for participants 8 years old and over (23 eight year olds and 25 psychology students) modality had an effect on valence, with happy responses for major mode melodies predominating. A slightly weaker effect was reported for melodic contour. The trend was for happy melodies to be associated with rising contours and sad melodies with descending contours.
Gregory, Worrall and Sarge Andrew Gregory, Lisa Worrall and Ann Sarge (1996) investigated the development of emotional response to music in young children using modified and original versions of eight nursery tunes. Two parameters were
- 185 - manipulated — the modality (major or minor) and the harmony (absence or presence). Three groups of participants were tested: forty children aged three to four years, 28 children aged seven to eight years, and 28 adults. A positive relationship between modality and valence was clearly established by the age of seven to eight years.
Although the study focussed on the development of emotional perception in music, it is important with respect to the present study because it is one of the few which examined interactions between musical features: Adding harmony to the melody had an additive effect upon the valence rating. In contrast, Kastner and Crowder
(1990) found that the addition of harmony to the melody shifted valence toward the negative pole. Also, Kastner and Crowder found the valence-mode associations developed much earlier (by the age of three to four years instead of seven to eight).
Gregory, Worrall and Sarge (1996) suggested several possible explanations for these discrepancies. The most important difference was that the Kastner and Crowder
(1990) study was conducted on American children, while the Gregory, Worrall and
Sarge study was conducted on English children. For example, English nursery rhymes were more likely to contain disagreement between mode-valence association and the verbal message. The researchers found “plenty of [English] nursery rhymes in the minor mode, including several familiar cheerful ones such as ‘Old King Cole was a merry old soul,’ while several sad rhymes such as ‘who killed Cock Robin?’ were set in the major mode.” Gregory, Worrall and Sarge continued, “If there is no clear
- 186 - relation between emotion and mode in nursery rhymes, then this in itself may delay the learning of the association” (p. 347).
Hevner Among a series of experiments on emotional response to music (1935, 1936, 1937),
Hevner (1936) modified a single musical feature for groups of compositions with the assistance of expert musicians (1936, p. 254), each group containing works expressing a wide variety of emotions. The features modified were the “rhythm or motion”, melodic direction and harmony. Each change was dichotomous. To change motion, or “rhythm”, Hevner produced two versions of the piece, one consisting of “a firm beat with a full chord on every beat as in a hymn tune” and the other “smooth and flowing motion in which the supporting chords were broken up and spread evenly throughout the measure” (p. 256). I am using the first eight bars of Felix
Mendelssohn’s Song Without Words, Op. 19. No. 1 as an example (musical scores are in Hevner, 1936, pp. 255-257). The original version consists of semiquaver arpeggiations underneath a legato crotchet melody with slight ornamentation.
Hevner classes this as the flowing motion version. The reworking, called the firm rhythm version, consists of crotchet block chords with melodic quavers introduced only if they were an essential part of the melody. From this example, it appears that naming the variable “motion” is more appropriate than “rhythm”, however the difficulty in operationalising rhythm is a problem that has remained with researchers long after Hevner’s time (for an examination of these problems see Gabrielsson, 1973;
Clynes & Walker, 1982).
- 187 - The Mendelssohn selection was also used to demonstrate how the melodic direction was manipulated. For this variable the original version of the Mendelssohn was classified as “descending melody”, with the reworked version labelled “ascending melody”, consisting of a melody that started rising instead of falling, followed by a downward leap instead of an upward leap, and so on. Some liberties were taken with harmonies in order to maintain the required direction of the melody. Hevner admitted that “the inversions of the melodies were never perfect, but … they were as exact as … other considerations would allow” (p. 259; for a further discussion of the effect of the manipulation of melodic direction, see Levi, 1979). The third variable, harmony, was mostly the alteration of simple, consonant harmonies to complex, dissonant harmonies. The complex version had “augmented and diminished intervals and modern effects” (p. 259). In two other studies Hevner also examined mode (1935), tempo and pitch (1937) with methodologies similar those of the 1936 study (except that in the 1935 study Hevner was establishing the adjective checklist discussed on page 54 in Chapter 2). A summary of the findings are presented in
Table Chapter 4 -6 on page 193.
The 1935 paper clearly demonstrates that mode is related to valence, with positive valence terms related to the major mode and negative valence related to minor mode.
The results of the 1936 paper indicate that pieces with simple, consonant harmony were associated with words of a positive valence (happy, graceful and serene), while complex, dissonant harmonies were associated with high arousal terms (exciting and vigorous) or negative valence (sad). Finally for the 1936 study, flowing motion
(referred to as
- 188 - flowing rhythm by Hevner in her conclusions) was related to positive valence terms
(happy, graceful and dreamy), while firm motion received most votes in the vigorous and dignified clusters. For the 1937 study a piece transposed up an octave (for the purpose of raising the pitch while keeping the key constant) was rated as being graceful, serene, happy and dreamy, while its low pitched counterpart was associated with the words sad, vigorous, dignified and exciting. Finally, tempo was reported as being exciting and happy when fast, and serene, dreamy and dignified when slow.
Given the numerous citations of the these major contributions to empirical aesthetics, some further discussion of Hevner’s work is warranted. Specifically, it is important to examine how well the Hevner adjective circle maps onto the two-dimensional emotion space. The mappings proposed here and shown in Figure Chapter 4 -2 are based on the results of Experiment II (see Table Chapter 3 -8 on page 134 in Chapter
3). Cluster 1 (Figure Chapter 2 -3 on page 55 in Chapter 2) does not map well onto the 2DES. Sacred, solemn, sober and serious imply low arousal with a negative to intermediate valence (Quadrant 3, and toward Quadrant 1), but the other members of this cluster have no obvious position (spiritual, lofty, awe-inspiring and dignified).
Cluster 2 is well suited to Quadrant 4, with the exception of a few words which could indicate heightened arousal (tragic and frustrated) or have no obvious place (heavy and dark). Therefore, with aggregated scores, Cluster 2 can at best be related to the negative valence side of the emotion space. Cluster 3 mixes valence terms (dreamy, yielding, tender and sentimental pitted against longing, yearning, pleading and plaintive), meaning that, at best, it is only likely to provide information on low arousal. Clusters 4, 5 and 6 map fairly
- 189 - neatly onto the emotion space, belonging to Quadrant 4 (low arousal, positive valence), in between Quadrant 4 and 1 (positive valence, intermediate arousal) and
Quadrant 1 (positive arousal and valence), respectively. Cluster 7 maps fairly well onto the high arousal, central valence part of the emotion space, but the words agitated, restless and impetuous skew the mapping. Finally, Cluster 8 would not map onto the 2DES successfully because several words are not obviously definable in terms of arousal and valence (e.g., ponderous and robust). Therefore, unless scores for individual words are provided (which in most cases they are not), or unless they come from Clusters 4, 5 or 6, it is difficult to determine where responses might fall on the two-dimensional emotion space. Farnsworth’s (1954) reworking of the Hevner adjective checklist alleviates the problems of incompatible adjectives sharing a group, but this revised list cannot be applied to those studies which do not report responses to each word of a cluster.
In spite of the obstacles to mapping, the Hevner studies provide valuable data for generating hypotheses of the relationship between musical features and emotion. In order to utilise this data, Figure Chapter 4 -2 indicates how the preceding mappings might appear on a two-dimensional emotion space. The large ellipses (1, 2, 3, 7 and
8) indicated poor mapping. That is, if Hevner were to conduct an experiment to determine where the clusters fell on the emotion space, she might expect large deviation scores either due to the aggregation of distinct, but different emotions
(Clusters 2, 3 and 7), or due to the ill definition of the words in terms of valence and arousal (Clusters 1 and
- 190 - 8). A proposed mapping of Hevner’s findings onto the emotion space are listed in
Table Chapter 4 -6.
Elements of Hevner’s design are questionable and should be treated as a lesson for future researchers. The main problem discussed here is the semantic density of the words used in the checklist. Ideally, words within each cluster should have a similar meaning, each cluster should cover specific areas in semantic space and the clusters should cover a large cross section of semantic space. For example, the lack of words, and more seriously, the lack of a cluster to describe high arousal, negative valence emotions such as anger, fear and terror can account for findings that are anomalous.
Yet the literature is replete with citations of these misleading conclusions.
- 191 - Figure Chapter 4 -2 Suggested Mapping of Hevner Adjective Clusters onto the Two- Dimensional Emotion Space. Words contained in each cluster are Cluster 1: awe-inspiring, dignified, lofty, sacred, serious, sober, solemn and spiritual; Cluster 2: dark, depressing, doleful, frustrated, gloomy, heavy, melancholy, mournful, pathetic, sad and tragic; Cluster 3: dreamy, longing, plaintive, pleading and sentimental; Cluster 4: lyrical, leisurely, satisfying, serene, tranquil, quiet and soothing; Cluster 5: delicate, fanciful, graceful, humorous, light, playful, quaint, sprightly and whimsical; Cluster 6: bright, cheerful, gay, happy, joyous and merry; Cluster 7: agitated, dramatic, exciting, exhilarated, impetuous, passionate, restless, sensational, soaring, triumphant; Cluster 8: emphatic, exalting, majestic, martial, ponderous, robust and vigorous. Smaller, thicker ellipses indicated more concise mapping.
7 6
8 2 5 1 3 4
- 192 - Table Chapter 4 -6 Hevner’s Findings Mapped onto the Two-Dimensional Emotion Space
Musical Feature Significant Clusters Hevner’s report Region on Quad (most significant Emotion Space first) Major mode * “happy, merry, positive valence, 1 graceful and playful”+ high arousal Minor mode * “sad, dreamy”++ negative valence 3, 4 Firm motions (or 1 and 8 “vigorous, dignified”+ no mapping “firm rhythm”) suggested Flowing motion (or 6, 3 and 5 “happy, graceful, positive valence 1 “flowing rhythm”) dreamy, tender”+ and arousal Simple, consonant 6, 5 and 4 “happy, graceful, positive valence 4, 1 harmony serene and lyrical”+ Complex, dissonant 7 “exciting, agitating, high arousal 1, 2, 3 harmony vigorous, and inclined toward sadness”+ Ascending melody no highly “not clear-cut, distinct, no mapping significant results or consistent”+ suggested Descending melody 7 “not clear-cut, distinct, no mapping or consistent”+ suggested Slow Tempo (63, 72 4 and 3 “dignified and … clam- low arousal 3, 4 & 80 bpm) serene”++ Fast Tempo (102, 6 and 7 “happy-gay and high arousal, 1 104, 112 & 152 exciting restless”++ positive valence mean bpm) Register down (or 2 and 8 “sad … vigorous- negative valence 2, 3 low pitch) majestic and dignified serious”++ Register up (or high 5 “sprightly- positive valence 1, 4 pitch) humorous”++
* Datum on each adjective was available enabling mapping to be made without the assistance of Figure Chapter 4 -2. + Hevner, 1936, p. 268 ++ Hevner, 1937, p. 624
An example comes from the supposed effect of tempo upon emotions. Hevner reports the effect of fast tempo as expressing happiness and excitement. This inferred positive valence has pervaded much of the music-emotion empirical literature (e.g., Bruner, 1990; Rigg, 1964). Rigg (1964) summarises the effect of fast tempo: “Other things being equal, a fast speed has an effect in the direction of joy, whereas a slow speed tends toward
- 193 - sorrow” (p. 435). As a report of Hevner’s conclusions, Rigg’s interpretations may be well founded, for, as indicated in Table Chapter 4 -6, Hevner does at least imply positive valence terms for fast tempi. However, Hevner’s results do not indicate a necessary relationship between valence any more than they do arousal, and the results are in contradistinction to more intuitive theories of the emotional effect of tempo (Imberty, 1975; Jackendoff, 1991; McFarland, 1985).
Table Chapter 4 -6 indicates that for slow tempi the significant response clusters map onto the low arousal portion of the emotion space, whereas the clusters associated with fast tempi map onto high arousal, positive valence. Now, high arousal does not exclude positive valence as being a possible response to increased tempo, however the conspicuous lack of a category that clearly defines negative valence and high arousal (Quadrant 2 emotions) indicates that it would be very difficult to demonstrate that anything could express negative valence in tandem with high arousal. This problem may have been exacerbated by Hevner’s desire to choose pieces and reworkings that were pleasing (which may have worked against her other intention of choosing a wide variety of examples). The pieces used to investigate the effect of tempo were unnamed sections of Beethoven variations, two nocturnes and two preludes (1937, p. 622). More information would be needed before it could be assumed that any of these pieces could express emotions related to terror, fear or anger. These criticisms apply to the subsequent studies also reported in Rigg’s review, namely by Gundlach, Rigg and Watson, although they tended to include a greater variety of musical selections. Bruner (1990, p. 95) must have been so overwhelmed by the results of these earlier studies that in
- 194 - his reports of later findings he neglected to mention the relationship of arousal with tempo even when these studies did report it (e.g., Scherer & Oshinsky, 1977).
Melodic direction was not found to produce significant emotional effects. Levi (1979) claimed that the procedure used by Hevner for changing the melodic direction from descending to ascending, as in the Mendelssohn example, did not necessarily produce a perceptual experience that was different between the two versions. Levi stated that “The important question is whether, in the original version, a descending melody is heard, while in the second an ascending melody is perceived” (p. 53). He suggests that the two versions of the melody are not heard as being significantly different and that therefore there is no reason why a change in the expressed emotion should be perceived. Levi then demonstrates that the direction of melodic line, along with several other concurrent musical features, can express different emotional effects provided that particular psychological (Gestalt) principles are applied.
Despite Hevner’s innovative design, the method of choosing pre-existing compositions and then manipulating them in a controlled manner was not taken up by later research (the Gerardi & Gerken study is the only exception cited). No doubt this was due to the large amount of work required in organising the reworked versions, but it is conceivable that some musicologists would have scorned at the bastardisation of great works, further discouraging future investigators from taking such an approach. Another reason may be the development of sophisticated statistical
- 195 - techniques, which appear to have taken over the role of insightful solutions to multidimensional problems. In one sense it no longer became such a problem if the stimulus was complex, for the statistics could “sort it out”. The experimental psychologists (and their experimental participants) could then take over the role that previously required musicologists. This is evident in some of the literature which followed the landmark works of Wedin (1969, 1972).
Pre-Existing Pieces
Gundlach Ralph Gundlach (1935) used 40 single, pre-recorded phrases from a “diverse” range of pieces that were essentially from the Western art music repertoire. He analysed each musical score and created an index for several musical features, although the techniques of coding were at times unclear or unexplained. Tempo and loudness were each rated by two people on a five point scale. Range of the melodic line and orchestral accompaniment was also coded, but the method of coding is not very clear. Gundlach stated that this feature was measured by using “the eight notes to the octave” (p. 629 and p. 633), but the treatment of accidentals was not explained.
Judging by the results, he probably assigned a value of 1 to the lowest note (in the melody or the score) and counted up the diatonic scale to the highest note in the passage. Perhaps accidentals were not encountered, or they were rounded, or they were simply ignored. Based on Gundlach’s treatment of intervals (interval qualities
— major, minor, augmented or diminished — were not distinguished), the latter possibility seems most likely.
- 196 - The central pitch, or “relative pitch” as Gundlach puts it, was determined by finding the mid-most tone in the melodic line. This note was then converted to a number, presumably related to its absolute pitch. Successive steps of the melody line were tallied, with the percentage of each kind of interval recorded (unison, second, third, fourth, fifth and those greater than a fifth).58 Rhythms were divided into three categories: smooth, rough and uneven. Gundlach defines the three categories in terms of examples:
Smooth rhythms include units that move along using just the temporal
duration, as in the Doxology, or more rapidly moving doublets, triplets, or
quadruplets. Uneven rhythms involve the small rhythmic units that are easy
flowing, but not equivalent, as in the customary waltz tune. Rough rhythms
involve the vigorous jerking such as those parts of Marseilles [sic] or Soliloquy
that are not smooth.59 (p.629)
In this description Gundlach referred to a tautological “temporal duration”. Perhaps he really meant the underlying pulse of the music. For the sake of clarity this will be assumed. The direction of the melodic line was also recorded but discarded as it
“has shown no significance for our problem” (p. 629). Finally, the instrument carrying the melodic line was coded. The
58 The emotional effects of various intervals has received little attention in the literature, making Gundlach’s investigation interesting. In The Beautiful in Music (1928), Max Schoen refers to an empirical study on the effect of intervals conducted by an “Italian investigator”. Although no details of methodology are provided, Schoen reported the findings (pp. 61-63). There were noticeable inconsistencies in response with the exceptions of m2 — negative valence, M3 — positive valence, m6 — tranquillity, the seventh (as a group) — high arousal, negative valence. The problems of intervals and their emotional character are partly rooted in the variety of intervals available within each scale. Without considering the position of the interval with respect to its tonal framework, the results are
- 197 - relevant and significant findings of the Gundlach study are reproduced in Table
Chapter 4 -7 and Table Chapter 4 -8.
Table Chapter 4 -7 Characterisation by Rhythm, Interval, Pitch and Tempo. Source: Gundlach (1935, p. 637 and p. 638) Musical Features Character Quad Many Rough Rhythms grotesque, uneasy 2 Many Uneven delicate, sentimental, dignified, exalted, sombre ? Rhythms Few Uneven Rhythms flippant, animated, grotesque, brilliant 1, 2 Many Smooth brilliant, animated, flippant, glad 1 Rhythms Many 1sts and 2nds uneasy, mournful, awkward 2, 3 Many 3rds triumphant 1 Many Large Intervals glad, exalted, delicate 1, 4 High Pitch sentimental, whimsical, animated, glad 1, 4 Low Pitch mournful, sombre, tranquil, dignified, grotesque 2, 3, 4 Wide Range uneasy, animated, grotesque, brilliant, glad 1, 2 Narrow Range tranquil, dignified, delicate, mournful, awkward, sombre 3, 4 Fast brilliant, animated, uneasy, glad, whimsical, flippant, 1, 2 grotesque Slow dignified, sombre, tranquil, melancholy, mournful, delicate, 3, 4 sentimental
Table Chapter 4 -8 Characterisation by Instrument or Family Source: Gundlach (1935, p. 636) Instrument / Suitable for Characterisation of Quad Less Suitable for Family Characterisation of Brass triumphant, grotesque 1, 2 melancholy, tranquil, delicate, sentimental Woodwind mournful, awkward, uneasy 3 brilliant, glad Piano delicate, tranquil, sentimental, 1, 4 mournful, awkward, brilliant triumphant, sombre Strings glad 1
Table Chapter 4 -9 Consistent and Reliable Findings in Relationship between Musical Characteristics and Meaning as Reported by Watson Adapted from Watson, 1942, p. 33. Adjective Selected More Quad Musical Feature Frequently amusing 1 increase in irregularity of rhythm and dynamics very happy 1 increase in volume and tempo very exciting 1, 2 increase in pitch, volume, speed, and sound peaceful 4 decrease in dynamics pleading 2 increase in pitch and irregularity of dynamics
likely to be ambiguous. For a discussion of interval frequencies within the major and minor modes see Butler and Brown, 1994). 59 Marseillaise. - 198 - Watson In a series of developmental studies, Brantley Watson (1942) used thirty excerpts of various styles of Western Art Music (p. 8) each of approximately one minute duration. In one of these studies, Watson found some relationships between musical characteristics and adjective groups. Some important findings are summarised in
Table Chapter 4 -9. Wing criticises Watson for choosing too many selections that are performed at fast tempi, leading to effects of harmony being suppressed by the effects of rhythm (cited in Valentine, 1962, pp. 306-7).
Mull Helen Mull (1949) examined humour responses to three pieces of music: Richard
Strauss’s Till Eulenspiegel’s Merry Pranks (first part) and Ständchen (song for piano), and Rameau’s La Poule (played on cembalo). Ständchen was included as a control, to check that participants were not responding to everything as humorous. Humour tended to be attributed to incongruities and surprises such as notes played out of expected sequence, rhythm changing back and forth, repetition and the imitation of animals and mechanical sounds.
Nielzén and Cesarec Sören Nielzén and Zvonimir Cesarec (1982b) used two sets of music to study musical and emotional experience. One set consisted of specially composed pieces and the other, of thirteen excerpts, was intended to represent a wide variety of the Western art music repertoire “with variations in structural elements and musical style … compositions from Bach to Maderna and Blomdahl …” (p. 10). To code the musical structure of each piece, eight
- 199 - musically educated people were asked to assess the following nine features on a five point, bipolar scale: harmony (dissonant-consonant), modality (major-minor), melody (melodious-amelodious), intensity (pp-ƒƒ), pitch (bass-treble), rhythm
(marked-vague), rhythmic articulation (sophisticated-unsophisticated), continuity
(staccato-legato) and tempo (fast-slow). Inter-rater reliability was checked and the ratings were subjected to a factor analysis.
In the main experiment participants indicated the emotion they experienced in response to each piece of music on semantic differential scales. This design produced two sets of factors, one describing the musical features and another describing emotional response. By comparing these factors Nielzén and Cesarec determined some structural correlates of emotional response. It was found that the emotional factor of tension (tension-relaxation factor) increased with dissonance, minor modality, sophisticated rhythmic articulation and lack of melody. Music rated with higher levels of gaiety (on the gaiety-gloom factor) was associated with loudness, marked rhythms, staccato articulations and fast tempi. Finally, the attractiveness (on the attractive-repulsive factor) was found to relate to consonance, major key, unsophisticated rhythm and presence of melody, although this latter finding applied only to the pieces not composed especially for the experimenter.
By interpreting the gaiety-gloom factor as a valence dimension, we come across unexpected associated musical features (Rigg, 1964; Bruner, 1990). Much of the literature suggests that the valence dimension is related to some of the scales which
Nielzén and Cesarec found to be associated with the
- 200 - attractive-repulsive factor (e.g., modality). The disagreement could be explained by an investigation of an earlier study from which the emotional scales and factors were obtained (Nielzén & Cesarec, 1981). In this study, Nielzén and Cesarec proposed that the attractive-repulsive factor, and not the gaiety-gloom factor, was related to
Osgood’s evaluative factor (1981, p. 20). On inspection of these factors, the scales that relate to emotional valence measures are distributed across the two factors, and this may, in part, explain the disparity.
Another part of this disparity may be accounted for by the factoring of musical features. One would presume that the purpose of performing factor analysis on these musical feature scales would be to check for redundancies across scales.
However the factor analysis was used to group musical features and use these groupings as a succinct analytic description of the pieces. For example, a piece that is accurately described by some of the scales in that musical features factor will have all the features of that factor assigned to it, because it is the factor and not the component features that are used to describe the piece. This, to my mind, indicates a loss of some possibly important musical features and the false assignment of others to the music. The only other explanation is the absurd premise that (by assigning a predetermined factor to a piece of music) when a piece is, say, loud, then, according to the vivid-placid musical feature factor (1982b, p. 13), it is also likely to have marked rhythms, staccato articulations and fast tempo. Perhaps it would have been more useful to keep judged musical feature scores unfactored and to use these scores as independent variables in a
- 201 - regression analysis, thus allowing each selection to be described by its actual musical features.
Nielsen Frede Nielsen (1983) examined the relationships between continuous tension responses to the first movement of Haydn’s Symphony No. 104. Nielsen’s analysis relates formal, musical structures based on the theorem of Lerdahl and Jackendoff
(1983), in addition to lower level features such as loudness and pitch contour, to the tension response curve. The most notable result was that the loudness response was related to the tension curve in several sections of the music. High tension tended to occur in loud passages and low tension at soft passages. Relationships were not analysed quantitatively, and time series analytic techniques were not used (see
Chapter 6).
Thayer Julian Thayer (1986) asked participants without formal musical training to rate the emotion experienced in response to 17 ninety-second excerpts of a variety of Western art music selections. Musical features were coded by the “untrained” participants.
After listening to an excerpt they rated, among other things, the two musical features of pitch and tempo, each on a bipolar scale (high pitched to low pitched and fast to slow respectively). Based on a factor analysis, tempo loaded onto the activation factor (fast tempo relating to high arousal and low tempo relating to low arousal) and pitch onto the pleasantness factor (high pitch associated with positive valence and low pitch associated with negative valence).
- 202 - Flowers Patricia Flowers (1988) reported a developmental study of descriptions used by children and adults about four pieces of music. The pieces were selected because they combined two dichotomised musical features of tempo (fast/slow) and modality (major/minor). The pieces used are listed in Table Chapter 4 -10. They consisted of approximately the first minute and a half of the movements mentioned.
The adults judges were 62 elementary education majors enrolled in a beginning music class. Only the responses to descriptions of music provided by this group are discussed here. Of the words reported by these participants, those occurring most often (more than five times) and consisting of emotion word descriptions are shown in Table Chapter 4 -10. The table demonstrates that high arousal words distinguished the fast pieces from the slow. The relationship between modality and emotion was not so clear. Flowers pointed out that the effect of tempo overrides the effect of mode in these selections. That is, using a simple (2 x 2) design, Flowers identified a probable interaction between tempo and modality. In supporting the view of such an interaction, Kastner (cited in Kastner & Crowder, 1990, p. 197) suggests that conflicting tempo and mode (fast with minor or slow with major) may lead to an increase in response time.
- 203 - Table Chapter 4 -10 Musical Stimuli used by Flowers, with Associated Emotion Words Emotion words used more than four times for any piece are shown (with number of occurrences in parenthesis).
Piece Category Emotion words Quad Mendelssohn - Symphony No. 4 in fast, major happy (7), energy (7), lively (5), 1 A major, Op. 70 ("Italian"), first excite (5) movement (Allegro vivace) Beethoven- Symphony No. 9 in D fast, minor excite (9) 1.5 minor, Op. 125 ("Choral"), second movement (Molto vivace) Dvorak - Symphony No. 9 in E slow, major sad (14), relaxing (14), beautiful 3, 4 minor Op 95 ("New World") (8), peaceful (8) second movement (Largo) Tchaikovsky - Symphony No. 4 in slow, minor sad (11), relaxing (10) 3, 4 F minor, Op. 36, second movement (Andantino in modo di cantone)
Collins In one of a series of experiments, Sylvie Collins (1989) examined the relationship between musical features and emotional response. Twelve musical stimuli were chosen which expressed a variety of emotions. In contrast with Thayer (1986), musical features were evaluated by twenty-two participants who had “extensive experience and knowledge of classical music” (p. 29). Musical attributes of melodic shape, harmony and rhythm were rated using eighteen seven-point unipolar scales: melodic, amelodic, smooth, disjunct, legato, staccato, consonant, dissonant, major, minor, simple, complex, loud, soft, fast, slow, high-pitched and low-pitched. Collins summarised her findings of the musical features which correlated with the emotion word scales. The summary is reproduced in Table Chapter 4 -11. An additional column indicating the mapping of the emotion words onto the 2DES highlights the omission of Quadrant 3 emotions such as sadness and melancholy.
- 204 - Table Chapter 4 -11 Summary of Musical Features and Emotional Responses by Collins. Source: Collins (1989, p. 45).
Excerpts are Emotion Quad likely to contain not likely to contain interesting ? staccato phrasing frightening 2 minor harmony major harmony amelodia well-developed melody disjunct melody smooth melody relaxing 4 consonant harmony well-developed melody amelodia smooth melody disjunct melody legato phrasing staccato phrasing sophisticated rhythm slow tempo fast tempo piano dynamic forte dynamic high pitch happy 1 major harmony minor harmony surprising 1.5 consonant harmony amelodia well-developed melody disjunct melody smooth melody staccato phrasing legato phrasing sophisticated rhythm simple rhythm forte dynamic piano dynamic fast tempo slow tempo high pitch exciting 1 amelodia well developed melody disjunct melody smooth melody staccato phrasing legato phrasing sophisticated rhythm forte dynamic piano dynamic fast tempo slow tempo high pitch
Namba, Kuwano, Hatoh and Kato Seiichiro Namba, Sonoko Kuwano, Tadasu Hatoh and Mariko Kato (1991) measured responses to different performances of the “Promenade” movements from Pictures at an Exhibition by Modeste Mussorgsky. Namba and associates kept fairly clear of making connections between the responses and the characteristics of the corresponding performances, with the following exceptions: They concluded that
“instantaneous impressions had close relations to the sound-pressure levels and the tempos of the performances” (p. 270). “Magnificent” and “powerful” may have been
- 205 - responses to increasing sound pressure level and “leisurely” was indicated more often when the tempo decreased.
Sloboda In a study by John Sloboda (1991), participants chose their own pieces and indicated one or several sections of these pieces that evoked physical emotional experiences such as crying, shivers or laughter. By performing a structural analysis of several pieces, (a common technique for analysing music in musicology, but rarely used in music psychology), Sloboda compiled a list of musical features and responses. Up until Sloboda’s study no empirical literature was cited that dealt with harmony in more than a cursory manner. The common scenario was to call a variable
“harmony” if it had two values - simple and complex, dissonant and consonant, or perhaps a continuum between such extremes. In contrast, Sloboda undertook a detailed examination of harmonic structure and voice leading. Ten categories of musical features were reported (p. 114):
1. Harmonic descending cycle of fifths to tonic
2. Melodic appoggiatura
3. Melodic or harmonic sequence
4. Enharmonic change
5. Harmonic or melodic acceleration to cadence
6. Delay of final cadence
7. New or unprepared harmony
8. Sudden dynamic or textural change
9. Repeated syncopation
- 206 - 10. Prominent event earlier than prepared for
Six of these features had a systematic relationship with the physical emotions experienced, namely 2 and 9, each with significant chi-square statistic at p < 0.001; and 1, 3, 7 and 10, each with significant chi-square statistic at p < 0.02. Features 1, 2 and 3 provided most examples producing “tears” response. For example, the opening six bars of the third movement of Serge Rachmaninov’s Second Symphony comprised a harmonic descending cycle of fifths, melodic appoggiatura and a melodic sequence, and this excerpt produced physical responses of tears. The theme from Tomaso Albinoni’s Adagio was another example of a piece inducing tears through use of melodic appoggiatura and sequence (Sloboda, 1992).60 I experimentally mapped two of Sloboda’s physical emotion words onto the 2DES
(Experiment II, Figure Chapter 3 -8 on page 149 in Chapter 3). The word “tears” mapped well onto negative valence, but it mapped poorly into the arousal dimension. Therefore it seems reasonable that features associated with tears will move responses toward the negative valence side of the emotion space. Sloboda’s pioneering study provides a framework from which to derive a comprehensive emotional analysis of complex tonal musical structures. In general, the evidence suggests that harmonic dissonances tend to move responses toward the negative valence side of the emotion space.
60 Francés and d’Ollone (1952, cited in Francés, 1958/1988, p. 327) had a more vague interpretation on the affect of the appoggiatura: “Appoggiaturas have a different appearance depending on whether they are descending or ascending. In the first case, ‘they glide over the top of the actual note in a movement of matter or mind that lifts them momentarily higher than the point of support—whence the impression of ease, of flexibility, of fullness, generosity, or domination. Ascending appoggiaturas, on the other hand, needing to climb for their resolution, to find rest, seem to make a more humble and supplicating effort and gesture’ (d'Ollone, 1952, p. 88)”. Clearly, Sloboda provides a much more specific view on the effect of the appoggiaturas which he has encountered. - 207 - Kratus John Kratus (1993) measured responses of children (6 to 12 year olds) to 15 sections of Johann Sebastian Bach’s Goldberg Variations, using a recorded performance by
Glenn Gould. Kratus examined emotional responses in terms of the musical features of rhythm (which incorporated tempo, rhythmic activity, meter), modality, articulation, dynamics, interval size, and use of imitation. Five bipolar scales were used: articulation (staccato-legato), dynamics (fortissimo-pianissimo), rhythmic activity
(“much activity regardless of overall tempo”-“little activity regardless of overall tempo”), strength of pulse (“strongly accented pulse”-“unaccented pulse”) and tempo (presto-largo). To remedy concern that these features had an element of subjectivity, Kratus enlisted five music education graduates to independently rate each feature on a five point scale. Another three musical feature variables were dichotomous, their values for each excerpt being determined by the author. Interval size was “theme consists primarily of steps” or “theme consists primarily of skips”, modality was major or minor, meter was duple or triple, and use of imitation was
“not an imitative form” or “imitative form” (p. 11).
With all variables coded, two sets of stepwise multiple regression analyses were applied using the valence (happy-sad) data to form the criterion variable for one set of analyses and the arousal (excited-calm) data for the other. Of importance here is that for the valence dimension, two features — rhythmic activity and articulation — explained most of the variance, and rhythmic activity and meter best explained arousal responses. Music rated as being more staccato was associated with positive valence and triple meter
- 208 - was interpreted as more exciting than duple meter. Kratus suggested that the prominence of rhythmic articulation in both criterion variables is in line with previous research.
However, as Kratus noted, rhythmic articulation is fairly collinear61 with articulation, dynamics and modality, and this lacking independence brings its usefulness into question. In addition, the single variable rhythmic articulation explains too much.
This variable is at best difficult to interpret and at worst ill-defined in terms of specific musical processes. Such problems demonstrate the delicate balance that exists between the need for experimental control and generalised validity. Kratus, as with the other researchers reported in this section, is concerned with the latter (p. 11-
12).
Panksepp Jaak Panksepp (1995) used popular music selections, selected by the participants, to investigate the sources of induced “chills”. The stimuli used were mostly music of the 1980s. In one study, Panksepp found that most chills were reported during a
“most intense and dramatic” crescendo in “The Final Cut” performed by Pink Floyd
(p. 190). Since it was found that both “happy” and “sad” music could elicit thrill responses (p. 193), and given the physiological implications of a chill response, it seems reasonable to assume that a chill response is not related to the valence dimension of emotion, but perhaps more to the arousal dimension. This interpretation is tenable given that a crescendo, which consists of a movement from soft to loud, may produce an increase in arousal, all other features remaining constant.
- 209 - Introspective Inquiry Introspectionists, for the purpose of this dissertation, are people who have approached the question of emotion in music through their own experiences and thoughts. Although in stark contrast to the tradition of experimental psychology, introspective inquiry has a rich and long history. Again I emphasise that by examining different approaches to understanding the relationship between musical features and emotional response, we are more likely to derive a clearer picture. The earliest writers on this relationship were introspectionists. The ancients provide important examples (see Historical Overview on page 2 in Chapter 1). Such writers encompass a range of disciplines, including philosophy and musicology as well as film and theatre studies. A detailed review of the philosophy of musical features and emotional response is beyond the scope of the present study and there are several volumes which consider this problem (Budd, 1985; Fubini, 1987/1990; Katz &
Dahlhaus 1987-1992; Kivy, 1990; Lippman, 1986-1990; Peterson, 1994; Sloan, 1990).
Pertinent are those writings which may provide information suitable for generating testable hypotheses on the relationship between elements of music and emotional response.
61 See Collinearity on page 309 in Chapter 6. - 210 - Table Chapter 4 -12 Basic Terms and Their Associated Descriptions Abstracted from Cooke. Source: Gabriel (1978, p. 15).
Basic Term Pitch Combinations Description Quad No. 1 1-2-3-2-1 minor Brooding-an obsession with gloomy feelings. 2, 3 Trapped fear, a sense of inescapable doom. 2 5-3-2-1 minor A passionate outburst of painful emotion which then 2, 3 falls back into acceptance. Restless sorrow. 3 8-7-6-5 major A confident, incoming emotion of joy. All acceptance 1, 4 of comfort, consolation or fulfilment. 4 5-1-2-3 minor A bold acknowledgement of the existence of tragedy. 2 5 1-2-3-4-5-6-5 minor A powerful assertion of fundamental unhappiness. 2 6 1-2-3-4-5 major An outgoing expression of joy. 1 7 5-4-3-2-1 minor Final acceptance of and yielding to grief. Passive 3 suffering to the point of death. 8 1-2-3-4-5-6-5 major Innocence and purity. Ultimate happiness. 1, 4 9 8-7-6-5 minor An incoming painful emotion. An acceptance of or 3 yielding to grief. Passive suffering. 10 descending chromatic Weariness. Life ebbing away altogether. 3 11 1-2-3-4-5 minor An outgoing feeling of pain. An assertion of sorrow. 2, 3 A complaint, a protest against misfortune. 12 5-4-3-2-1 major Passively experienced confident joy. Accepting or 1, 4 welcoming blessings, relief, consolation, reassurance or fulfilment. 13 5-6-5 minor A burst of anguish. 2 14 5-1-2-3 major An outgoing expression of joy. 1 15 1-2-3-2 minor Brooding grief welling out briefly into a burst of 2, 3 anguish and then dying away again. Agitation. 16 5-6-5 major A joyous vibration. 1
Cooke and Makeig Deryck Cooke (1959) researched the Western tonal music literature to produce a lexicon of 16 basic melodic terms, each having a proposed emotional association
(Table Chapter 4 -12). The basic emotion terms provide information about melodic pitch contour and modality. In general, rising melodic contour represents an outgoing emotion and a descending contour represents an incoming emotion.62
Modality best represents the valence of the
62 The present two-dimensional representation of emotion does not account for incoming or outgoing emotion, A third dimension, labelled submissive-dominant, may be a suitable extension to account - 211 - emotion, with the major-happiness and minor-sadness associations. Although
Cooke’s arguments were supported by numerous examples he was still criticised for selecting pieces that fitted his hypothesis (Zuckerkandl, 1960). Gabriel (1978) tested the relationships empirically, but his failure to find support for the predictions might have been a reflection of the highly controlled environment in which he performed the experiments (at the expense of valid musical context).63 I have included suggested emotion space mappings of the basic terms onto the emotion space in
Table Chapter 4 -12.
Scott Makeig (1982) was also interested in pitch and emotion relationships. He proposed a theory of affective perception of musical intervals which was based on the work of Danielou who mapped intervals as combinations of frequency ratios onto a three dimensional affective space. For example, the interval of a third was sweet, suave and sensitive and the fifth was dynamic and active. Combining these intervals, according to Makeig, produced a just major seventh and should consequently produce an affective quality of the combination of the perfect fifth and the just major third. However, Makeig suggests that context is an important factor in determining the emotional interpretation of a musical interval. He cited the study by
Boomsliter and Creel (1963) who found that accomplished musicians preferred a version of the Marseillaise whose opening interval was related at a ratio of 27:20 rather than perfect fourth ratio of 4:3. Makeig then demonstrated to several musicians that the raised fourth interval of 27:20 expressed pride and glory
for emotional “direction”. Therefore, with suitable modification, Cooke’s theory is directly testable within a dimensional paradigm of emotion. 63 Gabriel’s study was mentioned on page 162. See Collins (1989), for a more detailed review of Cooke (1959). - 212 - more than did the 4:3 ratio, and sounded more in tune when imagined in the context of pride.
Sloboda (1984) was critical of theories such as those of Makeig and Cooke because there was no rule to determine which pitch intervals or motifs carry the strongest affective component in longer melodies. According to their theories, emotional response should change every time an interval or motif changes, yet, Sloboda argues, longer melodies containing a wide variety of intervals or several motifs may actually express very few emotions. In defence of these theories, perhaps emotion expressed by musical intervals is related statistically to the frequency of interval occurrences. If a particular interval occurs more often than others, then it might make a greater contribution to determining the emotional effect (in contrast with the additive effect proposed by Makeig). Gundlach (1935) used such an approach in the empirical arena by tabulating the number of each successive interval in an excerpt of music.
His findings do lend some support to this statistical defence of Makeig’s argument.
Peterson and Sorantin Mark Peterson (1994) proposed a theory that the aural variables of pitch, duration, volume, articulation and timbre determine the expressive qualities of music.
Peterson argued that one process through which this expression can be achieved is imitation. For example:
An imitation of disappointment is successful if it involves some but not all of
the following characteristics: the downward direction of pitches,
- 213 - small intervallic magnitude, slow tempo, soft volume, legato articulation, dark
timbre. (p. 95)
This physiognomic nature of Peterson’s theory is similar to that of Sorantin’s theory and to the approach of the Gestaltists (mentioned under Levi on page 164). These researchers posit that emotional states can be expressed by clusters of musical features. Erich Sorantin (1932) described the musical features appropriate for expressing lamentation, joy, longing and love.64 Sorantin provided several musical examples of each affect, and Rigg (1937, discussed above on page 180) has demonstrated that such theories are of great value for empirical researchers.
As outlined in Chapter 1, the bulk of musicologists make general, expressionist descriptions about music, or they make formalist analyses, void of emotional expression (see Historical Overview on page 2 in Chapter 1). However, another group can be added to the formalists and the expressionists — those who specify a relationship between musical features and emotional expression. Many such writers become known for their theories of the effect of one or two features upon the emotions. Peterson and Sorantin are unusual because they propose reasonably specific clusters of musical features of being suitable for expressing reasonably specific emotions. Although I make no assertion that specific emotions are necessarily expressed by music, using an emotional label to signify something more complex makes the research task significantly more tenable.
64 For examples Sorantin’s descriptions, see under Rigg on page 180. - 214 - Meyer Few would deny that Leonard Meyer’s Emotion and Meaning in Music (1956) has been the single most influential non-experimental work upon the empirical study of emotional response to music. Meyer’s main thesis was that a disruption of the expected flow in music produces arousal in the listener (p. 14). He makes clear his opposition to the notion that music should be interpreted in terms of specific emotions. For Meyer, happiness or sadness is subjective and susceptible to varying associations.
Private images, even when they are brought to consciousness without psychic
distortion, are problematical because it is almost impossible to trace the
relationships existing either between the musical stimulus and the image
processes aroused or between the image processes and the resultant affect. The
peculiar experience of an individual may, for example, cause a “happy” tune to
be associated with images of a sad occasion.
Even where the original association appears to be relevant and appropriate to
the character of the music being played, affective experience may be a result of
the private meaning which the image has for the particular listener. For
example, the image of a triumphal procession might within a given culture be
relevant to the character of a piece of music; but the association might for
private reasons arouse feelings of humiliation or defeat. Thus while the image
itself is relevant to the music, the significance which it has for the particular
individual is purely personal. (p. 257)
- 215 - It is such arguments that incline Meyer to examine music only in terms of its ability to induce generalised arousal.65 Meyer even tries to avoid the use of the term
“surprise” as a descriptor (p. 29). So, to apply Meyer’s theory to the two- dimensional paradigm of emotion (i.e., by transforming his numerous, exemplary, arousal producing musical structures onto the emotion space) is fraught with danger.66 Yet it is because Meyer is so meticulous in demonstrating the kinds of musical situations that lead to arousal, that his view (the futility of explaining responses in terms of specific emotions) could be subjected to empirical investigation.
Indeed, even before Meyer’s volume, significant empirical studies had revealed that people are able to report and agree upon fairly specific emotional responses to music.67 Meyer’s influential but disparaging view of atomistic empirical investigations (pp. 5-6) has, possibly, contributed to the dilatory nature of such research in the ensuing years (Sloboda, 1991; Waterman, 1996, p. 53).
To discuss the examples that Meyer provides on emotion aroused through unexpected musical events could constitute a separate volume. An example of one of Meyer’s descriptions is chosen here because of the reference made to rhythm, a musical feature commonly studied in the empirical literature
65 Such an approach is not new. For example, Edmund Gurney (1880/1966, p. 120) also believed that music could only express non-specific emotions. 66 I realise that I am taking some liberty in assuming that Meyer’s concept of arousal will transform to the arousal dimension of emotion. However, the literature reviewed suggests that if the transformation were not strictly isomorphic, there would still be at least some relationship between generalised arousal and the arousal dimension. Therefore, I will continue to use the two forms of arousal interchangeably. 67For example, the important empirical investigations of Hevner and Rigg were published several years before, yet, conspicuously, Meyer chose to cite an even earlier study by Heinlein (p. 228). Heinlein, also a dreaded atomistic empiricist, interpreted empirical data to suggest that the minor-sad, major-happy associations of Western culture were overstated, an interpretation which suited Meyer’s contentions. This interpretation has since been convincingly refuted by Crowder (1984). - 216 - and a feature that has been considered to be of global importance in emotional response by some (such as Gurney, 1880/1966 and Kratus, 1993). The example is taken from the “Liebstod” of Wagner’s Tristan and Isolde.
… Each of the opening measures establishes a clear iambic rhythm with
trochaic subgroups [Figure Chapter 4 -3a]. This organisation is supported by
the phrasing in the clarinets, the harmonic motion, and by the rhythm of the
text itself. Notice that the main rhythmic accent always occurs on the top note
of the ascending melodic line, after or before a skip of a fourth. When this top
tone appears, even though out of its expected order, it is given an important
accent partly because of its kinship with earlier accented tones [Figure Chapter
4 -3b] . Since it is the first tone of a group, it becomes the accented portion of a
trochaic group; and this change from an iambic rhythm to a trochaic one
constitutes a rhythmic reversal which in conjunction with the melodic changes
is a powerful affective force. (p. 113)
The question remains as to whether the effect perceived by many listeners could or could not be further refined than “a powerful affective force”, or, indeed, if there is any affect at all.
- 217 - Figure Chapter 4 -3 Opening Bars of Vocal Part from “Liebstod” in Wagner’s Tristan and Isolde Source: Meyer (1956, p. 113). a
b (reversal) *
In the context of the present study, the most important issue raised by Meyer’s approach is the temporal nature of musical structure and emotional response, and although this is an area still largely ignored by empirical researchers, it is considered a key to the research question which I am investigating. Research on the relationship between musical features and emotional response has been fixated on the selection of stable musical stimuli, expressing, if possible, a single emotion. Meyer’s work suggests that it is the changing structure of music that also provides a richness of experience, and therefore it may be profitable to examine music not at sections of stability and control, as do many empiricists, but at points of transience.
Correspondingly, it would become the direction of emotional response to the changing musical structure that would be of interest and perhaps shed further light on this long standing question.
Dowling and Harwood (1986), in following the work of Meyer (1956) proposed that melodic leaps in contrast to step-wise movement, can produce
- 218 - “subtle surprises”. In support of their claims, Dowling and Harwood provide evidence from works by Mahler and Verdi where a theme is modified by a leap greater than in previous renditions of that theme, and that such a leap may signify a heightened dramatic moment. A similar response is said to occur if, in the course of a repeated melody, a durational delay occurs. As Meyer put it, emotion is aroused when a tendency is delayed or inhibited. Like Meyer, Dowling and Harwood refer to the generalised arousal, and therefore, at best, only a direction of response can be implied on the emotion space.
Philosophers and Critics on Key Characteristics In his book on semiology and music, Jean-Jacques Nattiez (1990) provided a convenient table which summarised the various associations ascribed to the twenty four common keys of Western music as according to Marc Antoine Charpentier, Jean
Philippe Rameau, Ernst Theodor Amadeus Hoffmann and Albert Lavignac.68 The aggregated responses are shown in Table Chapter 4 -13. At a first glance, there appears to be some divergence of descriptions within most keys. However, by separating the major keys from the minor keys I found that, to some extent, the mode of the tonality was related to valence. But just as with the empirical studies, agreement was not unanimous. For example, Charpentier describes C major as
“warlike” and g minor as “magnificent”.
68 The sources cited by Nattiez were Antoine Charpentier’s (1634-1704) Résumé des règles essentielles de la composition et de l’accompagnement, Jean Philippe Rameau’s Traité d’harmonie of 1722, E. T. A. Hoffmann’s (1776-1822) Kreisleriana and Albert Lavignac’s la Musique et les musiciens, 1942. - 219 - Empirical work, also, has yet to shed light on this issue, based on the studies reported by Young (1991).69 He referred to crude key changing experiments conducted in the eighteenth century by Johann Joachim Quantz and another reported by an anonymous author, in addition to a more recent experiment by Martin B. Tittle.
Young implied that in the latter two experiments the pitch was probably a confounding variable, for changing key will also change pitch. He suggests that these latter experiments “would need to be repeated many times under controlled conditions” (p. 237). Given Young’s reserved view and the bemired picture that the
Nattiez collection presents, it is difficult to argue that the effect caused by change in key, if any, would not be swamped by a change in mode (if such a change were to occur) nor pitch (which will always occur). The issue becomes more complex in a time when equal temperament is the normal practice of tuning because equal temperament provides fewer perceptual cues to key.
69 For other studies focussing on key relationships see Francés, (1958/1988, p. 323-327), Steblin (1983) and Swinchoski (1947). - 220 - Table Chapter 4 -13 Associations Expressed by 24 Keys. The data are shown by key, aggregated from M. A. Charpentier, Rameau, E. T. A. Hoffmann and Lavignac. Adapted from Nattiez (1990, p. 125).
Tonality Associations C major cheerful, warlike, liveliness, rejoicing, simple, naive, free, common G major sweetly joyous, songs tender and gay, rustic, gay D major joyous, quarrelsome, liveliness, rejoicing, gay, brilliant, alert A major joyous, pastoral, liveliness, rejoicing, free, sonorous E major quarrelsome, shrill, songs tender, gay. or grand, magnificent, firmness, courage, brilliant, glittering, brilliant, warm, joyous, sonorous, energetic B major hard, plaintive, energetic Gb major soft, calm Db major alarming colour, full of charm, placid, suave Ab major gracious spirits, soft, caressing, pompous Eb major cruel, hard Bb major magnificent, joyous, storm, rages, rustic, springlike, noble, elegant, gracious F major raging, quick tempered, storms, rages, passionate dialogue, pastoral, rustic A minor tender, plaintive, tormented charm, simple, naive, sad, rustic E minor effeminate, amorous, plaintive, sweetness, tenderness, sad, agitated B minor solitary, melancholy, savage, sombre, energetic F# minor no descriptions C# minor brutal, sinister, sombre Ab minor country of eternal desire, dismal, anguish, very sombre Eb minor horrible, hideous Bb minor gloomy, terrible, gloomy songs, funereal, mysterious F minor gloomy, plaintive, tenderness, lament, dismal, morose, sorrow, energetic C minor gloomy, sad, tenderness, lamentation, sombre, dramatic, violent G minor severe, magnificent, tenderness, sweetness, melancholy, suspicious D minor solemn, devout, sweetness, sadness, serious, concentrated
Musicologists on Harmonic Structure Apart from the ground breaking work of Sloboda (1991), the serious inspection of the relationship between emotion and harmonic structures remains within the realm of pure musicology. Although Meyer has much to say on the matter, his view that only generalised arousal is produced by a variety of musical syntaxes, or their disruption, makes a detailed analysis of
- 221 - his ideas somewhat fruitless.70 In fact, there appears to be a resistance by pure musicologists in producing anything more specific than vague or general emotional descriptions.71 This is not necessarily a criticism of their approach, for these pure musicologists might be correct in assuming that no more than some general emotion may be deduced from this or that particular harmonic structure, or conversely, that the description of the emotion expressed by a structural analysis cannot be generalised to other similar examples. However, the empirical approach suggests that this lack of knowledge about the relationship between specific emotions and musical features should in itself be a reason for further investigation.
A rare instance of specific emotions being related to harmonic structure was cited in the work of Jean-Jacques Nattiez (1990) who, with reference to Max d’Ollone and
Robert Francés described some of the effects of the diminished seventh chord:
For Max d'Ollone, the diminished seventh chord expresses a particular feeling
of anxious expectation, and for this reason Puccini uses it in Madame Butterfly to
underscore Cio-Cio-San's vigil, as does Berlioz in Roméo et Juliette, and
Tchaikovsky in the Pathetique (1954 I: 113). The diminished seventh chord is a
pivot chord to many keys; it evokes aberration, uncertainty, trouble. If it
resolves to a perfect triad (as it
70 In my discussion of Meyer (from page 215), I suggested that his work would be suitable for testing. I stand by this view and emphasise that further empirical research on specific musical examples is required as distinct from further analysis of his view. 71 Walter Everett (1993) is another musicologist who, like Meyer, addressed emotions at a fairly general level but, unlike Meyer, admitted to the importance of the effect of musical mode upon valence. Everett’s approach is interesting because he applied highly formalist Schenkerian analytic techniques to the problem of understanding the expressive nature of music. Another departure from
- 222 - frequently does in Liszt, Schumann, or Chopin) it releases a feeling of light, of
triumph. On the other hand, the sense of aberration increases if seventh chords
follow one another in succession (as in Meyerbeer and Wagner) (see Francés
1958: 369), which explains why Wagner's music seems to be in such a constant
state of tension. (p. 121)
The diminished seventh has been applied to the composition of music for empirical work by Thayer and Levenson (1983) to aid in the expression of horror:
The horror … music was composed of a repetitive figure based on diminished
seventh chords and harsh timbres. (p. 47)
One of the reasons that empirical research has been slow in investigating the relationship between harmony and emotional response has been the difficulty in operationalising harmony along some perceptual continuum. When harmony is examined, psychologists prefer to dichotomise it into categories such as dissonant and consonant. At this level, again it is Francés and d’Ollone who make a contribution.
The auditory experience of harmonic sequences and of the most frequent
chords in the tonal syntax can engender a whole network of significations in
which the links belonging to the syntax acquire expressivity through the transfer
of syntactic relationships into the psychological domain. Thus, the consonant chords
seem to symbolise order, balance, rest; and the dissonant chords anxiety, desire,
torment (d'Ollone, 1952). For some, the melodic designs resting on a major
triad express states of stability, adequacy, and calm; for others, both major
the strict Schenkerian model was that Everett analysed popular music in addition to the works of the great German Romantics. - 223 - and minor triads express those states. It is necessary to specify that melodically
or harmonically only the tonic triad gives these sentiments fully; the other
chords give them to a lesser degree.
… while the resolution of a dissonance to a consonance is to us a synonym of
“calming, reconciliation, solution,” its resolution to another dissonance — an
uninterrupted chain of dissonances — is equivalent to “incessant movement,
agitation, passion, disorder, feelings of development” (d'Ollone, 1952, p. 186;
see also Hoffman, 1949). (cited by Francés, 1958/1988, p. 327-8)
These descriptions, then, suggest that dissonance in harmony leads to movement toward negative valence. In addition, this provides an explanation of why the minor mode is associated with negative valence and the major mode with positive valence.
As Helmholtz (1863/1954) proposed, the minor key contains more dissonances and therefore produces more negative valence.
Film and Theatre Writers Another area in which clues to the relationship between musical features and emotional responses may be found is in the literature about music for film and theatre. Film composers and directors, particularly during the silent movie era, have been interested in the connotations and designations that music can evoke and portray. This is reflected by the publication of film-music lexicons and resources such as Eugene Ahern’s What and How to Play for Pictures (1913), Lyle True’s How and
What to Play for Moving Pictures (1914), Giuseppe Becce’s Kinobibliothek (1919, cited in
Berg, 1976) and Ernest Rapee’s
- 224 - volumes Motion Picture Moods for Pianists and Organists: A Rapid Reference Collection of
Selected Pieced Adapted to Fifty-Two Moods and Situations (1924/1970) and Encyclopedia of Music for Pictures (1925/1970). Along with other volumes containing lists of musical selections and their associated emotions (Capurso, 1952/1970; Bonny &
Savary, 1990), this is a rich repository of information available for the investigation of musical features and emotion. Restriction in space and time precludes such analysis here, but the detailed examination of this body of information may be a profitable venture.
Instead, I am reporting the methods composers use to evoke or support emotional messages in film and theatre scores. Claudia Gorbman (1987) refers to “connotative cuing”, the purpose of which is to express:
moods and connotations which, in conjunction with the images and other
sounds, aid in interpreting narrative events and indicating moral/class/ethnic
values of characters. Further, attributes of melody, instrumentation, and rhythm
imitate or illustrate physical events on the screen. (p. 84)
Much Hollywood movie music is based on musical clichés and effects which serve as connotative cues. Gorbman briefly mentions some of the techniques used to achieve these cues. Another broad discussion is provided by Zettl (1973) who includes a convenient table (p. 343) summarising descriptive and expressive influences related to pitch, timbre, duration, loudness, attack, decay and mode.
- 225 - An example of a narrower examination of the musical features and their affects can be found in Marlin Skiles’s Music Scoring for TV and Motion Pictures (1976). Skiles, a composer and arranger, devoted a short chapter to the topic of instruments and their associated characters. He included a list of instruments that are suited to expressing particular “mood categories” (see Table Chapter 4 -14). Comparing this table with the empirical work of Behrens and Green (1993) and Gundlach (1935), for example, demonstrates the apparently precarious nature of making any assumptions about emotions which an instrument can evoke. By the same token, keeping in mind that all other musical features have been stripped, such listings may provide a baseline for comparison. That is, Table Chapter 4 -14 should be viewed as indicative of the kind of emotion an instrument could express, and not the kinds of emotion it must express.
Charles Berg (1976) researched the approaches taken by musicians to achieve desired effects when accompanying silent movies. For example, he cites the silent film critic
Clarence Sinn who refers to chase scenes (or “hurries”) as “having to be played ‘fast’ to convey the idea of ‘excitement’” (p. 187). This example suggests an intuitive relationship between increasing tempo to increase arousal. Film music analysis presents an interesting insight into not only the relationship between musical features and emotional response but also into the possible origins of these associations.
- 226 - Table Chapter 4 -14 Mood Categories and Associated Instruments. Source: selections from Skiles (1976, p. 70). ? denotes quadrant not determined.
Quality Quad Instruments Drama ? Low Strings French horns or trombones Low woodwinds English horn (low register) Bass flute (low register) Contrabass clarinet (low register) Piano Mystery 2, 3? Low flute Strings (tremolando) Contrabassoon (low register) French horns (stopped or muted) Novachord or Hammond Organ Yamaha organ Moog synthesiser Romance ? Violins (middle and high register) Bb clarinet (middle register) Oboe (with caution) flute (middle register) Bass flute (middle and low register) French horn (middle and high register) Bass clarinet (high register) Violas and celli (middle and high register) Vibraphone Humour 1 Bassoon (middle and low register) Oboe (middle and high register) Clarinet (all registers) Xylophone Bass clarinet (low) Horror 2 Contrabass clarinet Contrabassoon Tuba Low trombones Electronic instruments (effects) Piano (low bass clef) French horns (low register, stopped) Timpani Bass drum
- 227 - 2DES Transformation Summary The review of literature demonstrates a myriad of approaches to tackling the question of what musical features, or combinations of musical features, best express particular emotions. In order to integrate past research, the following subsections consist of operationalisation and transformation of musical features. Each musical feature is transformed onto a two-dimensional emotion space, based on the above findings and theories.
Throughout this summary, three important points must be emphasised:
1. The transformations of musical features onto the emotion space are
hypothetical and approximate. They are based on the research of Russell
(1980, 1989) and Whissell (1989) and Experiment II reported in Chapter 3.
2. Not all musical features are reported. These excluded features can
contribute to emotional expression. The reason for their absence, however
is because either (a) there was not enough information in the literature to
make an informed transformation onto the emotion space, or (b) the
musical features in question could not be expressed in terms of arousal or
valence, meaning that a transformation was not possible.
3. The musical features are isolated, not because they are capable of
expressing a hypothesised emotion on their own but because, with all other
features held constant, they are likely to shift responses in the direction
indicated on the emotion space from the central (neutral) position.
- 228 - The literature on emotional responses to music has resulted in a variety of variables which may be contribute to definition of the musical signal. The literature reviewed demonstrated a focus on the following features, which are assembled under one of the three basic groups of sound elements: loudness, pitch and duration:72
Loudness related: Duration related: • Dynamics • Tempo • Articulation Pitch related: • Note Onset • Mean Pitch • Vibrato • Pitch Range • Rhythm • Variation in Pitch • Metre • Melodic Direction/Contour • Register • Mode • Timbre • Harmony
For each feature, a definition is provided with the purpose of coding the feature, and the proposed position for different values of the variable are shown on the emotion space. I have attempted to restrict this list to features that are perceptually and musically meaningful. For example, I have omitted the regularly reported construct of complexity73 because it is not necessarily specific to a particular musical feature.
Findings are indicated separately where there is disagreement by one or a few researchers. The region is identified by the first letter of the author’s
72 The elements listed in each group are not necessarily exclusive from other groups. 73 For example, Gfeller, Asmus and Eckert (1991. p. 140) refer to the use of “music of higher complexity in order to evoke negative feelings”. While this may be taken to imply, for example, more
- 229 - surname followed by the last two digits of the year in which the finding was disseminated. Where a researcher matches a portion of the area reported by another researcher or researchers, the larger area takes precedence. For example, if author A shows that downward pitch contour moves arousal toward Quadrants 3 and 4
(sleepy with positive or negative valence), but author B finds that it shifts arousal and valence toward Quadrant 3, then the larger area (Quadrants 3 and 4) is indicated, provided that author B has not refuted the effect in Quadrant 4. The researchers whose findings are mapped onto the emotion space are listed below the sketch. Researchers who appear here are not necessarily taken from the literature review of the first part of this chapter.
This summary was used as a guiding framework in the selection of musical features suitable for parameterising the musical signals used in an experiment (Experiment
III) designed to investigate the continuous 2DES instrument. The experiment is reported in Chapter 5. A more detailed definition and coding procedure is discussed for the selected features in that chapter (Selection of Musical Features on page 256).
complex harmony, the complexity of the music can refer to several varying, interacting and concomitant musical features, rendering “complexity” of no direct interest in the present study. - 230 - Dynamics — the loudness of the music. Loudness has been calculated in numerous ways. One example of coding has been to rank the score markings, for example pp is ranked 1 and ff is ranked 5. Other common techniques include calculating the intensity or amplitude, and sometimes even without transformation based on Weber’s law of the sound signal. These untransformed and unweighted methods of coding are questionable from the point of view of perceptual validity. A more refined method of measuring and coding loudness is discussed in Chapter 5 (Loudness on page 262).
Figure Chapter 4 -4 Dynamics Transformed onto the 2DES
loud in speech
loud
moderate to low (GJ96)
soft
soft in speech
Sources: Dolgin and Adelson (1990), asserted but not tested empirically; Gabrielsson and Juslin (1996); Heinlein (1928); Kotlyar and Morozov (1976); Namba Kuwano Hatoh and Kato (1991); Nielsen (1983); Scherer (1981); Watson (1942); Gabrielsson and Juslin (1996); Imberty (1975); Jackendoff (1991); McFarland (1985); Nielzén and Cesarec (1982b).
- 231 - Mean Pitch — the absolute, average pitch across a section of music. The pitch series is usually taken across the melodic line. A definition of pitch is discussed in Chapter 5
(Melodic Pitch on page 270).
Figure Chapter 4 -5 Mean Pitch Transformed onto the 2DES
high pitch
low pitch
Sources consulted for transformation: Scherer’s (1981); Scherer and Oshinsky (1977); Thayer (1986); Collins (1989).
- 232 - Pitch Range — the absolute values of the difference between the highest pitch and the lowest pitch (usually melodic) in a section of music.
Figure Chapter 4 -6 Pitch Range Transformed onto the 2DES
wide range
narrow range
Sources: Scherer (1981); Gundlach (1935).
- 233 - Variation in Pitch — relatively small deviation away from a central pitch. For example, a note played at exactly the written pitch contains no deviation, whereas the same note played sharp or flat is a deviation. For faster oscillations to and from the main pitch, see
Vibrato (on page 245).
Figure Chapter 4 -7 Variation in Pitch Transformed onto the 2DES
large variation
large small variation variation (SO77) (SO77)
small variation
Sources: possibly Makeig (1982); Scherer (1981); Scherer and Oshinsky (1977).
- 234 - Melodic Direction/Contour Melodic direction or melodic contour may be defined as the gradient, or rate of change of melodic pitch. A positive contour suggests a rising pitch and a negative contour suggests a falling pitch.
Figure Chapter 4 -8 Melodic Direction/Contour Transformed onto the 2DES
Sources: Gerardi and Gerken (1995); Peterson (1994); Scherer and Oshinsky (1977).
- 235 - Register — the octave in which a piece or a musical line within a piece is played. For example, playing a melody in an upper register means playing it an octave higher (or more) than normal. This definition is at odds with conventional interpretations of register and tessitura. The reason for the present definition is that, as Hevner (1937) and Young (1991) report, a melody played in a transposition that was not related by the octave to the original, would also constitute a change of key, a different musical feature. In addition, changing instrumental register (i.e., playing in an instrument’s high or low register, as the conventional definition applies) is accounted for by other variables, such as timbre.
Figure Chapter 4 -9 Register Transformed onto the 2DES
Source: Hevner (1936), but referred to as pitch.
- 236 - Mode — the series or gamut of notes from which the notes of a piece are selected. Mode infers a pitch relationship between the notes. For example, the major mode and the minor mode consist of seven notes (degrees) of the twelve notes available in the
Western tonal system, however the minor differs from the major in that its third degree is always one note flatter than its major counterpart. In addition, the sixth and seventh degrees of the minor mode may be altered with respect to the corresponding degrees of the major mode.
Figure Chapter 4 -10Mode Transformed onto the 2DES
Sources: Collins (1989); Crowder (1984); Dolgin and Adelson (1990); Flowers (1988); Gerardi and Gerken (1995); Gregory, Worrall and Sarge (1996); Heinlein (1928), after Crowder (1984); Hevner (1935); Kastner and Crowder (1990); re-analysis of Sherman (1928).
- 237 - Timbre — the tone colour of a sound. This is a highly complex element in sound and is used inconsistently in the literature due to its various levels of meaning (Krumhansl,
1989). Timbre is affected by changing the harmonic structure of a sound, and because harmonic structure is one of the features that provides a musical instrument with its character it is not uncommon to see the term “instrument” and “timbre” interchanged. Families of instruments have also been grouped in such a way. For example, when a woodwind section is being examined, we may refer to its
“sonority”. In the present study sonority will still be treated as timbre.
Another method is to describe the timbre of a sound in terms of its perceptual qualities. For example, a bright, sharp sound is likely to contain more energy in the upper harmonics than another sound that is judged dark or soft (Kendall &
Carterette, 1996; see Centroid on page 266 in Chapter 5). Also, harmonics that are particularly close together tend to be judged as sounding rough or harsh (Sundberg,
1989, pp. 70-75). An interesting attempt to operationalise timbre is by treating the number of harmonics in the sound as an independent variable. Scherer and
Oshinsky (1977) used such a strategy, treating the variable as dichotomous, with either the value of “many harmonics” or “few harmonics”. Because a clear continuous relationship has not yet been found that relates perceived tone colour to the combinations of harmonics that cause these perceptions, timbre is usually treated as a categorical variable, with each instrument, instrument family or
- 238 - perceptual description treated as a value of a nominal variable.74 Variation in coding strategies makes the integration of results difficult.
Figure Chapter 4 -11Timbre Transformed onto the 2DES
Sources: Behrens and Green (1993); Gabrielsson and Juslin (1996); Gundlach (1935); Skiles (1976); Scherer and Oshinsky (1977).
74 See also the discussion of Centroid on page 266 in Chapter 5. - 239 - Harmony — the vertical or simultaneous combination of notes. Notes can be combined to form harmony by being played at the same time, or implied harmony can be deduced by a series of successive notes. Because of the many possible combinations of musical notes, and because the Western tonal language imposes some restrictions on the kinds of harmonies that are used in certain styles of music, operationalising harmony becomes particularly difficult. Like rhythm, the most common solution has been to code harmony on a perceptual continuum, such as simple to complex or consonant to dissonant. This tends to bunch the wide range of dissonances used in Western tonal music together to a great degree, meaning that it is difficult to distinguish one kind of dissonance (such as a melodic appoggiatura) from another (such as a dominant seventh).
- 240 - Figure Chapter 4 -12Harmony Transformed onto the 2DES
Sources: Collins (1989); d’Ollone (1952) cited by Francés (1958/1988, pp. 327-8); Dolgin and Adelson (1990); Hevner (1936); Nattiez (1990); Sloboda (1991); Thayer and Levenson (1983); Thompson and Robitaille (1992).
- 241 - Tempo — the number of musical beats that occur per unit of time, usually ranked along a continuum from slow (few beats per unit time) to fast (many beats per unit time). A beat is the basic subdivision of each bar of music. In Western music notation this is indicated by a combination of tempo and time signature. For example, a fast 6/8 contains two dotted crotchet beats per bar, but a slow 6/8 contains 6 quaver beats per bar. Tempo coding is discussed in more detail in Chapter 5 (Tempo on page
273).
Figure Chapter 4 -13Tempo Transformed onto the 2DES
fast
slow
Sources: Collier (1996); Dolgin and Adelson (1990); Flowers (1983); Gabrielsson and Juslin (1996), except ‘fear’ (Quadrant 2) was expressed by irregular tempo; Gundlach (1935); Hevner (1937); Imberty (1975); Namba, Kuwano, Hatoh and Kato (1991); Nielzén and Cesarec (1982a); Rigg (1940) re- analysed; Scherer (1981); Scherer and Oshinsky (1977); Thayer (1986); Thompson and Robitaille (1992).
- 242 - Articulation/Duration Articulation is the shaping of a sound. For example, a sound can be short and separated from one another (staccato articulation) or long and connected (legato articulation). More technically, articulation refers to the duration of a note. A short note duration tends toward staccato, and a long note duration tends toward legato.
Therefore, I have used articulation to also mean duration.
Figure Chapter 4 -14Articulation/Duration Transformed onto the 2DES
Sources: Baroni and Finarelli (1994); Collins (1989); Dolgin and Adelson (1990); Gabrielsson and Juslin (1996); Kratus (1993); Nielzén and Olsson (1993); Peterson (1994).
- 243 - Note Onset — the attack of a note. That is, the temporal difference between the time at which a note first starts and the time at which the steady state portion of that note begins. For example, the fastest note onset time occurs when the steady state part of a note begins as the note is played. Note onset is a characteristic of an instrument as well as an expressive device. For some instruments, such as the harpsichord, note onset time cannot be adjusted by expressive means.
Figure Chapter 4 -15Note Onset Transformed onto the 2DES
rapid onset
slow onset
Sources: Gabrielsson and Juslin (1996); Kotlyar and Morozov (1976).
- 244 - Vibrato — the periodic wavering of pitch or intensity, referred to by Gabrielsson and Juslin
(1996) as pitch and intensity vibrato. The two kinds of vibrato are not often distinguished in the literature. Vibrato can be described by two parameters: depth and rate. Depth refers to the distance between the extreme changes in pitch or loudness, with “deep” referring to a large change and “shallow” referring to a small change. Rate refers to the number of waverings that occur per unit of time and is sometimes referred to as being either fast or slow.
Figure Chapter 4 -16Vibrato Transformed onto the 2DES
Sources: Gabrielsson and Juslin (1996), for electric guitar.
- 245 - Rhythm In the broadest sense rhythm can refer to the ensemble of musical features related to the temporal aspects of music, as distinct from the pitch, loudness and timbre aspects of music. However, it can even be argued that rhythm has a relationship with loudness through accents. A narrow definition of rhythm is the interrelationship of note durations. For example, what is referred to as a dotted rhythm (which may consist of, say, a dotted quaver followed by a semiquaver) is one kind of rhythm.
The metrical structures of poetry, such as the iamb (short-long), trochee (long-short) and the anapaest (short-short-long) are further examples. Due to the many groupings and subgroupings of different durational units possible, and due to its elusive relation with an objectively quantifiable construct, rhythm is extremely complex and difficult to operationalise. The most common and perhaps somewhat oversimplistic method of coding rhythm is to categorise it according to whether it is perceived as being rough, smooth, even or uneven. Another method is to treat the perceptual property of rhythm as a continuum from simple to complex (e.g.,
Pressing, 1997). These problems and complexities alone are enough reason for the lack of consistency in the literature on how rhythm may be transformed onto an emotion space.
- 246 - Figure Chapter 4 -17Rhythm Transformed onto the 2DES
sophisticated rhythm (C89)high pitch rhythmic activity pitch contour up(K93) rough rhythms (G35) smooth rhythms (G35)
flowing motion (H36)
pitch contour down
high pitch (G35)
low pitch
Sources: Collins (1989); Gundlach (1935); Hevner (1936); Kratus (1993).
- 247 - Metre — the grouping of beats in music. The two most common groupings are simple meters (divisible by two) and triple metres (divisible by three). Compound metres are divisible by both two and three. For example, the metre of 6/8 is compound and often falls into two beats, each subdivided into three.
Figure Chapter 4 -18Metre Transformed onto the 2DES
triple meter (K93)
duple meter (K93)
Sources: Kratus (1993).
- 248 -
Chapter 5 Continuous Response to Music
I proposed in Chapter 2 that an instrument for measuring emotional response to music must be able to do so both meaningfully and continuously. In Chapter 3 an experiment (Experiment II) was reported which demonstrated that the newly developed Two-Dimensional Emotion Space (2DES) satisfies the first of these criteria, but the second criterion was not addressed.
The aim of this chapter is twofold: (1) to report modifications made to the
EmotionSpace Lab software controlling the 2DES such that it could measure continuous emotional responses to music, and (2) to report two experiments intended to test the validity (Experiment III) and the test-retest reliability
(Experiment IV) of the modified instrument. The data collected in Experiment III were then used to address the main research question of the relationship between emotion and musical features. The analysis of these data is reported in the chapters that follow (Chapter 6 and Chapter 7).
- 249 - Experiment III: Continuous Two-Dimensional Emotion Space
Aims
The use of the 2DES was extended from the measurement of emotion expressed by static stimuli, such as words and pictures of faces, to measuring emotion expressed continuously to music. As this instrument had no precedent,75 the experiment was largely exploratory. The specific aims of the experiment were:
• to determine the spread of emotions expressed by musical stimuli
according to the 2DES,
• to test the construct validity of the continuous 2DES instrument, and
• to examine the relationship between musical features and emotional
response.
Since the emphasis of the present chapter is to demonstrate the reliability and validity of the 2DES, the analysis of the third aim, which is more concerned with the principal research question of this dissertation, will be presented in Chapters 6 and 7.
75 Frede Nielsen (1983, 1987) is the pioneer of continuous self-report emotional response research, and his research was also highly exploratory. I am reluctant to use his approach as my model for experimental design and analysis for three primary reasons: (1) Nielsen examined response along a single dimension (tension); (2) Analysis of lower level features were either approximate (as for melody) or not clearly explicated (as for loudness in the 1987 paper); and (3) Analysis was based on visual inspection — no inferential statistical time series techniques were applied. Tyler’s (1996) instrument was developed independently of my own. - 250 - Method
Modification of 2DES The EmotionSpace Lab stack was modified so that it could accurately record and synchronise participant responses with the musical stimulus. This was achieved by installing CoreCD (Sudderth, 1995) software into the stack as an “external function”
(Goodman, 1993, pp. 929). CoreCD enables the control and reading of audio compact disks (CDs). The software required CD-ROM hardware and appropriate audio CD-
ROM software. CoreCD provided a function that enabled start, stop and pause control; music track selection and detection; and the external function could return the time elapsed (in minutes and seconds) within a playing track. EmotionSpace Lab read the track number and time elapsed value once per second and stored it in tandem with the cursor coordinates (on the emotion space) while the music played.
Additional information such as a unique identifier for the music track being played and the bar numbers corresponding to each unit of time were also collected by
EmotionSpace Lab.
The modular design of EmotionSpace Lab allowed it to have an extra phase added which would contain the sequence of cards, messages and dialogs required for the procedures of the experimental investigation. The chronological flow of the program is outlined in Table Chapter 5 -1. For details of wording and screen layout of each card, message or dialog, see Appendix D from page 484). The Sound Check card
(Appendix D, Display 95 on page 485 to Display 97 on page 486) asked the participant to put on headphones. To ensure that headphones were on and that the audio signal could be heard, the instruction to continue was transmitted by pre- recorded voice over the
- 251 - audio output channel of the computer. Correct response to this instruction allowed progress to the next card which indicated what was about to happen and what the participant was required to do (Appendix D, Display 98 on page 487).
Pilot work demonstrated that participants found it difficult to make the distinction between describing the emotion expressed by the music and reporting their own emotional experience. To help circumvent this problem, a prominent message was presented reminding the participant that the task was cognitivist (Appendix D,
Display 99 on page 487). At this point the participant was ready to commence listening and responding.
By moving the cursor to the centre of the emotion space, a countdown began
(Appendix D, Display 100 on page 488). If the cursor was moved away from the centre, the countdown was aborted. After the countdown, the music began playing and responses were recorded (Display 101 on page 488). At the conclusion of the piece a message appeared, indicating that the task was complete. This was followed by a series of questions related to the piece that had just been presented (Appendix D from page 489).
At the conclusion of the questions, the participant had the opportunity to rest, access the help module or continue with the next musical example (Display 109 on page
492). When responses to the four musical examples were completed, EmotionSpace
Lab moved to the concluding sections of the experiment (Appendix B from Display
75 on page 472).
- 252 - Table Chapter 5 -1 Flow of Music Phase Module used in Experiment III as Controlled by EmotionSpace Lab
Section Flow Card, Message or Dialog Next Example
Introduction START • Music Phase Sound Check ←→ • Sound Check • Sound Check Help ←→ • Sound Check Feedback Instructions ←→ • Music Phase Instructions ←→ • Cognitivist Reminder Message ←→ • Prepare to Start ← 2DES ←→ • Recording Questionnaire ←→ • Post Listening Questionnaire Information ←→ • Overall Response ←→ • Overall Response Feedback ←→ • Word List • Word List Help • Non-Word List Dialog ←→ • Word List Feedback
→ • End of Example → ? [→ END]
Help • Go to Help Module ←
Arrows denote the next step of flow i.e. followed by all participants. Two way arrows (←→) denote card, message or dialog visited by all participants followed by return to next step of the flow. Vertical line without arrow heads () denotes optional card, message or dialog which is accessible to the participant prior to continuation of the flow. ? denotes that direction of flow is determined by the participant. [→ END] denotes that when all stimuli have been played, the program intervenes in order to exit the flow loop. Details of each card-message-dialog are shown in Appendix D from page 484
Stimuli Stimulus selection criteria for the experiment were:
1. pieces of a familiar style,
2. a variety of emotions expressed,
3. pieces contain no words that could be understood, and
4. aggregate length of pieces restricted to about 20 minutes.
Kratus (1993) deliberately chose music of one, similar style. Although several researchers advocate the use of a variety of styles in studies related to emotional response (e.g., Hargreaves, 1986; Hargreaves & Coleman, 1981),
- 253 - Kratus’s approach is credible. By selecting music from one style, the researcher is keeping one variable (musical style) constant in the extremely complex web of variables with which he or she is concerned (Terwogt & Grinsven, 1991, also take this approach).76 As a caveat, the researcher making such a decision should be aware that the results of the study may not be generalised to music outside that style.
Alternatively, the experiment should be repeated with other styles of music, and in so doing, a broader generalisation may be vindicated or refuted.
Selecting music that expresses a variety of emotions is an important part of experimental design (Roberts & Wedell, 1994), but it is particularly important in instrument development. The minimum requirement is that the examples express emotions in each of the four quadrants of the emotion space. Although such a requirement can only be confirmed post hoc, measures were taken to ensure that this was a likely outcome.
Most researchers of emotion in music avoid using selections with understandable words, unless it is the relation between the words and the music that is of interest.
Selecting pieces without words ensures that the possible confound of emotion being conveyed by words, instead of the music, is alleviated.77
The maximum time considered acceptable for listening to music for experimental study was modelled on the Madsen, Brittin and Capperella-Sheldon study (1993), in which responses to a single extract of
76 See also Limitation 1: Romantic, Western Tonal Music on page 24 in Chapter 1. 77 I use the term “alleviated” instead of “eliminated” because one could argue that some music may be associated with words, and the mere playing of the music activates those words and their meaning. - 254 - twenty minutes duration were recorded. Therefore, care was taken to select music that did not exceed a total of twenty minutes. This duration may seem surprisingly long in the light of some past research where, for example, Asmus (1985) uses three relatively short pieces to reduce participant fatigue. However, Asmus asks participants to make numerous responses at the end of each piece, and this may place great demands on memory that are not present when responses are continuous.
With all these considerations kept in mind, a selection of potential pieces was examined. Music-Emotion lexicons and empirical studies were consulted, and questionnaires were distributed to highly experienced musicians.78 Some of the strong candidates were movements from the Planets by Gustav Holst and movements from Peer Gynt orchestral suites no. 1 and 2. A list of potential selections was made, placing each piece into the quadrant that it was deemed most likely to express.
In order to avoid disrupting the participant during the experiment, a single CD was used. After an extensive search of a variety of commercially available CDs, four pieces appearing on the list were chosen from a compilation CD, as listed in Table
Chapter 5 -2. The hypothesised quadrant expressed by each piece is shown in the right hand column. Three pieces
78 I conducted two pilot studies — an interview study and a questionnaire study, both approaches asking the participants to indicate pieces that expressed a variety of emotions. The 11 participants were highly experienced musicians. Although they were free to choose any musical style, all but one participant chose Western Art music, and of these, many pieces were from the late nineteenth century instrumental repertoire. One participant chose music from the jazz idiom. Although the bias in
- 255 - hypothetically expressed emotions in all four quadrants — “Slavonic Dance” No. 1
Op. 42 by Dvorak (Slavonic Dance), “Morning” from Peer Gynt by Grieg (Morning) and the Adagio movement from Rodrigo’s Concierto de Aranjuez (Aranjuez).
However, these pieces had a total length of 17 minutes and 15 seconds. Because the maximum length was set to 20 minutes, a short Polka by Johan Strauss Jr. and Josef
Strauss (Pizzicato) was chosen. Although the piece duplicated Quadrant 1, it was an appealing selection because it was considerably contrasting in character to the other pieces, being performed with pizzicato articulation throughout.
Table Chapter 5 -2 Stimuli Used in Experiment III79
Title Composer Performers Length80 Abbreviation Qua d “Slavonic Antonin Slovak 3:45 Slavonic 1 Dance”, Op. 46 Dvorak Philharmonic Dance No. 1 Orchestra, Zdenek Kosler (conductor) “Pizzicato Johann (Jr.) and [not mentioned] 2:30 Pizzicato 1 Polka” Joseph Strauss “Morning” from Edvard Grieg CSSR State 3:38 Morning 4 the incidental Philharmonic music to Peer Orchestra, Stephen Gynt Gunzenhauser (conductor) “Adagio” from Joaquin Gerald Garcia 10:52 Aranjuez 2 & 3 Concierto de Rodrigo (guitar), CSSR State Aranjuez for Philharmonic guitar and Orchestra, Peter orchestra Breiner (conductor)
response toward Western art music reflected the bias within the participant pool, Sloboda (1991) and Collins (1989, p. 26) found similar response bias from their participants. 79 All selections are from Discover Classical Music, CD 2. (1993) HNH International Ltd. 8.550008-9 . 80 This is the length of the track as it appears on the CD cover. The time includes a few seconds of silence. - 256 - Selection of Musical Features In the literature review of Chapter 4 a variety of musical features were reported as potential predictors of emotional response. It was beyond the scope of this study to provide a comprehensive analysis of all musical elements and their relationship with emotions. However, it was essential to select musical features which, together, could encompass a reasonably adequate representation of the music.
My thesis is that emotional response can be expressed quantitatively and meaningfully in terms of combinations of musical features. As a preliminary step, I therefore need to be able to quantify the musical features to be used as predictors (or regressors) of emotional response. As reported in Chapter 4, methods of coding musical features have varied widely. Important and constructive criteria for coding musical features are that they should be perceptually relevant and objectively quantifiable. For example, it makes sense to code loudness as a continuum from soft to loud because we are able to perceive and distinguish different gradations of loudness. Consequently, by selecting musical features where such perceptual gradations occur, we are likely to obtain data that indexes an objectively quantifiable aspects of music. This rules out coding which involves dichotomisation of potentially useful information. It also means that analytic techniques which could deal with multilevel variables, such as correlation and regression modelling
(L’Hommedieu, 1992), would be employed.
The conditions for initial musical feature selection may be summarised as follows:
- 257 - • Together, the features provided a reasonably adequate representation of the
musical stimulus;
• Theory existed that allowed generation of hypotheses on at least one
musical feature’s relationship with emotion; and
• The features could be coded as objectively quantifiable, perceptually valid,
multilevel variables.
Only five musical features were selected initially. The limitation was made because too many musical features may invalidate the regression model and increase the chance of falsely detecting a relationship (Type I error; see Selecting Lags on page 307 in Chapter 6).81
In order to be meaningful, the musical features should represent some aspect of the basic, separable elements of music:
Pitch
Articulation
Rhythm
Tempo
Dynamics
Texture
Timbre
Harmony
Because of the restriction to five musical features, not all of these elements could be represented. Not represented were rhythm, articulation and
81 The limitation to five variables was a function of the sample size and the number of lags. See Selecting Lags on page 307 in Chapter 6. - 258 - harmony. The primary reasons for their absence was that they could not be coded as multilevel variables or they could not be coded easily and accurately. Absence of harmony coding was further justified by the circumstance that the music consisted of mostly tonal harmony. However, in the final analysis all musical features were considered to enhance explanatory power and to explain anomalies (see Chapter 6 and Chapter 7).
Of the eight elements, those represented were pitch, tempo, dynamics, texture and timbre. Self-report emotional response to the first three have been investigated by past researchers (see Figure Chapter 4 -8 on page 235, Figure Chapter 4 -13 on page
242, and Figure Chapter 6 -1 on page 304 respectively, in Chapter 4). Exploratory variables were formulated from the last two features in the form of the number of instruments playing (for texture) and centroid of the frequency spectrum (for timbral sharpness). They were chosen because they complemented the other three features and they could be coded as mulitlevel variables. A refined definition of each musical feature and the method of coding is described in the following subsections.
Texture Musical texture provides an opportunity to code a higher level musical feature and to investigate a parameter that has been previously neglected in emotion-music research (Levy, 1982; Bruner, 1990). The term, however, is highly ambiguous. The
New Grove Dictionary of Music and Musicians (Sadie, 1980) states that texture is
- 259 - A term used loosely when referring to any of the vertical aspects of a musical
structure, usually with regard to the way in which individual parts or voices are
put together. (p. 709)
This broad definition does not provide a firm basis for coding texture. One way of defining texture, as the New Grove entry goes on to indicate, is on the distinction between homophonic and polyphonic textures. This poses the problem of a lack of an established coding continuum from homophonic to polyphonic. Dichotomisation, instead of multilevel coding, would be the main option. Further, the music selection, being essentially in a Romantic style, is largely homophonic. Such a coding of texture would not help in differentiating important musical events. Although the definition is not incorrect, this interpretation of texture is not suitable here.
The Macquarie Dictionary (1985) defines musical texture as “(a) A combination of timbres and tone colours. (b) The pattern of relationships between the parts of a musical form” (p. 1757). It is definition (a) which provides a clue to suitably coding texture. Texture may be simply coded as the number of instruments playing at any given time. A similar approach was used by Nielsen, (1987) who referred to the variable as “instrumentation”.82 My coding procedure involved simply counting up the number of independent voices at a given point in time. The decision as to whether or not to count a voice was largely pragmatic, and the following rules were devised:
82 Nielsen (1987) also referred to the “thinness” of texture, no doubt in the sense of Meyer (1956) in that a thin texture should lead to an increase in tension. This was more a comment in passing than a fully fledged thesis. No other references to texture were cited that used a coding strategy similar to that which I am proposing. - 260 - 1. An instrument that doubled another instrument of the same section and in
the same octave was omitted from the count. For example, two flutes
playing in unison was counted as only one. A cello and double bass both
playing C3 was likewise counted as only one because they were both
members of the string section.83 However, a flute and an oboe playing the
same note would be counted as two because they belonged to different
instrument families.
2. The same instrument producing two different notes simultaneously
counted as two notes. A violin playing double stopped added two to the
texture count.
3. Sustained notes were added to the count. Excluding doublings, as
discussed above, any instrument that was playing, as according to the
musical score, was added to the texture count.
This method of coding possesses several potential problems. A blanket count of instruments on a musical score, playing at a given point, is not necessarily perceptually valid — Instruments that are meant to be playing according to the score do not necessarily contribute to the texture of the sound in the performance.
Whether this is due to poor orchestral balance during performance and recording production, or due to poor orchestration during composition, it was an issue that was of concern on occasions. Further, a simple count does not distinguish the different sound produced by 10 brass and percussion voices versus 10 string and
83 My use of the term “section” appears somewhat tenuous here. Celli and double basses are really members of the same group (the chordophone group) rather than the same section. However, the term “section” helps to distinguish instrumental timbre; for example, the flute section from the clarinet section, and the trumpet section from the horn section. A violin and a viola playing the same pitch will sound far more homogonous than these other combinations, and so the distinction I use when referring to a “section” is necessary. - 261 - woodwind voices. These problems were not considered prohibitive, but further research is required into the use of this variable.
An additional problem was that loudness and texture may often be measuring essentially the same thing.84 When the orchestra becomes louder, more instruments are likely to be playing. This suggests that texture is redundant if loudness is already being coded. However, texture was kept as one of the variables because there were clear signs of some independence from loudness. Indeed, composers used a full orchestra (full texture) in very soft passages, and conversely had brass and percussion only (a “thinner” texture) playing quite loudly. In its favour, this method of coding texture was objective and straight forward.
There was no predictive theory cited in the literature regarding texture. The use of this variable and its relationship with emotion is therefore exploratory. The texture of each of the four pieces is plotted in Appendix E from page 493.
Loudness Musicians use the term dynamics when referring to loudness. A system of notating dynamics was developed in Italy from the sixteenth century and remains firmly rooted in the Western music-literate world. The system has evolved to indicate graded dynamics from very soft, pianissimo, through to very loud, fortissimo, as well as gradual rises: soft to loud crescendo and loud to soft diminuendo. However, loudness is in part both subjective and context dependent. Consequently, such a system is mainly suitable for
- 262 - relative changes in loudness (Donington, 1980; Campbell & Greated, 1987).85 For example, a passage marked forte should be played louder than a preceding passage marked piano, but an orchestra playing piano is likely to sound louder than a clarinet playing mezzo piano (slightly “louder” than piano). In order to code loudness, then, a perceptually more stable scale was required.
In terms of acoustic parameters, the loudness of a simple tone is mainly a function of its intensity and frequency. The human ear is most sensitive in the band of frequencies from 300 to 4,000 Hz, the range in which important speech information is transmitted (Goldstein, 1989, p. 393). Therefore, a simple tone of fixed intensity will sound louder in this region of frequencies than for higher or lower frequencies.
Psychoacoustic experiments by Fletcher (1953), Stevens (1955) and others were used to determine the exact nature of the human’s sensitivity to loudness. From these studies a variety of loudness scales were developed.
The intensity of the sound signal has a strong relationship with loudness, and this relationship is consistent with Fechner’s psychophysical law where, as with pitch
(see page 271), the perceptual quantity is linearly related to the logarithm of the physical property. For loudness, this transformation is measured in decibels (dB).
As mentioned, for the pure tone, perceived loudness also varies with frequency, and therefore the decibel scale was modified by experimentally determined weighting curves. Different
84 This problem is referred to as collinearity, and is discussed in more detail under Collinearity on page 310 in Chapter 6. 85 Campbell and Greated (p. 107) proposed an approximate, absolute relationship between dynamic markings and loudness levels. - 263 - weighting curves were required for different signal intensities. A commonly used weighting scheme is A-weighting (dBA), intended to calculate loudness level of low intensity, pure tone sounds. True measures of loudness are far more involved and complex (Moore & Glasberg, 1996; Zwicker & Scharf, 1965; Moore, Glasberg & Baer,
1997; Campbell & Greated, 1987; Rossing, 1990).
The measurement of loudness level using the dBA scale is intended for pure tones.
However, music rarely contains pure tones. Complex tones, and several tones occurring together do not add to the loudness in a simple manner. The effect of various kinds of masking can make a sound quieter than the dBA scaling predicts.
Masking refers to a physiological effect, where one sound component causes the basilar membrane to become highly active in a particular frequency region, meaning that another sound component close to this stimulating frequency is swamped and therefore goes unnoticed (Rossing, 1990, pp. 101-105). Keeping in mind that dBA does not account for several loudness-affecting aspects of sound, the coding was used as a very rough approximation of loudness (Rossing, 1990, p. 99; Cowan, 1994, pp. 36-37).86
A plot of the A-weighting function is shown in
Figure Chapter 5 -1. The formula for the A-weighting curve for any single frequency band may be stated as:87
86 The headphones used in Experiment III had fairly poor response in the bass frequency region. Since low bass response (relative to other traditional weighting schemes) is one of the characteristics of the dBA scale, dBA as a measure of loudness is further justified. I thank Densil Cabrera for pointing this out to me. 87 I am grateful to Assoc. Prof. Joe Wolfe for providing me with this formula. - 264 - Equation 5-3 2 4 (12200 × fn ) An ( fn ) = 0.5 0.5 f 2 + 20.6 2 f 2 +12200 2 f 2 +107.7 2 f 2 + 737.9 2 ()n ()n ()n ()n
Where An(fn) is the untransformed (physical domain) A-weighting for the
frequency band number n, with centre frequency, fn. This weighting was used
to multiply the corresponding individual intensity components, in,s within the nth sample. The weighted components were then summed across the N
frequency bands (“vertically”) and then summed again across each of the S
samples (“horizontally” in time) to give the overall estimate of loudness for
the tth second of the music. Finally, this value was logarithmically
transformed into the perceptual domain using 1,000 Hz as the reference. This
procedure can be expressed as:
Equation 5-4 S N A ( f )i ∑∑()n,s n,s n,s dBA(t) = 20 log s=1 n=1 10 S × A(1,000) Where dBA(t) is the A-weighted loudness of the physical signal for the tth
second of music. Because the reference tone was 1,000 Hz, A-weighting
produces no change at this frequency. For frequencies below 1000 Hz and
above 6,000 Hz, A-weighting attenuates the signal intensity (see Figure 5-1).
Three procedures were used to calculate loudness: (1) a graphical printout
using standardised loudness meter readings1, (2) an algorithm written by myself in Hypertalk and based on and Equation 5-3 and Equation 5-4, and (3) an
88 A-weighting was produced by a Bruel and Kjaer Type 2609 Measuring Amplifier, and tape was produced by a Bruel and Kjaer Type 2306 Level Recorder.
265 algorithm by Cabrera (1997) written in CSound.88 The Hypertalk algorithm required the sound spectrum data as its input. This was generated by converting each stimulus audio CD track into a sound file and using SoundEdit 16 (1994) software to transform the file into a multiband frequency spectrum.89 As a preliminary investigation, all three kinds of loudness calculations were taken for one of the four musical stimuli (Morning). The second by second correlations were high across each method of calculation (r > 0.94, p = 0.001, N = 216). Because Cabrera’s algorithm was the fastest, it was used for calculating dBA loudness for the three remaining pieces. The loudness of each of the four pieces is plotted in Appendix E from page
493.
Figure Chapter 5 -1 A-Weighting Curve
Adapted from: Campbell and Greated, 1987, p. 132.
88 I am grateful to Densil Cabrera for allowing me to use his software, “dB&dBA&Centr”, and for implementing and supporting it. 89 The main difference between the algorithm used by Cabrera and my own algorithm is that Cabrera used octave bands from 31Hz to 16Khz for his calculations at greater than 100mS intervals whereas I used linear bands of 21.5Hz from 21Hz to 11kHz using Equation Chapter 5 -4 at 745mS intervals. I used linear bands because of the SoundEdit 16 spectral data exporting routine did not support logarithmic conversion. This made the Cabrera algorithm preferable. - 266 - Centroid Timbre is a physically and perceptually complex element of music. It does not code neatly into a multilevel, perceptual quantity. Instead, timbre is multidimensional both in terms of its physical features and in terms of its perceptual characteristics
(Krumhansl, 1989).
An important physical aspect of timbre is the sound spectrum. The sound spectrum consists of the frequency components which, together, contribute to the characteristics of the sound. A pure tone sound provides the simplest example. A pure tone consists of a single frequency component, this frequency being the fundamental frequency.
The pure tone is a trivial example. Nearly all musical instruments produce more complex tones. A complex, harmonic tone may be thought of as a group of frequencies sounded at the same time as the fundamental frequency. For harmonic tones, the frequencies are related to the fundamental by simple multiples. For example, if the fundamental frequency were 100 Hz, then a complex tone with four additional frequencies
- 267 - (or partials) at 200, 300, 400 and 500 Hz respectively (see top of Figure Chapter 5 -2).90
It is the intensity of each of these partials which determines, in part, the timbre of the complex tone. Other factors such as masking (Gelflan, 1981; Rossing, 1990; and see the discussion of Loudness on page 262) and transience (Dillon, 1979; Rasch &
Plomp, 1982; Rossing, 1990) also affect timbre perception, but the spectral envelope has tended to dominate research.
Grey (1977) found relationships between particular physical parameters and perceptual judgements of timbre. Three physical dimensions of timbre were found to have varying strengths of relationships with perceptions of timbre. Krimphoff,
McAdams and Winsberg (1994, cited by Donnadieu, McAdams & Winsberg, 1994, p.311) found a high correlation between the centroid of the spectrum and the perceived “brightness” of the sound (r = 0.94). The labels used to describe the perceptual quality have varied. Bismark (1974) referred to “sharpness”, while
Kendall and Carterette (1996, p. 91) designated the label as “nasality”. Because there is no widespread agreement on the perceptual label which relates to the “timbral brightness” quality, I will refer to the physical representation of the timbral correlate
(that is, the A-weighted frequency spectrum centroid).
90 Percussion instruments, such as snare drums and cymbals, are more complex still, for they produce many harmonics that are not related in the simple manner in which harmonic sounds are. - 268 - Figure Chapter 5 -2 Analogy of Centroid with Centre of Gravity The top diagram indicates the centroid (arrow at 225) for a hypothetical frequency spectrum of a complex tone with 5 partials. The next diagram shows the analogous situation where the intensity of each partial is treated as a mass and positioned along a plank. The plank will balance if the axis is placed at the centre of gravity. Otherwise, the plank will tilt.
- 269 - The centroid of the spectrum is like finding the centre of gravity of a plank of wood containing a series of weights. Imagine that each partial in a complex tone was a small weight distributed along the plank. Now imagine carefully picking up this plank and finding the point where it balances perfectly on a pivot point. This point on the plank is the centre of gravity and is analogous to the centroid of the spectrum, as shown in Figure Chapter 5 -2. Mathematically the centroid frequency, C, is expressed as:91
Equation Chapter 5 -1
j ∑Fn An n=1 C = j ∑ An n=1
Where Fn is the frequency of partial number n (or the distance of the nth weight from the extreme edge of the plank) and An is the amplitude (or weight) of the corresponding partial. This produces a frequency-spectrum centroid position on the frequency axis, with the units of measurement being in Hertz. Although this method of calculating centroid is conventional, Kendall and Carterette (1996, p. 92) proposed that the centroid be divided by the fundamental frequency, producing a unitless value (unitless centroid). This approach was not taken here because for complex, multi-voice sounds determining fundamental frequency becomes extremely difficult and perceptually questionable.92 The coding of “brightness” using frequency
91 Adapted from Kendall and Carterette (1996, p. 92) 92 Frequency-spectrum centroid can be calculated without knowing the fundamental frequency of the sound. Unitless centroid requires information about the fundamental frequency, which is almost an irrelevant quantity in the context of a large combination of various complex tones such as a chord played by a large orchestra. The lowest present frequency will not necessarily be the fundamental frequency, neither harmonically (if the chord is inverted), nor acoustically (if virtual pitch is perceived). The problems of using unitless centroid and the complexity of calculating it provide good reason for using the pitch centroid coding of Equation Chapter 5 -1. - 270 - spectrum centroid was implemented using Cabrera’s (1997)93 algorithm written in
CSound. The algorithm applied the A-weighted (see Loudness on page 262) frequency spectrum centroid (taken from Hall, 1987, p. 34), where the weighting is applied to octave bands. with each was based on the summation of octave band
Cabrera’s algorithm produced an A-weighting transformation of the spectrum, making the result perceptually more realistic than the unweighted version. The centroid of each of the four pieces is plotted in Appendix E from page 493.
Melodic Pitch In the music under investigation, melody may be defined as a perceptually prominent and identifiable sequence of pitches. This includes the extraction of a line of pitches from a multivoiced musical texture. Melodic pitch is simply the coded stream of pitches that represent the melody in a given piece of music.
Pitch is the perceptual dimension of sound that distinguishes the highness or lowness of sound. An important physical quantity determining pitch is frequency.
For a simple tone, the number of vibrations per second of air molecules is the tone’s frequency. Higher oscillation rates are perceived as having a higher pitch, all other parameters being equal. However, the relationship between frequency and pitch is not a one-to-one mapping. For example, consider two simple tones, a pitch C5 is generally perceived as being one octave higher the C4 (an additive process) whereas the frequency
93 See footnote 88 on page 266. - 271 - associated with C5 is a multiple of two times the frequency of C4. As Fechner
(1860/1966) proposed, the relationship is logarithmic. By taking the logarithm base two of frequency, a reasonably perceptually valid measure of pitch can be obtained.
For complex, harmonic tones, the perceived pitch is usually determined by the fundamental frequency of the tone (see discussion under Centroid from page 267).
There are a variety of techniques for coding pitch (see Lloyd, 1980; Rossing, 1990).
Each pitch in a melody can be coded according to pitch category, or semitone count
(Lloyd, 1980, p. 789). Using a rising, equal temperament (enharmonic equivalent) chromatic scale, each pitch is represented by a consecutive note number. The note number is calculated by combining the register number, indicating the octave from 0 to 9, and the chroma number, indicating the pitch class from 0 to 11 (C = 0 and
B = 11). This procedure can be summarised as:
Equation Chapter 5 -2 Pitch Category = 12 x Register + Chroma
For example, the pitch of middle C (C4), which is in register 4 and has a chroma of 0, is evaluated as:
Equation Chapter 5 -3 12 x 4 + 0 = 48
Such a system is used for coding pitch in MIDI devices. Because of the popularity of the MIDI device, I shall refer to the units of this coding system
- 272 - as the MIDI note number.94 The MIDI note number system is a standardised, objective way of coding pitch and it is perceptually valid. A higher number corresponds to a higher perceived pitch.
The musical stimuli used consisted of large ensembles playing acoustic instruments, available in the mixed down format of a commercial recording. This meant that the melodic pitches could not be determined directly and objectively from the sound sources. Therefore, no automated system could be used for coding melodic pitch.
Instead, the musical score was used to identify the melodic line and its corresponding pitches. An example of the coding procedure is shown in Figure
Chapter 5 -3. The actual time in seconds is shown underneath this figure.
Figure Chapter 5 -3 Pitch Coding Sample: Opening Melody in Morning.
Pitch Category (MIDI Note Number) 71 68 66 64 66 68 71 68 66 64 . . . etc.
0 1 2 3 4 5 6 7 8 9 Time (s)
Since the response sampling rate was at one second per sample, the melodic pitch was also sampled at one pitch per second. This posed the problem of how to code multiple pitches occurring within one second. Two alternatives were considered: (1) calculate the mean pitch of all melodic notes played per second, or (2) determine the salient pitch per second. Using the mean pitch
94 This notation is used even though no MIDI devices were used for coding, since the music consisted of recordings of acoustic performances. - 273 - method the first sample (t1) in Figure Chapter 5 -3 would be coded as
([71 + 68 + 66]/3 = ) 68.3, and the second sample (t2) coded as ([64 + 66]/2 = ) 65 .
Alternatively, using the salient pitch method, the melody outlines an E major arpeggio, and therefore the salient pitch for the first sample will be the B5, coded as
71, and for the second sample the salient E5 is coded (64). The averaging approach smooths out contour information, and this was considered undesirable, since past researchers have proposed some importance in the relationship between melodic contour and emotion (Dolgin & Adelson, 1990; Gerardi & Gerken, 1995). Therefore, the latter method was adopted for all pitch coding. The melodic pitch of each of the four pieces is plotted in Appendix E from page 493
Tempo Tempo has received much attention in music-emotion research. Italian tempo markings used in traditional Western music notation, at best, provide a range of possible acceptable tempi. The more specific metronome markings, indicating the exact number of beats to be played per minute, are seen by some musicologists as a limitation on artistic expression (Fallows, 1980; see also Lochhead, 1996). However, for the purpose of performance analysis, the actual number of beats played per minute provides an objective measure of tempo. Several music-emotion studies have dichotomised tempo into slow and fast, however, the beats per minute (bpm) measure provides a far richer and more definitive source of tempo coding.
In order to code tempo, each recording was transferred to a computer readable sound file and opened by sound editing software, SoundEdit 16
- 274 - (1994). The software enabled visual representation of the musical signal. Available for display were the waveforms and spectra of the sound (see Figure Chapter 5 -4 on page 277 for examples). Tags were placed at the beginning of each bar of the display so that the duration of each bar could be measured. These values were then tabulated and converted into bpm, according to the formula:
Equation Chapter 5 -4 bpm = 60 x beats / (durationn+1 - durationn) where beats is the number of beats in a bar, duration is the number of seconds elapsed from the beginning of the piece until a point in time denoted by the subscript: The onset of the first beat of the current bar is denoted by n and the onset of the following bar is denoted by n+1. Finally, these values were matched with the sound recording on a second by second basis. A tempo code at time t seconds corresponded to the tempo of the bar playing at that time.
Even though the visual representation enabled by the sound editor allowed resolutions far greater than human hearing perception, it was still not possible to achieve coding with complete objectivity and accuracy. The onset of the first beat of a bar sometimes occurred in an ambiguous location. For example, a loud passage suddenly changing to a soft passage resulted in the masking of the new passage’s onset. By isolating this masked passage on the computer’s display, it becomes evident that masking obliterates the visual cues. Without the context of the bar or two leading up to the ambiguous section, the task of determining beat onset became even more difficult. Judging the beat onset by playing from a few bars before can result in an
- 275 - inaccurate location of the onset since the higher resolution is not available. That is, there was a trade off between resolution and salient cues. Since errors will tend to average across one bar to the next, such problems should mostly cancel out. There were no algorithms available, to my knowledge, that could adequately automate the task of determining tempo or rhythm comparable to the hands on method described
(for a review of two automated approaches and algorithms, see Desain, 1993).
Examples of both difficult to find onsets and easy to find onsets occurred in the
Slavonic Dance as shown in Figure Chapter 5 -4. The waveform and spectrum for the entire piece is shown at the top, and then section by section blow-ups until a few bars of the piece appeared on the computer display. The reduced score below the waveforms and spectra indicates the corresponding point in the music for the last waveform and spectrum. The loud section, articulated by minim cymbal crashes, provide an unmistakable hemiola. The cymbal crashes give rise to the sharp peaks in the frequency spectrum. Subsequently, the frequency spectrum provides a convenient indicator of the bar onset. However, the sudden change to the soft section makes the onset of the following bar difficult to ascertain. Only by playing the section several times could a rough estimate be made of the bar onset. The tempo of each of the four pieces is plotted in Appendix E from page 493.
- 276 - Figure Chapter 5 -4 Sample Waveforms and Spectra of Slavonic Dance Source: SoundEdit 16 (1994) screen dumps. Dotted arrows indicate range of blow-ups. Top row indicates time elapsed in seconds, second row indicates bar onsets (cue number). Cue 9 to 10 covers two bars of music. The first screen dump is of the entire piece. Condensed score of Cue 9 to 10 is appended.
waveform
frequency spectrum
difficult to determine bar onset
easy to determine bar onset
⊗ ⊗ ⊗ (cymbal crash)
- 277 - Material The experiment was fully controlled by the EmotionSpace Lab software, which consisted of a Hypercard stack (see The Computer Program on page 107 in Chapter
3). The program was loaded onto a Macintosh LC520, operating system 7.1, with audio CD-ROM drive and software.
The software could be run on any Macintosh computer with a reasonably fast processor (68040 processor or better recommended) and sufficient memory (8
Megabytes RAM). Subsequently, some of the participants were tested in the
Macintosh Laboratory LG49 in the Morven Brown Building at the University of New
South Wales, because it contained the more powerful 6300 Power Macintoshes. This laboratory was used for four participants, and only when the labs were not in heavy use by other students.
All other materials were the same as for Experiment II (see Material on page 126 in
Chapter 3). Modifications to EmotionSpace Lab software are discussed on page 251.
Participants Since the research question was concerned with musical features rather than individual differences, an effort was made to obtain an unbiased participant pool. To counter the problem of limiting participation to undergraduate students, I asked several other people who were either very musical or non-musical and who were not students, including friends and acquaintances to take part in the experiment.
Balancing gender groups was also a consideration. However, it proved difficult to obtain the services of enough males and enough non-musicians.
- 278 - Sixty-seven participants took part in the experiment. No gift, credit or payment was provided. The distribution of participants according to gender, age, and musical experience are shown in Figure Chapter 5 -5 and Table Chapter 5 -3. As Table
Chapter 5 -3a and b indicate, fewer males than females took part and more students than non-students took part. A majority of the students were enrolled in a music course (22 versus 19), but only three professionally performing musicians from the non-student group were involved. Figure Chapter 5 -5a indicates a wide spread of age groups, however, there was a large number of twenty year olds and most of them were students. Table Chapter 5 -3c indicates that the younger participants were more likely to be females, however from the age of 30 upwards, the balance was fairly even.
In many studies, musical and non-musical groups are determined according to the criteria of how long the participant has studied a musical instrument. Figure
Chapter 5 -5b indicates the distribution of people who had learnt at least one instrument. Nine people had never learnt an instrument, but the largest group had learnt a musical instrument for over ten years. Singing was counted as a musical instrument. Players who were in their twenties made up nearly half of the “greater than ten years of playing” group (Table Chapter 5 -3d) and the number of years spent playing an instrument was fairly evenly distributed across males and females
(Table Chapter 5 -3e).
An additional measure of musicality was collected by asking participants how much they liked and listened to the Western instrumental art music, since the musical stimuli used was of this style. Participants were also asked distracter questions about their behaviour toward other kinds of music, but - 279 - these data are not reported. The results, shown in Figure Chapter 5 -5c and d indicate that participants tended to report high levels of exposure to instrumental art music, with a majority indicating that they liked or loved it. All participants had spent some time listening to this kind of music and no participant indicated hating such music.
To summarise, an attempt at gathering a broad range of participants produced a large range of ages, with the 20 year olds representing the largest group, as well as a large range of musical abilities, but with most participants being quite musically experienced both in terms of instrumental playing and in listening to music of the style under investigation.
Figure Chapter 5 -5 Participant Characteristics a. Age. b. Years of Playing a Musical Instrument. c. Exposure to Instrumental Western Art Music. d. Enjoyment of Instrumental Art Music. A a.
30
20
10
Std. Dev = 12. Mean = 30.6 0 N = 67.00 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0
AGE
- 280 - Figure Chapter 5 -5 Participant Characteristics b.
70
60
50
40
30
20
10 0 N ever played 3 to 5 years More than 10 years 1 to 2 years 5 to 10 years
Num ber of Years of Instrum ent Playing
c.
40
30
20
10
0 almost never a littl some a fair bi a lot constantly
Exposure to Instrumental Art Music
d.
50
40
30
20
10
0 don`t like it m uch so-so like it a bit like it a lot love it
Enjoym ent of Instrum ental Art M usic
- 281 - Table Chapter 5 -3 Dichotomised and Cross Tabulated Participant Characteristics a. Gender Distribution, b. Student and Musician Distributions, c. Gender by Age Group Crosstab, d. Time Playing Instrument by Age Group Crosstab, e. Time Playing Instrument by Gender Crosstab. a. M ales Females 29 38 b. Students Non-Students 41 26 Music Students Non Music Students Professional Performers Others 22 19 3 23 c. Age < 20 yrs 20-29 30-39 40-49 >= 50 Row Gender Total Male 1 13 5 7 3 29 % 1.5 19.4 7.5 10.4 4.5 43.3% Female 7 19 4 5 3 38 % 10.4 28.4 6.0 7.5 4.5 56.7% Column 8 32 9 12 6 67 Total % 11.9 47.8 13.4 17.9 9.0 100.0% d. Age < 20 yrs 20-29 30-39 40-49 >= 50 Row Total Played Never played 3 4 2 9 % 4.5 6.0 3.0 13.4% 1-2 years 1 1 2 % 1.5 1.5 3.0% 3-5 years 1 2 3 % 1.5 3.0 4.5% 5-10 years 6 8 14 % 9.0 11.9 20.9% > 10 years 2 20 8 7 2 39 % 3.0 29.9 11.9 10.4 3.0 58.2% Column 8 32 9 12 6 67 Total 11.9 47.8 13.4 17.9 9.0 100.0%
- 282 - Table Chapter 5 -3 Dichotomised and Cross Tabulated Participant Characteristics e. Gender M ale Female Row Total Played Never played 4 5 9 % 6.0 7.5 13.4% 1 to 2 years 2 2 % 3.0 3.0% 3 to 5 years 1 2 3 % 1.5 3.0 4.5% 5 to 10 years 3 11 14 % 4.5 16.4 20.9% More than 10 years 21 18 39 % 31.3 26.9 58.2% Column 29 38 67 Total 43.3 56.7 100.0%
Procedure Participants signed up for one hour time slots in which to complete the experiment.
Before the participant arrived, the computer was booted and the program reset. The opening screen of the EmotionSpace Lab program was explained, and the participant was told to follow the instructions on the screen. If any problems were experienced, the participant was invited to ask for help either from the interactive help provided by the program or from an attendant next door. A sampling of various cards, messages and dialogs is shown in Appendix B from page 432.
After an introductory screen, a questionnaire requesting demographic and preparatory set information about the participant was completed. This was followed by the introductory tutorials demonstrating the emotion space (see Experiment II,
Tutorial Phase on page 128 in Chapter 3). After a practice phase in which words and faces were used as stimuli, the participant began
- 283 - the music listening and responding phase, as detailed from page 251 and in Table
Chapter 5 -1 on page 253.
After a sound check, the required task was described to the participant. When the participant was ready, the music began to play. The four pieces were presented in random order over headphones. Cursor movements on the 2DES, controlled by the participant via the computer’s mouse, were recorded at one sample per second as the music played.
At the end of the piece the participant was asked to rate the overall emotion expressed by the music using only one point on the 2DES. As a validity check, the participant was also asked to select a word from a checklist. The checklist was formulated from the results of Experiment I (see Results and Discussion on page 112 in Chapter 3) and the words were grouped as shown in Appendix D, Display 105 on page 490. Alternatively a word not on the list could be entered if no word on the checklist was considered satisfactory. The data collected for this stimulus was saved to the hard disk. The program then switched to a card where there was an opportunity to rest, get help on any topic, or to continue with the next musical example. After all four examples were completed, the participant was asked to complete a brief exit questionnaire, thanked and allowed to leave, after which the
EmotionSpace Lab was ready to start another participant or to finish and close.
Instantaneous Results
Data were collected and stored continually along two dimensions for each of the four pieces of music. Some participants did not complete all four pieces. Due to time commitments and equipment failure, four participants did not
- 284 - complete Aranjuez and one did not complete either Pizzicato or Aranjuez.
Subsequently, these data were discarded. The mean responses were plotted and are reproduced in Appendix G from page 543 as line plots and in Appendix H from page
554 as scatterplots. Results pertaining to two aims of the experiment are reported here through the assessment of three forms of validity.
Validity Check 1: Content Validity — Range of Responses Responses were averaged across participants at each second of music. The resulting means for all four pieces are shown as a scatterplot in Figure Chapter 5 -6. The pieces expressed emotions in all four quadrants of the 2DES. Quadrant 2 and 3 emotions were expressed only by Aranjuez, and Quadrant 4 emotions were expressed only by Morning. All four pieces expressed Quadrant 1 emotions at some point. As the time line plots of the pieces indicate (Appendix G from page 543), the standard errors of the mean responses were sufficiently small to support the assertion that emotion was expressed in each quadrant at a statistically significant level (95% confidence intervals). However, significant Quadrant 4 emotion expressed by Morning occurred only for two brief periods, from t6 to t17 and at t206
(Appendix G, Plot 49 from page 544). Although the results suggest an adequate representation of the emotion space, Figure Chapter 5 -6 clearly demonstrates that there are many uncharted areas. Further work will be required to determine whether it is possible for music to express emotions in these regions, and whether the 2DES is able to measure these responses.
- 285 - Figure Chapter 5 -6 Composite Response Distribution on 2DES Contours denote regions of emotion space charted by each piece. Each dot indicates a mean response at each sample of music. High density of dots indicates many responses in that section of the emotion space.
Validity Check 2: Internal Consistency - Averaged versus Overall Response Two modes of investigation were pursued in an effort to determine the validity of the 2DES as a measure of emotion expressed by music. First, a comparison was made between the averaged continuous response for each participant and the self- rated overall judgement of expressed emotion. Averaged continuous response was the simple mean of the continuous response samples across a piece of music for each dimension. The overall judgement was made by the participant as a single points on the emotion space at the conclusion of each piece. Comparing these two sets of data addressed the issue of whether the 2DES was a valid measure of continuous response.
The statistics summarised in Table Chapter 5 -4 indicate that averaged responses correlated significantly with overall response for each emotional dimension
- 286 - and for each piece (at p < 0.001). The two measures were particularly highly correlated for Morning arousal (r = 0.849), Aranjuez valence (r = 0.837) and Pizzicato
(r > 0.84 for both dimensions). The high correlation supports the notion that the continuous 2DES measures the same construct as the static response measures.
A repeated measures t-test was performed on the same data sets. This analysis demonstrated that the mean responses between averaged and overall measures were statistically different (p < 0.001), with the exception of Morning arousal and Pizzicato arousal (see Table Chapter 5 -4). This finding may suggest a counter claim to the validity of the instrument, for in continuous mode the instrument determines a mean response different to the overall measure. However, I suggest that the discrepancy can be explained in several ways without necessarily negating the validity of the continuous 2DES.
A pattern in mean responses (M in Table Chapter 5 -4) occurs as a function of the piece’s distance from the origin of the 2DES. Averaging the continuous response tended to bring scores towards the centre of the 2DES (Figure Chapter 5 -7). For example, a high arousal piece, such as the Slavonic Dance had an averaged response closer to zero than the overall judgement (48% versus 72%). Similarly, Aranjuez, a low arousal piece, had an averaged arousal value which was closer to zero than the overall judgment (4.9% versus -8.4%). A conclusion which may be drawn is that people scale their overall emotional judgements and tend to over-estimate them. The converse possibility is that, on the whole, people do not like to use large regions of the
- 287 - emotion space during continuous response. They prefer to keep something “up their sleeve” in case a more extreme episode is expressed. In either case, the problem is one of scaling. Importantly, although there are differences in the overall and averaged responses, they can be plausibly explained by some scaling factor. The validity of the 2DES as a continuous measure cannot be refuted on the basis of this information.
Table Chapter 5 -4 Averaged Versus Overall Response Averaged Overall Correlation Paired t-test M (%) SD SE M (%) SD SE r p t df p Slavonic N=67 Arousal 47.96 15.27 1.87 72.84 19.78 2.42 .422 .000 -10.59 66 .000 Valence 47.93 17.52 2.14 57.63 25.37 3.10 .750 .000 -4.71 66 .000 Morning N=66 Arousal 15.33 25.69 3.16 14.50 39.98 4.92 .849 .000 .30 65 .768 Valence 43.20 18.74 2.31 53.83 21.73 2.68 .570 .000 -4.56 65 .000 Pizzicato N=67 Arousal 29.46 20.54 2.51 32.48 29.31 3.58 .842 .000 -1.51 66 .135 Valence 46.63 19.68 2.40 52.06 26.82 3.28 .852 .000 -3.09 66 .003 Aranjuez N=62 Arousal 4.92 22.85 2.90 -8.39 33.77 4.29 .664 .000 4.15 61 .000 Valence -15.85 23.35 2.97 -29.98 31.27 3.97 .837 .000 6.41 61 .000
- 288 - Figure Chapter 5 -7 Scatterplot Showing Inward Trend of Averaged Response with Respect to Overall Response For description and identification of contours, see Figure Chapter 5 -6 on page 286.
Validity Check 3: External (Construct) Validity - Comparison with Checklist The second investigation of validity was performed by examining whether the 2DES was a measure comparable to another self-report emotion measurement instrument.
Checklist responses, collected at the conclusion of each piece, were processed and compared with 2DES data. Before comparing checklist and 2DES responses, I will discuss checklist responses alone.
The Pareto charts shown in Appendix I from page 557 indicate the highest frequency words which account for 50% of the total response. These words were then mapped onto the emotion space to produce a post-hoc predicted quadrant of 2DES response.
This “predicted” response quadrant was then compared against the actual overall and averaged responses. The words
- 289 - were also compared by clusters, where each cluster resembled the meaning of a particular quadrant (Appendix I on page 557). Chi-square tests were then conducted to determine the most significant cluster. The results are summarised in Table
Chapter 5 -5. The table indicates perfect quadrant agreement for just one piece —
Pizzicato. The word cluster tally for Slavonic Dance predicts the 2DES response to be in a region between Quadrants 1 and 2. However, the Pareto chart is strongly biased toward Quadrant 1 words. Therefore, the actual Quadrant 1 response on the 2DES demonstrates agreement with the prediction.
For Morning and Aranjuez the 2DES response is generally higher in the arousal dimension than that predicted by the words. As we saw in Experiment II (see Range of Mean Responses on page 136 in Chapter 3), the sleepy range of the 2DES was not used for the words tested to the same extent as the arousal regions (top half) of the instrument. It appears that the situation when listening to music is even more exaggerated. As suggested in Experiment III, either the stimuli chosen do not express sleepy emotions (the problem of semantic density), or the 2DES has a scaling problem. This latter suggestion supports the possible unipolar nature of the arousal dimension, and interestingly, it demonstrates a slightly different shade of meaning communicated directly by low arousal music in contrast with responses to the same pieces mediated by low arousal words. This finding provides abundant research fodder for investigators of semantics.
- 290 - Table Chapter 5 -5 Comparison of Two Checklist Quadrant Mappings with Three 2DES Quadrant Measures + Parentheses indicate coordinate of mean response on the 2DES. ++ Taken from scatter plots (see Appendix H from page 554). +++ Making up at least 50% of total responses based on Pareto charts (see Appendix I from Figure A - 1 on page 558 to Figure A - 3 on page 559 for more details). [Quad] is the quadrant mapping determined in Experiment II (see Appendix I, Table A - 1 on page 557). “?” denotes no mapping available for this word. *** Chi-square test of cumulated word groups significant at p < 0.001.
Checklist 2DES Stimulus Word+++ Word Scatter Overall Averaged (Frequency) [Quad] Cluster Quad Quads++ Quad(M)+ Quad (M) Slavonic triumphant (17) [1] 1.5 *** 1 1 (25,20) 1 (48,48) Dance exciting (10) [1] dramatic (8) [?] vigorous (8) [1] Morning tranquil (11) [4] 4 *** 1, 4 1 (53,14) 1 (43,15) serene (9) [4] dreamy (8) [4] lyrical (6) [?] Pizzicato cheerful (28) [1] 1 *** 1 1 (52,32) 1 (47,29) Aranjuez melancholy (23) [3] 3 *** 2, 3, 1, 4 3 (-30,-8) 2 (-16,5) mournful (8) [3]
Experiment IV: Test-Retest Reliability
Aim
A repeated measures design was used to investigate the test-retest reliability of the
2DES as a measure of continuous response.
Method
Material The equipment used was identical to Experiment III, however, the EmotionSpace Lab was modified to enable by-passing the training stages. Instead of the three training modules (see Experiment II, Tutorial Phase on page 128 in Chapter 3), participants had the option of doing a pretest.
- 291 - Pretest - Stimuli Ten facial and verbal stimuli were used for the pretest. The stimuli were those with the smallest deviation scores (highest agreement) from Experiment II (Table Chapter
3 -8 on page 134 in Chapter 3). A mark was deducted for each incorrect response.
Incorrect responses were determined by the area falling outside a 3/10 wide square about the experimentally determined, expected mean, as detailed in Experiment II.
For each stimulus, two marks could be lost, one for an incorrect first attempt, and another for an incorrect second attempt. The next stimulus was presented if a correct response was made or after the second attempt on the previous stimulus. If the participant lost more than three marks, they would be taken to the training modules.
This eliminated the possibility of participants continuing the experiment without having a good understanding of the 2DES concepts.
Participants Fourteen participants were selected at random from the initial pool of 67 participants who completed Experiment III. One participant could not take part due to absence, and so another participant was selected at random.
Procedure The experiment was conducted six to twelve months after Experiment III in order to reduce carry-over effects. The participants were not aware that they might be called back to participate again, and they were not informed that the study was a repeat of the first one.
The procedure was the same as for Experiment III except for the provision of the optional pretest. The four pieces of music were heard in random order,
- 292 - determined at the time of the experiment, and not based on the order of hearing in
Experiment III.
The pretest reduced the training phase time to less then ten minutes and as little as three minutes for several participants. This meant that the total testing time ranged from thirty-five minutes to one hour.
Results
Participant responses were collected continually for each of the four pieces and saved onto the hard disk. The raw, continuous responses were collected into data files and manipulated so that two columns of data were produced. One column contained the raw, continuous data responses of the fourteen participant responses from
Experiment III. The data would begin with a listing of the second by second arousal responses to Morning. The second by second response order was maintained. The valence response data to Morning were appended directly underneath the arousal data for the first participant. Then the arousal data for Slavonic Dance was placed underneath these data, and so on, until a single column of data contained all responses of the first participant, piece by piece, for both dimensions of emotion.
The column would be extended by the data collected, in the same order, from the second participant, and the procedure was continued for all fourteen participants.
This generated a single column of data consisting of 35,392 lines of data. The procedure was repeated for the retest responses, but in the adjacent column. The two, long columns were placed beside one another such that responses were matched. The arousal response at the first second of Morning for both
- 293 - listenings were adjacent. A Pearson correlation analysis was made between the test
(Experiment III) and the retest responses using the aggregated data of all four pieces across the fourteen participants. This produced the test-retest reliability coefficient for the 2DES of r = 0.735. For valence alone, r = 0.754 and for arousal alone, r= 0.710
(p < 0.001 for all three analyses)
Summary The 2DES developed in Chapter 3 was modified so that it could measure continuous response to music. Sixty-seven participants responded to four pieces of music continuously in an Experiment designed to test the validity of the continuous 2DES
(Experiment III). Fourteen of these participants repeated the experiment in order to provide data for test-retest reliability (Experiment IV).
The stimuli selected covered each of the quadrants of the 2DES with statistical significance (95% confidence interval). Further research is required to determine the extent of coverage across the instrument using a variety of pieces. Because of the twenty minute time restriction, it was only possible to examine four pieces of music, and this list was drawn from a much larger list. Testing the instrument with other pieces will provide further information about two key areas: (1) the ability of the instrument to measure a wide range of emotions, and (2) to gain insight about the emotions expressed by various pieces of music. The use of various styles of music is also an area for future investigation.
Experiments III and IV demonstrated that the 2DES exhibits a fair degree of reliability and validity. Static (overall) responses correlated significantly
- 294 - with the average of continuous responses, and checklist measures provided evidence that the continuous 2DES was measuring the construct of emotion expressed by music. Discrepancies between overall and averaged responses were explained in terms of a scaling problem rather than the violation of the validity of the instrument.
The sparse use of the sleepy quadrants suggests that the arousal construct might actually be unipolar. As with many research instruments, the question of reliability and validity will be ongoing. However, I argue that the self-report continuous measure is a more valid tool in understanding the dynamic music-emotion system than static measures of emotion such as checklists and semantic differentials.
The results of the analysis of musical features and emotional response were not reported in this chapter because they raise issues that require considerable detail in explanation and execution. Specifically, the data are time series, and therefore are likely to exhibit serial correlation. Serial correlation is detrimental to many conventional forms of analysis. Therefore, the following chapter will introduce the relevant, elementary techniques of time series analysis, and the application of these techniques is provided in the final chapter (Chapter 7), where regression models are used to propose simple relationships between the musical feature and emotional response data collected in Experiment III.
- 295 -
Chapter 6 Theory of Time Series Analysis
In the preceding chapter two kinds of data were defined and collected. One type of data was the musical features, such as loudness, melodic pitch and tempo. The other type was the emotional response dimension, namely valence and arousal.95 Based on the theoretical premises of the present research, these variables comprise a musical feature - emotional response (MF→ER) system. The aim of this chapter is to develop a technique for modelling the data in terms of simple linear combinations of musical feature variables and emotional response dimensions.
The problem discussed in this chapter is how to analyse the data. There are several possible approaches. A common technique is to regress the emotional response data variables onto the musical feature. One way of doing this is to find a straight line (or surface if more than one MF) that best predicts the relationship. The line or surface approximates a hypothesised
95 I have deliberately avoided referring to these variable types as “independent” and “dependent” (respectively) because the term “dependent” is used in a different context later in the chapter, namely in the discussion on collinearity. - 296 - true relationship between musical features and emotional response and is positioned so as to minimise the variability between it and the actual data points (Neter,
Wasserman & Kutner, 1983). This technique is referred to as ordinary least squares
(OLS) linear regression (Ostrom, 1990). OLS linear regression makes several assumptions about the data. A pertinent assumption in the present investigation is that the residual, or the part of the data not explained by the deterministic component of the model, is small and fluctuates randomly. As we shall see, this assumption is often violated by time series data.
There appears to be no conventional approach to the problem of dealing with time series data in the main stream of music-emotion research. This is surprising because the musical stimulus is a time series. Our inability to study “real” or naturalistic
(Hargreaves, 1986) music as a time series has inhibited our quest for greater experimental validity (Schmidt, 1996; however, for examples of time series analysis applied to music and sound, see Brown, 1993; Gregson & Harvey, 1992; Vos, van Dijk
& Schomaker, 1994). In the present study not only is the musical object defined as a multidimensional time series, but the continuous responses are also time series data
— in this case, bivariate. Therefore it was considered necessary to devise a procedure of data analysis suitable to the research question.
The contribution made in this chapter is to introduce suitable techniques of data analysis to the music psychology research community. The chapter which follows will then apply the analysis sequence to the data sets gathered in Experiment III.
- 297 - There are a variety of families of analytic techniques available that can address the problems associated with OLS linear regression. Some modern families of techniques include dynamic system models and chaos theory (Gregson & Harvey,
1997), neural network models (McClelland, Rumelhart & the PDP Research Group
1986; Todd & Loy, 1991) and time series models (Box & Jenkins, 1976; Gottman,
1981). These families are not mutually exclusive. Choosing a suitable technique for analysing the data was dependent on several criteria:
1. Simplicity. In order to introduce a technique to a field of study, it is
advisable to use one which builds on knowledge, step by step, currently
available in that field.
2. Interpretability. The models produced should be reasonably
parsimonious, expressing a response variable in terms of the fewest, most
meaningful predictors.
3. Accessibility. The technique should be available to the wider research
community. This means that standard statistical software packages
should have the capabilities of executing the technique.
4. Generalisability. All data sets can be modelled by using the same
technique.
5. Validity. The technique should be appropriate to the research question
and to the data sets.
After a variety of explorations, a specific sequence of time series analytic procedures was developed which fulfilled these criteria. In order to satisfy the simplicity criterion, two univariate regression models were developed for each musical stimulus — one for arousal and one for valence. The
- 298 - sequence of analysis was to lag, then difference the data and then make an autocorrelated adjustment in developing the final model. Consequently, this chapter will be an introduction to relevant time series analytic techniques in addition to defining and introducing the theoretical concepts of lagging, differencing and autocorrelated adjustment. The analytic procedures were tested upon and derived from a comprehensive examination of the data and several pilot analyses. The examples used in this chapter are based on the exploration of a subset of the data collected in the main study. The analysis of the complete data sets is reported in
Chapter 7.
There is no single, simple solution to modelling time series data. After a comprehensive exploration of the techniques available, I have chosen to use an analytic procedure which is simple and effective in modelling the important issues which address the research question. This section introduces some basic principles of time series analysis relevant to the approach I have taken.
OLS Linear Regression Model A time series is a set of observations that are ordered in time. In Experiment III, the observations were made over equally spaced time intervals (one per second). In the present stimulus-response system, I wish to examine the response in terms of predetermined musical features. The traditional approach for examining the relationship between multilevel musical features and emotional responses is to use
OLS regression. This can be written as:
Equation Chapter 6 -1 ER = b0 + b1 x MF1 + b2 x MF2 + … + et
- 299 - Where each b is a coefficient (b0, b1, b2, …) that is determined by the OLS method in such a way as to best explain variability in ER. In the present case ER will either be an arousal response, a valence response or some combination of the two, however I will only be examining the former univariate cases. MF1 might be loudness, MF2 might be melodic pitch and so on. The terms with a b coefficient indicate the deterministic component of the model. This is the part of the model in which we are usually interested. The final term, et, is the stochastic component of the model and is referred to as the error term.96 This part of the model is included to account for discrepancies between the deterministic component of the equation and the actual data value. Two fundamental premises of this model are that the error term, et, be reasonably small and that it fluctuates randomly.
To begin with, Equation Chapter 6 -1 is grossly oversimplified. There are numerous other variables apart from musical features, such as the mood and the personality of the participants, their familiarity with the piece, and the pleasure which they derive from it. All these variables may help to provide a truer picture of emotional response to music.97 Also, the model assumes that the relationship is linear. However, the present investigation will be restricted to the simplest case. I have decided to examine the role of moment
96 A note on notation: et indicates an error series that is a function of time. Strictly speaking this means that the model is a time series model. However, OLS regression models are not necessarily time series models. In other words, the error term as might be indicated with an e rather than et. I have declined to take this option for the reason of consistency when referring to the error term later in the chapter. 97 This problem of individual differences has been largely eliminated because only the average of the responses is considered. - 300 - to moment musical constituents only, on the premise that they may be responsible for explaining a large proportion of emotional response. The scope of the present work limits the investigation to these elementary relationships.
Goodness of Fit and Residual
When the coefficients for the model in Equation Chapter 6 -1 have been determined it is possible to replace the musical feature variables with values (in appropriate units) and make predictions about the expected emotional response dimension. If the original musical feature data were inserted into the equation we might hope to get values essentially the same as the original ER series. The success of this prediction compared with the actual ER is referred to as the model’s goodness of fit or just fit.
Model fit is indicated quantitatively by R2.98 High values of R2 (close to 1) indicate that the model fits the data well, and low values (close to 0) indicate poor fit.
Another way to describe this is to examine how far away the model predictions are from the data values. By subtracting each predicted value from the actual values of
ER at each point in time we obtain a new set of data referred to as the residual. This is an estimate of et in Equation Chapter 6 -1. Ideally this residual should be small and vary randomly. It describes those values not accounted for by the MF variables.
It is statistically unlikely that a perfect fit between predicted and actual values will be obtained for any real-world model. Even if every significant
- 301 - predictor of a response is known, there will still be variations in predicted and actual values through such factors as human error. OLS regression techniques are designed to tolerate such mismatches. For example, if a test on the residual indicates that the error fluctuates randomly, we can assume that the model has been successful. If, on the other hand, the residual contains some systematic change over time, then an assumption underlying the OLS model’s error has been violated. A residual series that varies as a non-random function of time often arises because important regressor variables have been omitted or there is serial correlation or both.
A second problem is that the OLS regression model assumes response is due to the action of contiguous, or instantaneous, variables. However, we do not know that people respond to musical features the instant that they are heard. In fact, this is unlikely. A more tenable proposal is that people respond slightly after the “causal” musical features, due to such processes as human reaction time. Mathematically this delay is referred to as lagging, and is the basis of dynamic response systems (Box &
Jenkins, 1976, p. 335). The issue of lagging and serial correlation will now be defined and discussed.
Lagging and Cross-Correlation Imagine the simplest MF→ER system, where a piece of music can be fully described by one musical feature, MF1 (e.g. loudness), and one emotional response dimension is being measured, say, arousal. Now suppose that MF1 is in some way causally related to the emotional response, and we want to find out what this relation is. Take as an example of this simple MF→ER system a section from “Morning” shown in
98 Adjusted R2 is used as the quantitative measure of fit for multiple regression models (Chatterjee & Price, 1991; Howell, 1996, pp. 521-522). - 302 - Figure Chapter 6 -1a. By examining the pattern of loudness and arousal it appears that there is a relationship between the two variables. However, a Pearson correlation of the two variables yields:
r = .2963 (p= .035)
This correlation is surprisingly low, and statistically non-significant at p = 0.01, even though through visual inspection there does appear to be a relationship between the two variables. The problem is simple. People do not (usually) respond to the MF instantaneously. There is a delay, or lag. The lag might be due to the emotion taking some time to determine and due to differences in individuals’ response profiles.
Lexical access literature suggests that extracting meaning from stimuli can take in the order of one second (Greene & Royer, 1994) and Schmidt (1996) reported the response latency in detecting information about musical features was in the order of
1 to 1.5 seconds. Also, after the response decision is made, it takes time to move the computer’s cursor to the appropriate position on the screen.99 Therefore, once the participant decides on the emotion expressed, she or he will take time to describe this on the measuring instrument.100
How can we determine the response time lag for this continuous data? Remember that, for now, I am assuming that a single MF determines the ER. If we also assume that ER is in response to a MF that happened a short time ago, this elapsed time can be determined by using the following procedure. To compensate for the response lag, move the MF time series forward by one
99 This access time justifies the use of a one second sampling rate in Experiment III, and suggests that sampling more than, say, twice a second is redundant. 100 Although unlikely, it is also possible that someone who knows the music very well will anticipate a response, suggesting a response before the “causal” features. - 303 - time unit (in this case, by one second), and recalculate and tabulate the correlation coefficient. Move the MF time series forward another second and repeat the process until a peak correlation coefficient is encountered. This procedure is referred to as a cross-correlation and can be produced by a cross-correlation function (CCF). Several statistical software packages provide a cross-correlation command.101
Evident in Figure Chapter 6 -1b is that significant correlations occur when the loudness series is moved forward by one, two, three, four, and five seconds. The pattern appears to be related, with correlation coefficients gradually rising and then subsiding across the time range. The reason for the distribution of significant correlation coefficients can be explained in terms of (a) the effect of averaging response over individuals (individual differences), and (b) the effect of averaging over musical events (dynamic MF→ER system). We may, then, for the sake of simplicity, tentatively conclude that arousal can be described as a function of the lag at which the dominant coefficient occurs — when loudness is shifted forward, or lagged, by three seconds. “Lagging” indicates the direction in which the ER variable is
101 The command to generate such a correlogram in SPSS is: -> CCF -> /VARIABLES=dba ar -> /NOLOG -> /MXCROSS 7. where dba refers to the loudness series and ar to the mean arousal series. The number after MXCROSS indicates how many times to execute the “shift and calculate” procedure. MXCROSS 7 instructs SPSS to repeat the process by shifting the dba series to the right seven times, and also to the left seven times. Only the right (positive) shifts are of interest here. - 304 - moved. I will describe such “Lagging” as “loudness shifted forward by three seconds” or loudness lag 3, and notate it as loudness3.102
Figure Chapter 6 -1 Loudness and Arousal Time Series and Cross-Correlogram for mm. 25 to 47 of Morning. (a) The solid line indicates the mean arousal response of 58 participants on a scale of -100 to +100. The sample data shown are for bars 25 to 47, or 50 seconds of music (starting at the 60th second). (b) Cross-Correlation Function (CCF) of mean arousal response with dBA loudness shown in (a).
(a) 80
70
60
50
40
30 Loudness (dBA)
20 A rousal (% ) m m.025.3 mm .029.4 mm .034.2 mm .038.2 mm .042.6 m m .0 4 7 .2 m m .0 2 7 .4 m m .0 3 1 .5 m m.036.1 m m.040.4 mm .045.1
BA R
(b) 1.0
.5
0.0
C onfid ence Lim its -.5
-1 .0 C oefficient -7 -5 -3 -1 1 3 5 7
-6 -4 -2 0 2 4 6 LAG Number of seconds by which loudness has been shifted forward relative to arousal
102 Actually, a lagging ER is indicated by a negative number (loudness-3) and a leading ER as a positive number. Because I am only examining lagged ERs I have dropped the minus sign throughout. Note that shifting an MF forward in time is graphically equivalent to leading the ER series. - 305 - Hence the present example may be modelled by initially re-writing the regression equation (Equation Chapter 6 -1 on page 299) and incorporating the dominant lag:
Equation Chapter 6 -2 Arousal = b0 + b1 x Loudness3 + et
The OLS technique can then be used to obtain estimates for b0 and b1.
For the data sample of Morning this produced a regression model with the following deterministic components:
Equation Chapter 6 -3 Arousal = -37.40 + 1.207 x Loudness3
All coefficients were statistically significant (p < 0.001) and this model accounted for
68% of the variations in arousal (R2 = 0.683), indicating that it fitted the data well.
The model could be further improved given that arousal is also correlated with other lags of loudness. By inspecting the correlogram of Figure Chapter 6 -1, the loudness variable shifted forward by 1, 2, 4 and 5 seconds, in addition to loudness lag 3, each correlate significantly with arousal. So the model becomes:
Equation Chapter 6 -4 Arousal = b0 + b1 x Loudness1 + b2 x Loudness2 + b3 x Loudness3 +
b4 x Loudness4 + b5 x Loudness5 where b0 to b5 are coefficients. The OLS regression model summary is shown in Table
Chapter 6 -1. At p = 0.01,103 only loudness lag 1 and 5 are significant, so by substituting the significant coefficients Equation Chapter 6 -4 becomes:104
103 The stringent rejection rate of 0.01 was chosen over 0.05 because no adjustment was made for the relatively large number of variables used in the stepwise regression procedure. 104 A more rigorous procedure would be to re-estimate the coefficients. This re-estimation leads to small changes in coefficients and a small decrease in R2. I have omitted this step for each analysis for simplicity. - 306 - Equation 6-5 Arousal = -89.84 + 0.628 x Loudness1 + 0.453 x Loudness5 There are two striking aspects about this model. First it explains a large
amount of the variation in arousal (84%, adjusted R2 = 0.843, p < 0.01, taken from Appendix K on page 571). Second, three of the lags at which high correlations were initially found, including the dominant lag 3, have non- significant coefficients at p = 0.01. Before any further analysis is made, this model should be viewed with suspicion. Further diagnosis is required. The problems associated with lagging and variable selection will be considered first.
In the model of Equation 6-5, several lagged versions of loudness were used to predict arousal response. This raises two questions:
1. How many lags should be included in the model?
2. Which variables should be lagged?
The first question was addressed by careful examination of exploratory cross correlation functions. Each musical feature was cross-correlated with an emotional response variable. Two typical kinds of cross-correlation profiles emerged: (a) those with little or no significant correlation at each lag, and (b) those with some significant correlations at certain lags of the musical feature variables.
307 Table Chapter 6 -1 OLS Regression Model Summary
Summary is of loudness as a predictor of mean arousal response of 58 participants for t90-110 of Morning.105 B is the coefficient of the variable, SE B is the standard error of the coefficient, Beta is the standardised coefficient, allowing comparison across coefficients, and T is the T-statistic testing the null hypothesis that the coefficient is zero. Sig T is the significance (p) of the T-test. DBA is the original loudness series. The number after each DBA indicates lag (in seconds). For example, DBA1 is loudness series shifted forward by one second (see Glossary for notation conventions and abbreviations). For more details, see Appendix K on page 569.
Variable B SE B Beta T Sig T DBA1 0.628130 0.125441 0.418966 5.007 0.0000 DBA2 0.269626 0.145756 0.180518 1.850 0.0711 DBA3 0.338923 0.156504 0.227245 2.166 0.0358 DBA4 0.312386 0.144921 0.210341 2.156 0.0366 DBA5 0.453040 0.127913 0.304778 3.542 0.0010 (Constant) -89.842825 9.330134 -9.629 0.0000
Selecting Lags For the purpose of explanation let us assume that there is a causal, underlying relationship between loudness and arousal. Figure Chapter 6 -1 on page 305 provides an example of the latter type of cross-correlation profile (b). The correlations in the figure are unusually high for reasons that will become evident, but the general structure of the profile is otherwise typical. According to the plot, responses stretch over a range of 5 seconds after the correlating loudness event occurs. As expected, no significant correlations occur with arousal before a correlating loudness event, and instantaneous responses (i.e., at lag 0) border on significance. This supports the intuitive notion that it is not necessary to consider variables lagged for which responses occur before a musical event. In other words,
“negative” lags can be ignored. But how many positive lags of the musical feature variables
- 308 - should be used? There are two complementary criteria which help to answer this question:
i. Include lags that explain the actual relationship of interest.
ii. Exclude spuriously correlated lags.
The second criterion refers to the issue of Type I error. Statistically, if correlations are attempted often enough, an incorrect significant correlation can occur through chance. Having too many lags will increase the likelihood of this happening.
Further, more distant lags may produce significant correlations due to later musical feature events. For example, suppose that there is a true relationship where arousal is correlated with loudness lag 2 and 3. Now suppose that a burst of loudness occurs twice in three seconds, say at t0 and t2.106 Then arousal will increase at t2 and t3 due to the t0 event as well as t4 and t5 due to the t2 event. If there were no restrictions placed on the number of lags included, we might erroneously attribute increases in arousal at t4 and t5 to the loudness event at t0. Using fewer lags will help to alleviate this problem.
After numerous cross correlation explorations with many lags and using many combinations of MFs with each ER it was concluded that lags 0 to 4 would be used in subsequent investigations.107 These 5 lags provided a good compromise between the two criteria; They are a sensible choice because
105 See footnote 112 on page 320. 106 tx should be read as “time at x seconds”. 107 I have mentioned earlier the unlikelihood of instantaneous response. The zero lag is necessary, though, because responses were recorded once per second. Zero lag actually incorporates some time
- 309 - they tended to group together in time and not too far backward in time for most cross correlations.108
Selecting Regressors Having decided upon the number of lags to examine, the next issue was to determine how many variables to choose in order to model the emotional response most efficiently. Intuitively, using the largest number of variables was appealing — having more regressor variables in the equation was likely to explain more of the variance in response (increasing R2). For each of the four pieces used in Experiment
III the musical feature variables coded were:109
1. loudness
2. melodic pitch
3. tempo
4. texture
5. centroid (of the frequency spectrum)
Lagging each of these variables by 0, 1, 2, 3 and 4 produced (5 x 5 =) 25 variables.
However, a problem with having so many variables is that the probability of a spuriously large R2 increases with the number of regressors (Howell, 1997, p. 522).
The most conservative rule reviewed by Howell (p. 522-523) suggests that 250 data points are required to reduce the possibility that the R2 value will be misleading for
25 regressors. The length of pieces used in
between the instantaneous sample and the sample one second later. Similarly, lag 4 covers some of the time before the fifth sample. 108 The exploratory cross-correlation analyses were actually conducted on first order differenced variables. Differencing is discussed later in this chapter. 109 For details, see Selection of Musical Features on page 257 in Chapter 5. - 310 - Experiment III were 150, 216, 225 and 654 seconds (at one sample per second), suggesting that even if most of the variables at each lag were significantly correlated with the emotional response, they could still be included in the regression model without drastically violating the estimation of the fit. But the limitation upon the number of regressors is not determined by the number of samples alone. Another problem that arises is referred to collinearity.
Collinearity Collinearity refers to the interdependence of regressor variables. If one variable can be expressed in terms of another, then it is pointless to use both in the regression model. The statistical significance of coefficients will be reduced and the validity of the model may even become untenable (Belsley, 1991).
One simple way of diagnosing collinearity is by calculating tolerance. If we attempt to regress one musical feature, say MF1, variable onto all the others, as in:
Equation Chapter 6 -6 MF1 = a2MF2 + a3MF3 + a4MF4 +… then an R2 of fit can be calculated, where an is the coefficient of the nth regressor. This
R2 indicates how well a linear combination of all the other regressors explains the suspect musical feature variable. Similarly the dependence of MF2 can be evaluated by determining the fit of the equation
Equation Chapter 6 -7 MF2 = a1MF1 + a3MF3 + a4MF4 +…
- 311 - Tolerance is described as the reflection of this fit value: 1-R2. Therefore, a tolerance of near 1 indicates that the predictor variable is essentially independent of the other predictors, while a tolerance close to 0 indicates that the variable is redundant.
For example, collinearity may well be expected to occur between texture and loudness variables because of the way each variable is coded. When loudness increases it is quite likely, though not necessary, that the composer used more instruments to achieve the increase. In some respects loudness and texture may appear to measure the same thing. This relationship can be quantitatively checked by calculating tolerance.
Belsley (1991) demonstrated that there is no strict rule for determining when tolerance measures indicate excessive collinearity. Suppose that a tolerance estimate for a musical feature variable was 0.40. This means that (100 x [1.00 - 0.40] =) 60% of the variation in the variable can be explained in terms of a linear combination of the other variables. One could argue that this variable is therefore collinear and should be omitted from the analysis. Conversely, this tolerance estimate also indicates that the variable in question contributes 40% of variation independently with respect to the overall variation. From this viewpoint the variable should be kept. The tolerance value at which collinearity becomes a serious problem is therefore a moot point.
Fairly low tolerance values will be accepted here so that unexplained variance is minimised. Regardless, tolerance values should be checked.
- 312 - Stepwise Regression Several techniques were explored in order to determine a suitable method of balancing the problems of Type I error and excessive collinearity with the requirement of sufficient explanatory power. Two methods used were (1) exploratory cross-correlations followed by tolerance calculations which were used to revise the selected variables and (2) stepwise regression. The latter technique was chosen because it automated the criteria for variable selection. Stepwise regression uses a predetermined criterion for selecting whether each of a list of variables should be included in, or excluded from, the final model (Howell, 1997, pp. 540-541). The process maximises R2 such that only variables which significantly contribute to the fit of the model are included. This has the added advantage of easing collinearity problems. Hence the procedure adopted was to include all 25 variables in the stepwise regression procedure and allow the algorithm to determine which of these musical feature variables made a significant contribution to explaining variability in emotional response.
To summarise the previous subsections, the MF→ER system may contain more than a single lagged musical feature variable, and the OLS model can be adapted by using lagged musical feature variables in the regression equation. However, the model of
Equation Chapter 6 -5 and its general form (Equation Chapter 6 -4 on page 306) is potentially seriously flawed in another, significant respect: the hidden effect of serial correlation on the model.
- 313 - Serial Correlation The major challenge in analysing time series data is managing the problem of serial correlation. In the context of the MF→ER system, serial correlation, or autocorrelation
(Gottman, 1981, pp. 67-77), occurs when the response is being affected not only by accounted external factors, such as musical features, but also by past values of itself.
It would be hard to imagine an MF→ER system without serial correlation.
Serial correlation may be thought of as memory. Consider a person’s response to unfolding music. When we reach the first beat of the tenth bar of the piece, the individual will not simply be responding to the musical event at that time. Apart from lagging response, discussed above, the person is also aware of what has happened in previous bars. This awareness may be conscious or subconscious. A context has been set. The response will be a function of the musical event of bar 10 but also of the events that preceded it. This is perhaps the single most important advantage of using naturalistic stimuli for music psychology testing. Using isolated musical stimuli does not provide the individual with the typical musical context.
That is, serial correlation has been removed. However, time series analytic techniques allow us to model serial correlation, and it therefore becomes possible for the researcher to quantitatively interpret responses to real musical stimuli.
Another way of viewing serial correlation is that it is a process which acts to impede sudden changes in the response. It has the effect of generating a kind of inertia (Box
& Jenkins, 1976, p. 335) upon the MF→ER system. The correlogram in Figure
Chapter 6 -1 indicates that peak arousal occurs after changes in
- 314 - loudness three seconds earlier. However, the peak is not sharp. This could be because different people respond at slightly different times, but also it could be due to the serial correlation in the system. Deterministic responses are gradual, and therefore are related not only to the stimulus that caused the change but also to preceding responses, which tend to slow the rate of change. Figure Chapter 6 -2 shows a hypothetical example of how response might be different if, all things being equal, serial correlation could be removed. If the musical feature shown at the top of the figure were correlated with the response, the response below (Figure Chapter 6 -
2a) might be expected if it contained little or no serial correlation, and the one below that (Figure Chapter 6 -2b) if it did contain serial correlation. An intuitive approach suggests that the latter would be the outcome, and, as will become apparent, this is the case.
The autocorrelation referred to so far has been the autocorrelation of the response.
However, the musical feature variables are also likely to be autocorrelated. A typical musical feature pattern is shown at the top of Figure Chapter 6 -2. The fact that it changes gradually suggests that it is autocorrelated. Think about the loudness in music. If listening to a completely unfamiliar piece, the best prediction of the loudness of the music could be determined by the loudness at the previous moment of the piece. Even if the piece jumps around, interchanging very loud sounds with very soft sound, the ambience of the performance space will be responsible for a non- instantaneous decay in loudness. The instrument
- 315 - producing the sound will stop, but the sound waves will continue to bounce off walls and objects and back into the ears of the listener for a brief time. A situation where loudness did change instantaneously from moment to moment would be unusual.
This serial correlation of the musical feature compounds the problem of modelling the system using OLS regression. The supposedly stochastic residual term will actually be systematically related across short periods of time.
Figure Chapter 6 -2 Comparison of Hypothetical Non-Autocorrelated and Autocorrelated Response. In both cases assume that ER (Emotional Response) is correlated with the MF (Musical Feature).
MF
Stimulus
(a) ER
Response with no autocorrelation
(b) ER
Response with autocorrelation
time
The problem with modelling a system containing autocorrelations is that, using the
OLS method, the autocorrelation component is actually being
- 316 - incorrectly attributed to the musical feature variables. The retarding effect of serial correlation acts on both response and musical features. We know that the response variable is changing a little more slowly due to its own autocorrelation. We also know that the musical features may be changing more slowly due to each of their autocorrelations, and therefore response and musical features appear to move together (with some lag factor) for reasons other than simple stimulus response correlation. OLS regression does not “know” this, and assumes that the high correlation with the response is entirely related to the predictive power of the musical features. As a consequence, OLS models fit autocorrelated data much better than the true underlying relationship.110
Serial correlation can produce incorrect inferences about the strength of relationship between musical features and emotional responses, especially if positively associated, as they are. The crucial issues then become how to diagnose serial correlation and what to do if it is present.
Diagnosis of Serial Correlation
The invalidity of the above OLS regression model (Equation 6-5 on page 307) can be assessed by examining its residual. Under the assumption of independent samples,
OLS regression will produce a residual that fluctuates randomly with a mean value of zero and a normal distribution (Ostrom, 1990). An example of the violation of this assumption is the case when the residual time series contains a trend.
110 See Ostrom, 1990, for an accessible but more mathematical account of autocorrelation. - 317 - Trends A trend refers to the general movement of the values of a time series in a particular direction. General, overall increases in the time series values are referred to as having a rising or upward trend, while those with overall decreasing values have a falling or downward trend (Figure Chapter 6 -3).
Figure Chapter 6 -3 Examples of Trends. (a) Rising or Upward Trend
(b) Falling or Downward Trend
time
By definition, a time series which exhibits a trend will be a deterministic function of time (Gottman, 1981, pp. 83-85). The best predictor of the next value in a time series with a trend will be the previous values of that series. Conversely, the next value from any point of a truly random series is equally likely to be higher or lower than its current value. If a time series exhibits an upward trend then there is a better chance
- 318 - that the next value of the series will be higher than the immediately preceding value.
In other words, the series will have some correlation with a lagged version of itself.
A simple technique for diagnosing trend is by visual inspection. However, trends can be hidden by other processes in the system. In order to diagnose whether a time series contains a trend or a drift or any other kind of serial correlation we rely upon several more sophisticated diagnostic tools: The autocorrelation function, The
Durbin-Watson test and the Box-Ljung statistic.111
Autocorrelation Function (ACF) Diagnostics
By making an exact copy of a series, shifting the copied series forward and performing a correlation analysis, a series with a trend will produce some correlation at that lag. By shifting the copied series forward again and recalculating the correlation coefficient an autocorrelation function (ACF) is calculated. There are three differences between the CCF (discussed on page 302) and the ACF. For the ACF: (1) the series is analysed against itself, (2) the correlation will be perfect (=1) at zero lag, and (3) the series is shifted in one direction only. The reason for the shift in one direction is because shifting the copied series to the left and the right about the zero lag will produce a symmetrical correlogram, rendering one half of it redundant.
Visual inspection of the residual plot (Figure Chapter 6 -4a) of the OLS regression model of Equation 6-5 indicates the presence of serial correlation. For example, there appears to be a drift pattern in the residual — the residuals do
111 Note that a trend is usually treated as something which is separate from serial correlation because the former refers to a deterministic component of the process, whereas serial correlation generally refers to the stochastic component of the process. For a clear explanation of the distinction, see Gottman (1981). - 319 - not fluctuate randomly over time. This drift consists of an upward trend over t80-92 and a decreasing trend over t93-103.112 This serial correlation is verified by examining the autocorrelogram of the residual. Figure Chapter 6 -4b indicates that when a copy of the residual plot is shifted across one time unit (one second) and correlated, a significant correlation occurs (r1 = 0.654, p < 0.05). When the copied series is shifted another unit along, a significant correlation is made again with the original time series (r2 = 0.382, p < 0.05). Because there exist significant autocorrelations within the residual, the non-autocorrelated residual assumption of OLS regression has been violated (Ostrom, 1990, pp. 16-21), and the model (Equation Chapter 6 -1) may not be valid.
Durbin-Watson Test
While the ACF produces a correlogram which is assessed by visual inspection, the
Durbin-Watson test produces a statistic that can be used to assess autocorrelation.
The Durbin-Watson test produces a statistic, d, which is a measure of the relationship between the lag 1 residual and the original residual series according to the formula
(Ostrom, 1990, p. 27):
2 2 Equation Chapter 6 -8 d = Σt (êt - êt-1) / Σt êt where êt is the original residual series at each point in time, t, and êt-1 is the residual copied and shifted forward, or lagged, one unit in time. Another way of referring to this one unit lag is first order. Hence, the Durbin-Watson statistic is a test statistic for the presence of first order autocorrelation.
112 tx-y should be read as “the time from x seconds to the time at y seconds”. - 320 - Figure Chapter 6 -4 Residual and its ACF for Lagged Loudness Regression Model of Arousal (a) Residual of predictions produced by
Equation Chapter 6 -5. (b) Autocorrelogram of (a). (c) Partial autocorrelogram of (a). see Appendix K on page 568 for SPSS output.
(a) 10
0
-10
-20 60 65 70 75 80 85 90 95 100 105 110
Time (seconds)
(b) Residual 1.0
.5
0.0
-.5 C onfidence Lim its
-1 .0 C oefficient 987654321 10
(c) 1.0
.5
0.0
-.5 C onfide nce Lim
-1 .0 C oefficient 987654321 10
- 321 - The Durbin-Watson statistic has the property that for values close to two the residual is not autocorrelated, for values near zero it is positively autocorrelated and for values near four it is negatively autocorrelated (Ostrom, 1990, p. 28). The statistic, then, provides a basis for addressing the null hypothesis that the residual is not autocorrelated (d = 2).
Durbin-Watson d statistic tables were consulted to determine the critical value at which to accept or reject this hypothesis, or to make no conclusion.113 The critical d value is determined by two parameters: (a) the sample size and (b) the number of regressors in the equation. The constant term must be present in the regression equation, but should not be counted as a regressor (SPSS/PC+ Trends, 1990, E-11).
For the present example, five lagged loudness regressors were used with 50 points in the sample. The Durbin-Watson critical d range for these parameters is dL = 1.335 and dU =1.771. dL is the lower bound critical value. If the statistic is below 1.335 then the null hypothesis of the presence of first order autocorrelation is rejected.
“dU” is the upper bound critical value, above which the null hypothesis is accepted.114 The test statistic can be generated by many statistics packages. In SPSS it is an option in the regression command and for the model of Equation 6-5 produced a value of d = 0.675 (listed in Appendix K on page 569). Since this is lower than dL (1.335), the null hypothesis is rejected and we conclude that the residual is autocorrelated at lag 1. That is, the residual is first order
113 SPSS/PC+ Trends, 1990, pp. E11-E16, which also lists the Farebrother corrections of mistaken entries. 114 If the statistic lies between dL and dU then the significance is the statistic is not clear (Ostrom, 1990). An alternative test, such as the Box-Ljung test (discussed in the following section), for first order serial correlation could be used. - 322 - autocorrelated. For higher orders, we can consult the auto-correlogram as discussed above (Figure Chapter 6 -4b).
The Durbin-Watson statistic is relatively easy to calculate and has a long history in regression modelling with respect to time series analysis. The statistic has the major drawback that it only diagnoses first order autocorrelation. If there were no first order autocorrelation then the Durbin-Watson test would indicate this. This does not exclude the possibility that higher order autocorrelations do exist. We already have the autocorrelation function to examine the higher order serial correlations.
However, there exists a more comprehensive method for diagnosing serial correlation quantitatively: the Box-Ljung statistic.
Box-Ljung Statistic
The Box-Ljung statistic is used to test “the null hypothesis that a set of sample autocorrelations is associated with a random series.” (SPSS/PC+ Trends, 1990, p. D1).
In SPSS the Box-Ljung statistic is printed out with the autocorrelation function output. The statistic appears in the SPSS output shown in Appendix K on page 569.
The Box-Ljung statistic appears in the second last column of the ACF output and the final column contains the probability that the null hypothesis is incorrectly rejected.
The statistic has a cumulative property. The statistic indicated at each lag refers to the probability that that lag or any lower order lag is associated with a random series.
The output in Appendix K is trivial, as the null hypothesis
- 323 - is rejected at every lag displayed, from the first lag upward (at p < 0.001). Therefore there is clearly serial correlation within the first 10 lags. We conclude that the residual is autocorrelated and that, therefore, the OLS regression model of Equation
6-5 is not valid.
So far I have examined ways of diagnosing autocorrelation in the error term. This diagnosis is used to evaluate the validity of the OLS regression model. I will now discuss two methods of dealing with the MF→ER system that contains trends and autocorrelations: differencing and autoregressive adjustment.
First Order Differencing Part of the reason the residual of an OLS regression is serially correlated is because the regressors (musical features) and the response are themselves autocorrelated. It is possible to remove some of the autocorrelation within variables by using an appropriate transformation which will also remove some of the residual autocorrelations. If autocorrelation is removed, then the OLS model might once again become valid.
One such transformation is the first order difference transformation, where the difference between the current value of a series and the immediately preceding value is used to produce the current value of the new series. For example, the series 50, 55,
55, 52 and 60 produces a difference series of (55-50=) 5, (55-55=) 0, (52-55=) -3 and
(60-52=) 8. Notice that the transformation causes the loss of the first time point. This transformed series is first order differenced. If the new series were difference transformed again (to become-
- 324 - 5, -3, 11), we would have a second order difference transformation, and the first two time points would be lost. I will be concerned only with first order differencing and will now discuss why it might be useful.
A time series which may, in part, be described as an additive process (adding previous values of itself) may be thought of as a first order integrated process.115 The series 50, 55, 55, 52 and 60 appears to be a first order integrated process because by removing the integrated component (through differencing) we end up with a series that fluctuates more randomly than the original series. First order integrated processes are abundant in time dependent systems. A simple way of removing some of this first order effect is by applying a difference transformation (Gottman, 1981, pp. 91-97). That is, differencing a series usually removes the trend or drift from the series. Consider Figure Chapter 6 -2 (on page 316) again. If each response in Figure
(b) was subtracted from its adjacent value to the left, it is conceivable that the response series (a), or something like it, will be produced.
First order difference transformations have another advantage in the present situation. They are meaningful. The values of the differenced series refer to the sample to sample change in a certain variable. For research purposes, we are often interested in how much ER1 changed after a change in MF1, rather than in the absolute values of each series. If loudness increases by five units, by how many units does arousal increase? This is a useful question and can be posed with regard to a series which has been differenced. Differencing
115 Note that an integrated series is not necessarily a series which contains a trend. An integrated series may be identifiable by drifts which behave like trends over short periods. - 325 - absolute pitch class has the advantage of transforming the variable into melodic contour, a variable that has received some attention by music-emotion researchers
(Dolgin & Adelson, 1990; Gerardi & Gerken, 1995). Also, by differencing the emotional response dimensions, the problem of scaling116 is eliminated. No assertion need be made about the absolute position of a response on the 2DES — instead, differencing response provides (less disputable) information about the direction in which the response moves.
The procedure for determining whether a variable requires a difference transformation is as follows:
1. Examine the autocorrelogram of the variable.
2. If the variable shows autocorrelation, take its first order difference.117
3. Examine the autocorrelation of the transformed series to verify that at least
some of the autocorrelation has been removed and no spurious additional
lag one autocorrelation has been introduced.
If the original series is not notably trended, it may be unnecessary to perform the transformation. After exploratory analysis it was found that most variables (musical feature and emotional response) contained trends. For the sake of consistency and simplicity, all variables were first order differenced.
116 See Range of Mean Responses on page 136 in Chapter 3 and Validity Check 1: Content Validity — Range of Responses on page 285 in Chapter 5. 117 A more sophisticated (though not guaranteed) diagnosis of linear trends is that the autocorrelogram decays at a rate slower than a straight line (Gottman, 1981, p. 83-85 and p. 97). See More Sophisticated Diagnostics: The PACF and the ACF Revisited on page 332. - 326 - In Appendix L plots are shown of the original loudness (dBA) and arousal (ar) series
(page 571 and 574 respectively), their differenced transformations (page 572 for loudness and page 575 for arousal), and their respective autocorrelograms (page 572 and 573 for loudness, page 575 and 576 for arousal). Because this is an important time series analysis procedure, the commands and output generated by SPSS are also included. The plots of the original and differenced data are provided to exemplify the effect of the transformation.
Notice that in both pairs of plots the differenced transformation changes more frequently, and the range has also been reduced because only changes in values are indicated. The differenced plot does appear to be more random. But to obtain a decisive view about the amount of autocorrelation, the autocorrelogram plots should be consulted.
The loudness ACF has two significant peaks at the first two lags (Appendix L on page 572). The differenced transformation removes these peaks, as well as reducing the autocorrelation at several higher orders (page 573). As expected, the arousal response is highly autocorrelated (page 575). The correlation coefficients of the first three lags are significant. Such high values are to be expected because the autocorrelation in the response is compounded by the autocorrelations of the stimuli.
Differencing the arousal series dramatically reduces the autocorrelation (page 576).
Now the second and third lag correlations are no longer significant and the first lag borders on significance.
- 327 -
First Order Differenced, Fourth Order Lagged OLS Linear Regression First order differencing is a common and useful transformation. If a variable contains trends, differencing is a worthwhile consideration. Having done this, the new version of the OLS regression model can be inspected. Again, because of the importance of this procedure, SPSS output is provided in Appendix M (from page
578). The procedure shown can be summarised as follows:
1. Difference transform all variables if autocorrelated variables are found.
2. Perform OLS regression using differenced variables.
3. Diagnose the amount of serial correlation in the residual.
The model now becomes:
Equation Chapter 6 -9 ∆Arousal = 0.167 + 0.384 x ∆Loudness1 + 0.459 x ∆Loudness3 + 0.258 x ∆Loudness4 where the delta (∆) preceding each variable indicates that the variable has been first order differenced.118 The subscript number at the right of each variable indicates its lag relative to arousal, as before. Only the coefficients at lags 1, 3 and 4 were significant at p = 0.01 (see Appendix M on page 578 for more details).
- 328 -
The model of Equation Chapter 6 -9 explains 60% of changing arousal (adjusted R2 =
0.602, p < 0.01). Although this explains less of the variance than did the model of
Equation 6-5 on page 307 (which explained an unlikely 84%), an attempt has been made to control the amount of autocorrelation in the MF→ER system through differencing, and therefore the present model has greater validity.
To check this, the Durbin-Watson statistic was evaluated (Appendix M on page 579).
The value returned was d = 1.675 which is close to 2 but just under dU of 1.771 (for 5 regressors and 50 samples). Since d is greater than dL (1.771) we are in the indeterminate range of the statistic. Therefore, we should inspect the ACF to evaluate the seriousness of the serial correlation. The ACF of the residual indicates no significant correlations, and the Box-Ljung statistic is non-significant at all lags shown (p = 0.335 [>> 0.05] at lag 10) and so the null hypothesis of no first order autocorrelation may be accepted. It appears that the OLS model is valid for the differenced data.
It is possible to criticise the use of differencing transformation in the situation where a series does not contain an integrated process component. By differencing such a series we risk over-differencing which may aggravate the
118 Another symbol used to denote differencing is del (∇). - 329 - problem of serial-correlation rather than mitigate it. Although this caution must be borne in mind, first-order differencing is unlikely to pose such problems for the data sets under investigation. Nevertheless, the issue can be resolved by examining the residual and diagnosing the effect of the transformation.119 Further outweighing the negative aspects of differencing is that it is a convenient transformation because the variable remains meaningful, and in some cases, as in the present, all significant autocorrelation had been removed from the MF→ER system.
Ostrom (1990, p. 57) stresses that first order difference transformation does not guarantee the removal of serial correlation. If the residual contains serial correlation after musical feature variables have been differenced, it becomes necessary to find alternative methods of modelling the serial process which remains in the system.
One of the more common serial correlation processes is the autoregressive process.
Autoregressive Adjustment If diagnostics suggest that there is serial correlation in the residual of a regression model there are several options. We have already discussed the possibility of reducing the effect of trends by differencing. However, if there still remains serial correlation other alternatives need be sought. A common approach is to treat the stochastic component of the regression model as having two components — a true stochastic component and a serially correlated component. There are three modifications of the regression model which can explain serial correlation: (1) autoregressive adjustment, (2)
119 The merit of first order differencing was examined thoroughly in preliminary analyses. - 330 - moving average adjustment (Box & Jenkins, 1976; Gottman, 1981), and (3) a mixed model consisting of both (1) and (2). The autoregressive model was the initial choice because it often provides a good representation of autocorrelated signals, it is relatively simple to calculate and it is widely available in statistics packages.
A first order autoregressive model assumes that the error term in the OLS regression model actually consists of two components:
Equation Chapter 6 -10 et = a1et-1 + vt
where et-1 is the error term from the previous point in time (1 time unit before time t) and vt is a true random variable, as et was in the OLS regression model (Equation
Chapter 6 -1 on page 299). The coefficient a1 indicates the proportion of the previous error term that is carried forward into the next point in time.
- 331 - In other word, the a1 coefficient indicates a type of serial correlation process known as first order autoregressive.120
If differencing has not removed serial correlation from the residual, the first order autoregression model may help to resolve the problem. Hence the final model becomes a first-order differenced regression model with a first order autoregressive adjustment. This will be the primary approach to modelling the data collected in
Experiment III. Before finalising the analytic sequence, two more issues will be addressed: (1) introducing more sophisticated diagnostics, and (2) introducing the notion of interrupted time series analysis.
More Sophisticated Diagnostics: The PACF and the ACF Revisited So far we have used the autocorrelogram as a diagnostic tool to indicate whether the
MF→ER system had serial correlation. If serial correlation was present, the variables were first-order differenced or first-order autoregressive adjusted or both. For example, a system with high or slowly decaying correlations at incrementing lags indicates a trend or the presence of an integrated serial correlation process (Figure
Chapter 6 -5). Differencing variables removes this serial correlating process.
However, the ACF provides far richer diagnostic information which I shall briefly explore.
120 It is possible to model error terms going back more than one time unit. Such models are higher- order autoregressive. - 332 - Figure Chapter 6 -5 Typical ACF Profile for Integrated Process
1 2 3 4 5 6 7 Lag Number
The autocorrelation command in SPSS comes with an option to display the partial autocorrelation function (PACF) in addition to the autocorrelation function. This pair of plots has been included in each of the previous examples, but the PACF has received no discussion until now. Put simply, partial autocorrelation refers to the dependency on points a fixed distance in time from one another. The effect of possible links through intermediate points is removed, or partialled out. In this respect, partial autocorrelation is the same as the principle of partial correlation.121
Together the ACF and PACF plots may be used to help diagnose the kind of serial correlation processes imbedded in the data. The shape of the ACF and the PACF can provide information about whether the residual is integrated (meaning that differencing is required) or autoregressive or something else.
As an example, consider a first-order autoregressive process. The error term is a function of the previous error term (Equation Chapter 6 -10 on page 331) which was itself a function of the previous error term:
121 For a more detailed definition and discussion of partial autocorrelation see Gottman (1981, pp. 141- 153). - 333 - et-1 = a2 et-2 + vt-1
and et-2 = a2 et-3 + vt-2
and et-3 = a3 et-4 + vt-3
… With the a coefficient less than 1, each error value propagates through the system in time, like a decaying memory.122 Therefore, the ACF for an autoregressive process will decay as the number of lags increases, as shown in Figure Chapter 6 -6. At the same time the PACF will only be significant at a lag of one time unit. The PACF will peak at lag one and then suddenly drop (Figure Chapter 6 -6).
The model developed so far has been based on predetermined musical features. But how do we know which musical features are suitable for including in modelling?
Although this is among the first issues that require consideration, the question will now receive further consideration.
122 For a formal mathematical proof, see Ostrom (1990, pp. 17-21). - 334 - Figure Chapter 6 -6 Theoretical ACF and PACF Profiles for a Typical First-Order Autoregressive Process.
ACF
1 2 3 4 5 6
PACF
1 2 3 4 5 6
Lag Number
Further Maximising Goodness of Fit: Interrupted Time Series Analysis The stepwise regression technique discussed above is useful for selecting variables for maximising fit. However, this technique will not always explain an adequate amount of variation in emotional response. By examining the residual it is possible to identify whether the regressors selected have adequately described the MF→ER system. If there remain patterns in the residual or the fit is low, further explanatory variables may be sought.
Assuming that all possible continuous variables and their lags have been utilised by the model, there remains the issue of dealing with musical feature variables which have not been coded. An important example is harmony.
- 335 - Harmony remained uncoded because there exists no simple, perceptually valid way of operationalising it as a multilevel variable.
A solution to such a problem is to dichotomise the musical feature variable and to apply interrupted time series analysis (McDowall, McCleary, Meidinger & Hay, 1980).
In the time series regression model, interrupted time series effects can be incorporated by using dummy predictorswhich can take the value of 0 or 1 only, corresponding to the values of the dichotomised variable. For example, in the case of harmonic progression, the occurrence of a perfect cadence may be coded as 1, with all other harmonic progressions coded as 0. The next step is to try to predict the kind of response associated with this changing variable. There are several models of response which may be used (McDowall et al., 1980, p. 66, Gottman, 1981, p. 50)
The details of interrupted time series analysis are beyond the scope of this dissertation. If the residual warrants further explanation, this will be achieved through inspection rather than formal mathematical modelling. The bulk of the modelling will rely on the relationship between coded, multilevel musical features and multilevel emotional response.
- 336 - Analysis Sequence Summary This chapter has served two important purposes:
1. To introduce basic ideas of time series analytic techniques and concepts.
2. To document explorations of analytic methods with a view toward
formulating a sequence of steps suitable for the analysis of data collected in
Experiment III.
My intention has been to introduce simple principles, step by step, in order to develop a technique for modelling time series data which (1) is easy to explain, (2) is easily understood by those not familiar with time series modelling, and (3) provides an adequate representation of the data.
The introductory nature of the chapter is intended to enable music-psychology and empirical aesthetics researchers not yet familiar with time-series analytic techniques to become aware of their benefits. I have documented some of the exploratory work for the purpose of exemplification and to justify why I have arrived at my final analytic sequence.123
The sequence of analytic steps is summarised in a flow chart in Figure Chapter 6 -7.
The sequence is repeated for each univariate emotional response dimension and for each of the four pieces giving a total of eight sets of analyses. The process and results of these analyses are reported in the following chapter.
123 For readers interested in more sophisticated time series models, there are several texts available, particularly in the field of economics. For example, see Box and Jenkins (1976); Gottman (1981); Hamilton (1994). - 337 - Figure Chapter 6 -7 Sequence of Steps Used in Time Series Data Analysis
Difference: First order difference all variables. Lag: Generate each variable at lags 0, 1, 2, 3 and 4. Stepwise Regression: Determine appropriate predictors. Diagnose Residual: Durban-Watsin; ACF/PACF; Box-Ljung Serially correlated residual? Yes: First order autoregressive adjustment. Diagnose residual. Serially correlated residual? Yes: ACF/PACF based model. Serially correlated residual? Yes: Try another model. Serially correlated residual? No: Accept Model. Inspect R2 and residual. If R2 is small and residual contains trends, suggest other variables w might improve model. Explain outliers.
- 338 -
Chapter 7 Time Series Analysis
The data collected in Experiment III (reported in Chapter 5) were analysed according to the procedures documented in the previous chapter. The present chapter begins by reporting and evaluating the analysis of the four test pieces and, within each piece, the two emotional response dimensions (ERs). Details of the analyses in the form of SPSS output are reproduced piece by piece in the Appendices (from
Appendix N on page 581 to Appendix V)124 and summarised in Table Chapter 7 -3 on page 370. A detailed analysis of a selection of outliers is provided to establish a method of categorising non-linearities. The second section of this chapter summarises the findings by grouping together the analyses according to musical features. In this way specific relationships among musical features and emotional response are examined.
124 The appendix appears in the second volume so that the reader may refer to it while reading the present chapter. - 339 - Piecewise Analysis
For each of the eight analyses, ordinary least squares (OLS) stepwise linear regression was not adequate for modelling the relationship between emotion and musical features. As demonstrated in the Appendices (for example, see Appendix P on page 597), all OLS regression analyses produced autocorrelated residuals, in turn violating an assumption of the regression model (see Chapter 6). This was reflected by the Durbin-Watson statistic being well below 2, autocorrelation (ACF) and partial autocorrelation function (PACF) producing significant correlations at one or more lags, and through a significant Box-Ljung statistic. Therefore, a first order autoregressive process was assumed to be present in the data and modelled accordingly using the autoregression function available in SPSS. For each of the eight data sets, first order autoregressive modelling (referred to as AR(1)) accounted for the serially correlated residual produced by the OLS model.125
Slavonic Dance Arousal For the arousal response gradient to the Slavonic Dance Op. 42, No. 1 by Antonin
Dvorak (Slavonic Dance), the AR(1) model fulfilled the criteria of non-serially correlated residuals. The model was:
Equation Chapter 7 -1 ∆Arousal = 0.00407 x ∆CEN0 + 0.00699 x ∆CEN1 + 0.00303 x ∆CEN2 + 0.396 x ∆DBA0 + 0.357 x ∆DBA1 + 0.190 x ∆DBA2 + 0.202 x ∆DBA3
The coefficient for the first order autoregressive component of the model (AR1) was
0.490. Although the coefficients for frequency spectrum centroid
125 This is shown in the ACF function output in Step 2 of the SPSS output in the Appendices (from page 581) for each of the eight analysis. - 340 - gradient (∆CEN) appear very small, they are in fact significant at p = 0.01. Centroid consists of numbers in the order of thousands, while the other variables move in the order of ones or tens. Smaller coefficients multiply the centroid variable so as to scale it to the range apt for changing arousal gradient values.
Also, all coefficients have a positive sign. This means that changes in the valence arousal gradient will be in the same direction as the change in each musical feature gradient when other musical feature variables are held constant. In other words, the partial correlations between musical feature and emotional response are positive in this case.
As with all the models discussed in this section of the chapter, the coefficient estimates were significant at p = 0.01. The actual significance of the models are shown in the appendices listing SPSS output (for the present example, in Appendix
O on page 588). A sample of this output is provided in Table Chapter 7 -1. Notice that the ∆Loudness lag 4 was dropped from the Equation Chapter 7 -1 because its coefficient was not significant at p = 0.01.126
Approximately 73% of the variance was explained by this model (Appendix O on page 591).127 This unusually good fit and the absence of autocorrelation in the residual (Appendix O on page 590) suggests that the model successfully explains changing arousal response in terms of loudness
126 See footnote 104 on page 306 127 The “R Square” estimate shown in the appendix is approximate because it was calculated by correlating the actual arousal data with the model predicted data. This is not a strictly correct procedure when data are serially correlated, but it is easy to understand and gives a rough idea of the model fit. The adjusted R2 in the print out is not relevant here because the regression command was used only to generate a correlation between predicted and actual data, and not for a formal model fit. This procedure was used for all analyses. - 341 - gradient, centroid gradient and a first order autoregressive process. Given the positive sign of the coefficients, increases in loudness coupled with “brighter” timbre each play a part in increasing arousal response gradient.
Table Chapter 7 -1 Summary of Slavonic Dance Arousal Model Coefficients AR1 is the first order autoregressive term. B denotes the variable coefficient, SE B is the standard error of the coefficient, T is the t-statistic testing the null hypothesis that the coefficient is zero and Sig T is the significance of the t-statistic. The number after a variable name (and before D) denotes the lag number of the variable. D1 after a variable name indicates that it has been first order differenced. For example, DBA4D1 is the first order differenced loudness variable lag 4. Variable abbreviations are listed in the Glossary. The table is extracted from Appendix O on page 588.
Variable B SE B T Sig T AR1 0.4903 0.0689 7.1215 0.0000 DBA1D1 0.3566 0.0533 6.6856 0.0000 DBA0D1 0.3962 0.0490 8.0885 0.0000 DBA2D1 0.1899 0.0560 3.3881 0.0008 DBA3D1 0.2024 0.0510 3.9702 0.0001 CEN1D1 0.00699 0.00117 5.9783 0.0000 DBA4D1 0.0478 0.0431 1.1100 0.2683 CEN2D1 0.00303 0.00104 2.9025 0.0041 CEN0D1 0.00407 0.00107 3.8222 0.0001 CONSTANT 0.2670 0.3362 0.7940 0.4281
The final stage in the analysis was to examine residual outliers. Residual outliers are points where members of the residual series fall more than three standard deviation units outside the mean. Using this stipulation, 99.7% of values should fall within this three sigma band. Values falling well outside this range require special attention and explanation because the model was probably inadequate for describing these points, or the points were spurious (for more detailed information on the treatment of outliers see Chatterjee & Price, 1991). Calling these values outliers is not strictly correct, for model mis-specification does not infer a problem with the data.
However, for convenience, I shall refer to all values falling outside the band as
- 342 - outliers. Further, I will only examine those outliers that are well outside this band in order to avoid situations where an explanation might be “forced”.
For the Slavonic Dance the model of Equation Chapter 7 -1 produced 5 residual outliers at t64 , t142, t160, t223 and t224. These outliers are shown graphically (page 592) and tabulated (page 593) in Appendix O. Residual outliers are shown graphically and in tabulated form in Step 3 of the SPSS output for each analysis. All but one
(t223) of the outliers was well over three standard deviations (3 x 2.49) away from the mean, however the last two occurred close together and were related. Therefore, I investigated all five outliers.
The t64 outlier produced an underestimated prediction of arousal response, hence a large residual. The model predicted that for the combination of musical features in the recent past, the arousal value should have been much smaller than it actually was. The musical event just preceding the t64 outlier was a sudden fortissimo outburst within a pianissimo context (note the difference between the model predicted arousal value and the actual difference arousal value at t64 in Figure Chapter 7 -1). This outlier provides a good example of the potential complexity of the MF→ER system.
The model assumes that lag in response relative to musical features is fixed. As an example, consider the two variables which, according to the OLS analysis, make the largest contribution to explaining variation in response. For the present model these variables are loudness lag 1 and 0 (Appendix O on page 584). For the sake of simplicity, we can assume that these lags are the ones most likely to guide arousal response, and therefore when loudness changes, a change in arousal is expected within the next two seconds.
- 343 - However, as shown in Figure Chapter 7 -1, the sudden outburst preceding t64 requires a model sensitive to the effect of the onset of the sudden, loud event. The sudden shock has pushed arousal responses suddenly upward, almost
“instantaneously”, or certainly within the one second sample (see t63-64 in Figure
Chapter 7 -1), while the dynamic response to the diminuendo (t65) has returned to the original, system predictable level.128 This uncharacteristic instantaneous response could be explained by the startle effect (Gaston, 1951), which is a response to a very sudden change in the environment. When startle occurs, a low level, innate
“physiological system” takes over from the high level “cognitive system” in order to orient the individual to the sudden change and to prepare for flight. The reaction times to startling stimuli are much shorter than to the subtle changes that usually occur in the music. I do not intend to use the term startle in this strict sense. Rather,
I use it to highlight the change in system dynamics. By t65 the system returns to more regular lagged correlations. An important point here is that although the AR(1) linear regression model was insensitive to this change in the system dynamics, it has still explained a large amount of variation, implying that a more esoteric or complex model is unnecessary.
128 I am asserting that a musical event was causal in this change because it appears, to me, to be a reasonable assertion. While I concede that inferring causation based on a single piece of evidence is risky, I also maintain that this position facilitates the formulation of a scheme for explaining and categorising rules through plausible reasoning. My “causal” reasoning seems plausible, and is consistent with the basic tenet of this dissertation, that there exist underlying, quantifiable rules which govern the relationship between musical features and emotional response. - 344 - Figure Chapter 7 -1 Slavonic Dance MF→Arousal at t60-68 (mm. 84-90) Music Score Source: Dvorak, 1989, p. 12.
40 actual and startle outlier expected 30 ² Arousal peaks are one lag apart 20 M odel Predicted (% )
10 ² A rousal (% )
0 ² Loudness (dBA)
-1 0 ² C e n tro id (100Hz)
-2 0 60 61 62 63 64 65 66 67 68 Time (s) 61 [m.84] 62 63 64 65 66 [m. 90]
- 345 - Figure Chapter 7 -2 Slavonic Dance MF→Arousal at t137-146 (mm. 166-180) Music Score Source; Dvorak, 1989, pp. 25-26.
10
0
-1 0
M odel Predicted (% ) overshoot ² A rousal (% ) -2 0
² Loudness (dBA) recovery time ² C e n tro id (100Hz) -3 0 137 138 139 140 141 142 143 144 145 146 Time (s) s 135 137 139 141 143 145 147 bar 180 185 190
- 346 - The t142 outlier occurs when the first fortissimo theme suddenly changes to the pianissimo theme (with a 10 dBA drop in loudness). This time there is an over- reaction in arousal gradient response, with the arousal value declining rapidly for one second after the new, softer theme has commenced. Recovery requires another second or so (Figure Chapter 7 -2). The reason for this response might be explained by participants trying to predict the next musical event, and being taken by surprise when the expected continuation of an event is changed. I refer to these two stages of response as overshoot and recovery, as shown in Figure Chapter 7 -2.
Another overshoot outlier occurs at t160. On this occasion the participants were expecting the continuation of a crescendo, and then having to suddenly change path when a subito piano was used to restart the crescendo. In this case three stages surrounding the outlier response can be identified: (1) the disrupted expectation — where the crescendo is interrupted but the arousal continues to increase, (2) the overshoot response — where the participants attempt to compensate for the unexpected event but move too far in the other direction, and (3) the participants recover to the more regular, model predicted level. The three stages of response are shown in Figure Chapter 7 -3.
- 347 - Figure Chapter 7 -3 Slavonic Dance MF→Arousal at t155-164 (mm. 181-194)
10 expectation disrupted
0
recovery
M odel Predicted (% )
-1 0 overshoot ² A rousal (% )
² Loudness (dBA) outlier ² C e n tro id (100Hz) -2 0 155 156 157 158 159 160 161 162 163 164 Time (s)
The final two outliers produced by the AR(1) regression model occurred simply because the piece had finished: the loudness diminished to silence while the arousal moved gradually back toward the origin. Apparent in Figure Chapter 7 -4 is the activity in arousal gradient response for the two seconds after the music has stopped.
The downward movement of the high arousal values is indicated by the negative values of the arousal gradient from t223. The gradient is negative, and therefore the previously high arousal becomes smaller but at a fairly slow rate, compared with the predicted rate of drop in arousal. This produced outliers at t223 and t224.
The effect of these outliers is similar to the after-glow effect which occurs after staring at a bright object. The feeling of arousal remains, even though the music has stopped. After-glow could be a genuine, underlying effect of the
- 348 - system or it could be an artefact caused by the averaging of participants who return immediately to zero at the end of the piece with those who forget to return to zero.
These outliers provide another example of changing dynamic system response which the regression model cannot explain.
Slavonic Dance Valence
The model proposed for the valence response gradient to the Slavonic Dance is:
Equation Chapter 7 -2 ∆Valence = 0.0507 x ∆BPM1 + 0.0356 x ∆BPM2 + 0.0258 x ∆BPM3 + 0.169 x ∆DBA0 + 0.137 x ∆DBA1
The coefficient for the AR1 component was 0.501 (p < 0.01 for all coefficients) as indicated in Appendix P on page 599. This model explained approximately 62% of the variance (page 602) and contained three outliers at t143, t168 and t224. (page 603).
The outliers are not of particular concern because they are fairly close to the three sigma band.
- 349 -
Aranjuez Arousal
The model describing the MF→ER system for the second movement of Rodrigo’s
Concerto de Aranjuez (Aranjuez) contains 11 statistically significant coefficients (at p < 0.01, see Appendix Q on page 611):
Equation Chapter 7 -3∆Arousal = 0.0388 x ∆BPM2 + 0.0305 x ∆BPM3 + 0.0312 x ∆dBA0 + 0.0713 x ∆dBA1 + 0.0598 x ∆dBA2 + 0.0534 x ∆dBA3 + 0.0277 x ∆MEL1 + 0.324 x ∆TEX2 + 0.327 x ∆TEX3 + 0.132 x ∆TEX4
The eleventh coefficient was 0.626 for the autoregressive parameter, AR1 and the model explained about 57% of the variance (page 615). Because the piece was fairly long (654 one-second samples), having so many predictor variables did not pose problems (see Selecting Regressors on page 310 in Chapter 6). The Box-Ljung statistic indicated no significant autocorrelation at p = 0.01, but some autocorrelation at p = 0.05 for some lags greater than 3 (page 614). The slight autocorrelation at lag 4 is responsible for this problem (r4 = 0.155 which is outside the 95% confidence interval of two standard errors of 0.4). This borderline significance did not necessitate a new formulation of the model, and the model of Equation Chapter 7 -3 was accepted. However, the model did produce eight outliers, and I shall examine the first group of these because it contains an outlier which is well outside the three sigma band (10.48/1.03 = 10.17 sigmas at t228 as shown in the outlier listing of
Appendix Q on page 617).
The first five outliers occurred in the space of 21 seconds from t213 to t233. In this section, the opening fragment of the first theme, played forte with a full texture, is juxtaposed against a pianissimo theme with a thinner texture. This bar for bar juxtaposition occurs over four bars (mm. 31-34) at t210, t217 and t226
- 351 - and t231. These contrasting bars are outlined by nearly instantaneous changes in direction of arousal movement for all but the first entry. The response to the last three changes actually occurred at t219, t227 and t232 (Figure Chapter 7 -5). Clearly, the model predicted these changes to occur at t220 t228/9 and t233 respectively — one or two seconds later than the time at which the actual responses occurred. In other words, the dynamic structure of the piece had changed during this section of sudden contrasts — arousal gradient changes faster than the model predicts (observe the horizontal dashes in Figure Chapter 7 -5), and in some cases this earlier than expected change can explain the “outliers”.
Once again, sudden change has been identified as a device for modifying the dynamic structure of the MF→ER system.129 The sudden changes in these bars would require a separate model to be developed. Although such a model may better describe this four bar section of the system, the option was still considered unnecessarily complicating.
129 Although I have referred to this kind of change in the dynamic response as startle, the term seems inappropriate in the Rodrigo example. - 352 - Figure Chapter 7 -5 Aranjuez MF→Arousal at t210-235 (mm. 31-34) Musical score source: Rodrigo, 1957, pp. 43-44 Since loudness and texture dominate the response, only those musical features are shown.
20
large outlier
10
M odel Predicted (% )
² A rousal (% )
0 C hange in ²A rousal direction occurs one lag before predicted change in direction -1 0 20
10
0
-1 0 ² Loudness (dBA)
² Texture (voices) -2 0 210 214 218 222 226 230 234
212 216 220 224 228 232 Tim e (s) 210 [m.31] 217 224 231 [m.34] 238
Later in the piece there is a brief moment of release in tension from a movement which is, for the most part, emotionally intense. This
- 353 - “scherzandesque” section appears quite suddenly half way through bar 52, and lasts for 2 bars (t360 to t368). The section is distinguished by staccato articulation and a faster tempo. The thematic material is borrowed from the exposition, however the changed starting pitch, staccato articulation and faster tempo makes the similarity quite subtle. Again, it is only one point — the point at which this section begins (at t363) — that the model cannot predict successfully. The section does not consist of a series of outliers, and therefore the model appears to be quite adequate. The listener may respond to the start of this section with surprise and either over-react or become momentarily confused while orienting to the newly expressed mood. I refer to such outliers as orienting. Alternatively, the variations in musical features cannot be reconciled by the model: while the participants appear to be confused, the problem is actually due to a weakness in the model. As Figure Chapter 7 -6 shows, the regressor variables are moving in different direction leading up to the outlier. Due to the positive coefficients in Equation Chapter 7 -3 (on page 351) the model works better when there is agreement in the direction of musical feature variables at the evaluated lags.
- 354 - Figure Chapter 7 -6 Aranjuez MF→Arousal at t360-370 (mm. 52-54) Musical score source: Rodrigo, 1957, p. 48-49.
20
orienting response 10 outlier
M odel Predicted (% )
² A rousal (% ) 0
² Loudness (dBA)
² Texture (voices) -1 0 360 362 364 366 368 370 361 363 365 367 369 358 [m. 52] 360 362 364 366 [m. 54] 368 371
Aranjuez Valence
The model describing the valence gradient response to Aranjuez was:
Equation Chapter 7 -4 ∆Valence = 0.0255 x ∆Mel1 + 0.0536 x ∆Mel2 + 0.0520 x ∆Mel3 + 0.0295 x ∆Mel4
- 355 - The autoregressive parameter had a coefficient of 0.477. All coefficients were significant at p < 0.01 (Appendix R on page 623). The model predicts that positive contour (rising melody) will have the effect of moving valence upwards. However, the model explained less than 33% of the variance. An important reason for the smaller explained variance relative to the previous models is that only one variable, with four lags, appears in the equation. The stepwise regression process determined that these four lags of melody significantly added to the fit of the model, while possessing significantly non-zero coefficients in the AR(1) model. The result suggests that something else, apart from loudness, texture, centroid and tempo, is required to further explain the response. An examination of the first of eight outlier provides a clue.
The most extreme valence outlier occurred at t363 (Appendix R on page 627) for valence. An arousal response at this point was also an outlier, but not as extreme
(Appendix Q on page 617). The literature suggests that light, staccato articulation increases the valence (see Articulation/Duration on page 243 in Chapter 4). As can be seen in Figure Chapter 7 -7, there is a notable rate of change in valence when the staccato passage commences at t360. The exclusion of a variable which codes articulation can explain this outlier. I therefore refer to this as a missing variable outlier.
- 356 - Figure Chapter 7 -7 Aranjuez MF→Valence at t340-365 (mm. 46-51) For details of music score see Figure Chapter 7 -6 on page 355. 20
missing variable outliers
10
0 M odel Predicted (% )
²Valence (% ) -1 0
²M elodic (M IDI note no.)
-2 0 360 361 362 363 364 365
Time (s)
Pizzicato Arousal Arousal gradient in Johann and Josef Strauss’s Pizzicato Polka (Pizzicato) was modelled in terms of lagged loudness variables and a lagged tempo variable:
Equation Chapter 7 -5∆Arousal = 0.136 x ∆dBA0 + 0.114 x ∆dBA1 + 0.0869 x ∆dBA2 + 0.0416 x ∆BPM3
The AR1 coefficient was 0.441 (Appendix S on page 634) and the model explained about 36% of the variation in changing arousal (page 636). The serial correlation in the residual was not significant (page 635) and two outliers were identified, at t70 and t79 (page 638). They occurred in the second part of the Trio section. This section consists of eight bars repeated, and connects the trio to the da capo. The distinguishing feature of the first section of this bridge is that it is the first loud point of the piece. The loudness is also quite sudden, explaining why the model may have failed at these two points. From Figure Chapter 7 -8 it becomes apparent that loudness and arousal move almost
- 357 - instantaneously for each of the loud outbursts at t69 and t78. The coefficient for lag 0 of loudness in Equation Chapter 7 -5 is relatively small meaning that the model cannot deal with such startle responses very well. The use of the term startle seems particularly appropriate in these example because not only is the dynamic structure of the system altered, but also the intensity is amplified: at each outlier in Figure
Chapter 7 -8 the actual arousal gradient is greater than the predicted value (which occurs one second later). This corresponds to the arousing characterisation of the physiological-motor startle response.
Figure Chapter 7 -8 Pizzicato MF→Arousal at t68-81 (mm. 47-69) Piano score reduction source: Strauss, Johann and Josef Strauss, 1943, p.17.
10 startle heightens arousal
0
M odel Predicted (% )
² A rousal (% ) -1 0
² Loudness (dBA) startle outliers
² Tem po (bpm ) -2 0 68 70 72 74 76 78 80
69 71 73 75 77 79 81
Time (s)
s 66 67 68 69 70 71 73 74 75 76 77 78 79 80 81 bar m.47 m.49 m.51 m.53 m.55 m.57 m.59 m.61
- 358 - Pizzicato Valence An autoregressive model for valence gradient which eliminated a sufficient amount of serial correlation from the MF→ER stepwise regression model was:
Equation Chapter 7 -6∆Valence = 0.0969 x ∆dBA1 + 0.0568 x ∆dBA2 + 0.0586 x ∆dBA3 with an AR1 coefficient of 0.501 (Appendix T on page 644). The model explained approximately 38% of the variance in changing valence (page 646). Two outliers appeared in the valence model, at t5 and t7 (page 648).
From Figure Chapter 7 -9 it can be seen that, at both outliers, valence rate is increasing while loudness gradient is decreasing. However, the model of Equation
Chapter 7 -6 predicts a positive relation between loudness and valence — rate of loudness is falling and so rate of valence should also be falling. Musical features other than loudness provide clues to this anomaly. The first four bars consist of short-duration notes in a major mode, with loud and soft chords juxtaposed and with rising in pitch. The silent pause occurs where there is an expectation of another loud chord. This combination of musical features provide ingredients appropriate for the expression of humour (Mull, 1949). Hence, the outliers may be explained in terms of missing variables — the effect of juxtaposed loudness followed by a silent pause.
Alternatively, the participants may have been adjusting to the mood of the piece: the model could not predict responses at these outliers because the piece was too close to the beginning.
- 359 - Figure Chapter 7 -9 Pizzicato MF→Valence at t1-8 (mm. 1-4) Piano score reduction source: Strauss, Johann and Josef Strauss, 1943, p.16. 10 orienting outliers
0
-10 Model Predicted (%)
²Valence (%)
²Loudness (dBA) -20 5 6 7 8
Time (s) s 0 2 3 4 5 7 8 bar m.1 m.2 m.3 m.4 m.5
Morning Arousal The autoregressive model for changing arousal in response to “Morning” from Peer
Gynt by Edvard Grieg (Morning) produced no serial correlation for the first four lags
(Appendix U on page 656). Since only lags 1 to 4 were used in the analysis, the model was accepted. In fact, the high serial correlation at lag 5 supports the selection of only four lags of musical feature variables because the higher order lags are detecting repeating sections of the piece (see Selecting Lags on page 308 in Chapter 6 for more details). As indicated in Appendix U on page 654, the model was:
Equation Chapter 7 -7 ∆Arousal = 0.111 x ∆BPM3 - 0.00191 x ∆CEN2 - 0.00245 x ∆CEN4 + 0.344 x ∆dBA1 + 0.332 x ∆dBA2 + 0.468 x ∆dBA3 + 0.197 x ∆dBA4 - 0.0983 x ∆TEX0
- 360 - This model explains approximately 67% of the variation in changing arousal (page
657).130 It produces two outliers, one at t49 and the other at t211 (page 659). The first outlier occurred at the first climax of the piece, and is marked by a crescendo.131 By examining the variables in Figure Chapter 7 -10, arousal gradient continues to increase after the climax. A very large increase in arousal takes place at this point and it appears that this increase requires more time than the model allows.
Therefore, in contrast to the startle responses discussed above, there appears to be an inertia response at this point — the after-effect of a prolonged build up.
Figure Chapter 7 -11 indicates the last arousal gradient outlier identified. It occurs in the final chord of the piece, which is sustained over two and a half bars. Within this sustained chord their is a hair-pin swell, where the chord becomes louder and then softer. The crescendo section of this hairpin peaks at t211, with a substantial rise in loudness from t210 to t211. The arousal response at this point appears more sensitive to the swell than the model predicts (Figure Chapter 7 -11); Not only does the dynamic structure of the system change (arousal response is faster than predicted, as in a startle type response), but the rate at which arousal increases is also affected.
This is an interesting finding from the point of view of the performer, for it suggests that the effect of a swell of loudness within a sustained chord can “artificially” increase the arousal expressed by the music.
130 Compare this finding with the higher, though less valid, R2 obtained in the preliminary analysis in Chapter 6. Two loudness lags explained 84% of the total variance (
Equation Chapter 6 -5 on page 307). 131 Of this section, Grieg wrote “I imagine the sun breaking through the clouds at the first forte.” (Cited by Fiske in Grieg, 1970, p. iv) - 361 -
Changing valence response in Morning could be expressed entirely in terms of lagged texture variables (as extracted from Appendix V on page 665):
Equation Chapter 7 -8 ∆Valence = 0.0895 x ∆TEX1 + 0.186 x ∆TEX2 + 0.227 x ∆TEX3 +
0.182 x ∆TEX4 with an AR1 coefficient of 0.393. This model explains approximately 40% of the variance (page 668) and produces five outliers (page 669). The outliers were each fairly close to the three sigma limit.
The Perfect Cadence as an Interrupting Time Series
So far, several suggestions have been made as to how outliers may be explained.
Among these is the addition of new variables. The variables used in the initial analysis were restricted to salient musical features which could be coded as multilevel variables. Because of the limitation to multilevel variables only, several important features were omitted, including rhythm, articulation and harmony. It is not the aim of this dissertation to present a comprehensive analysis of relationship between non-multilevel variables and emotional response. However, a brief digression is worthwhile in order to determine some techniques for improving model fit. Morning provides an interesting example of how coding one aspect of harmony might be used to improve the valence model fit, which in the present case is relatively poor.
- 364 - Figure Chapter 7 -12 Valence Response Gradient for Morning
Vertical lines indicate points where primary or secondary V7-I cadences occur.
123456 10 m.21 m.38 m.46 m.68 m.72 m.79
0
-1 0 1 23 45 67 89 111 133 155 177 199
12 34 56 78 100 122 144 166 188 210
Time (s)
An exploration of Figure Chapter 7 -12 suggests that when a V7-I cadential pattern occurs, the valence response gradient rises. Of the seven highest valence-gradient peaks, six are preceded by a cadential V7-I intervention or impact.132 Some valence-gradient peaks are not preceded by V7-I interventions, and some impacts do not precede a valence-gradient peak. It is the six V7-I cadences which precede the valence-gradient bumps that are of interest here. They are labelled in Figure Chapter
7 -12.
Composers tend to employ several, interacting musical features to obtain a desired emotional expression. One obvious example is the use of brass instruments in loud passages. In Morning, Grieg uses brass in each of the
132 Time series literature refers to such events as interruptions. However, it seems somewhat unnatural to refer to cadential points in music as interruptions. Therefore, I have borrowed the terminology of Gregson (1983) and McDowall, McCleary, Meidinger and Hay (1980) in this section (intervention and impact), but retained the common nomenclature in the subheading of this section. - 365 - three fortissimo passages (at m. 30, 38 and 46). Now, supposing that there was some consistency in responses just after each of these fortissimo passages, it may be incorrectly concluded that the intervention was due to the brass sonority. Evidence would be required that such responses were made just after all brass entries, and those entries would need to occur in a variety of musical contexts.133 Consequently, by labelling an intervention as “V7-I”, I should demonstrate that this harmonic process is the common thread of all the so called interventions. From this point of view, Morning is an interesting piece to analyse. Table Chapter 7 -2 summarises the musical events leading up to, during, and immediately following each of the six V7-I cadences under scrutiny. The main point to note in this table is that none of the columns contains the same information throughout. There appears to be no other musical feature or event that occurs each time a V7-I cadence occurs, and it therefore seems safe to conclude that the valence gradient increases which follow bars 21, 38,
46, 68, 72 and 79 are related to these perfect cadences and not to an interacting or confounding musical feature.134 Subsequently, these interventions may be modelled by a response function which approximates the alleged effect of the intervention.
This could be achieved by use of dummy variables in the regression equation or techniques prescribed by Box and Jenkins (1976), Gregson (1983) and McDowall,
McCleary, Meidinger and Hay (1980).
133 See the discussion on Collinearity on page 311 in Chapter 6. 134 It could be argued that the V7-I cadence occurs at structural points in the music. While it is true that they do, it is also true the V7-I pattern is partly responsible for producing this structural point. If the question is one of causation (the structural point versus the V7-I progression), we will need many more examples from various kinds of music. At the moment I am not concerned about which it is, and the V7-I reference may be treated as just a convenient label. - 366 - Table Chapter 7 -2 Events Surrounding V7-I Cadences in Morning Bar Antecedent Consequent Orchestration Antecedent Consequent dynamic dynamic material material m. 21 Crescendo Sempre forte full orchestra Extension of Theme 1 from piano to (no trombones) Theme 1 forte m. 38 2 bar crescendo 2 bar full orchestra Theme 2 Theme 2 from piano to diminuendo (no timpani) fortissimo from fortissimo to piano m. 46 2 bar crescendo 2 bar full orchestra Extension of 4 bar transition from piano to diminuendo (no timpani) theme 2 to theme 1 fortissimo from fortissimo to piano m. 68 piano piano horns, Extension of New material/ bassoons, theme 1 variation of oboes and flute theme 1 m. 72 piano piano horns, Extension of New material/ bassoons, theme 1 variation of oboes and flute theme 1 m. 79 piano with piano flute, strings General pause Theme 1 small (no first followed by 3 crescendo violins) long, dominant 7 chords
Summary of Outlier Types Time series analysis of the data collected in Experiment III was modelled using a first-order differenced regression model with first order autocorrelated adjustment, and lagged predictor variables selected so as to maximise fit via OLS stepwise regression. In each case a satisfactory amount of serial correlation was accounted for.
The models explained from as little as 32% up to 73% of the variation in univariate emotional response.
The models were also evaluated according to their outliers. Outliers fell into two broad categories: (1) alteration in the dynamic structure of the MF→ER system, or
(2) missing variable.
- 367 - Alterations in the dynamic structure of the system refer to outliers produced by responses occurring before or after the model predicted response. Such outliers reflect the complexity of the music-emotion system, because the lag structure changes under different musical conditions. Two types of lag structure alterations were identified — startle and inertia. Startle responses refer to responses which occur before the model predicted time. The label was chosen to reflect the sudden, almost involuntary response to abruptly loud passages in the music. Startle responses were the most common type of dynamic structure alteration identified.
There was some evidence that the startle effect was related to an increase in the amplitude of actual response compared to the model predicted value. Inertia responses were those which occurred later than the system predicted lag. Outliers caused by inertia responses were not as common, although several types were identified: orienting, overshoot-recovery and after-glow. Orienting responses refer to the extra time taken for the response to fall into the model predicted pattern.
Orienting outliers were usually identified at the beginning of some pieces, such as
Pizzicato, or at the start of a contrasting section. Two occurrences of overshoot- recovery outliers were found in Slavonic Dance. The after-glow effect, another inertial response, was identified as an explanation of the outliers at the conclusion of
Slavonic Dance, where actual responses did not return rapidly to zero. Because inertial responses did not produce many outliers, it is possible to conclude that the models are more sensitive to inertial variations in dynamic structure than they are to startle responses.
Missing variable outliers were values that could be explained by other variables which, for some reason, were excluded from the model. It was
- 368 - somewhat surprising that the number of missing variable outliers were so few. It provides evidence that musical features such as articulation, rhythm and harmony do not add much information to the five variables selected, and that the variables chosen were a reasonably good representation of the music. However, models with low R2 act as a counter claim to this argument and more work is needed to determine to what extent the musical signal may be reduced without forfeiting adequate representation.
The two categories of outliers are not mutually exclusive because a change in dynamic structure may be viewed as a missing variable which accounts for the change. Further, these outlier categories do not encompass all kinds of outliers.
Strictly speaking, they are not outliers at all, because they indicate mis-specifications in the model rather than errors in the data. However, for convenience, I have chosen to refer to all unexplained values as outliers.
Summary of Quantitative Analyses The first order autoregressive models discussed in the previous sections are summarised in Table Chapter 7 -3. Each variable, with its five lags, has its coefficient indicated in the appropriate column, piece by piece. A comparison of each musical feature across the four pieces is the focus of the final section of this chapter.
- 369 - Table Chapter 7 -3 First Order Autoregression Models Summary R2 is a rough approximation of the model fit. The values were obtained by squaring the correlation coefficient of model predicted and actual data. Outliers = number of points outside the |3*SD| (99.7%) mean residual range. Parameters = number of significant (p < 0.01) coefficients, including the first order autoregressive (AR1) coefficient. For a description of the musical feature (MF) abbreviations, see the Glossary. LAG 0 1 2 3 4 MF
Slavonic Dance Arousal R2 = 0.73 5 outliers 8 parameters AR1 .4903 BPM CEN .00407 .00699 .00303 DBA .3962 .3566 .1899 .2024 MEL TEX
Aranjuez Arousal R2 = 0.58 8 outliers 11 parameters AR1 .6255 BPM .03889 .03047 CEN DBA .0312 .0713 .0598 .0534 MEL .0277 TEX .3238 .3275 .1316
Pizzicato Arousal R2 = 0.35 3 outliers 5 parameters AR1 .4408 BPM .04163 CEN DBA .1365 .1135 .0869 MEL TEX
Morning Arousal R2 = 0.67 2 outliers 9 parameters AR1 .5149 BPM .111 CEN -.00191 -.00245 DBA .3444 .3317 .4682 .1972 MEL TEX -.0983
Slavonic Dance Valence R2 = 0.62 3 outliers 6 parameters AR1 .5012 BPM .0507 .0356 .02582 CEN DBA .1694 .1374 MEL TEX
- 370 - LAG 0 1 2 3 4 MF
Aranjuez Valence R2 = 0.33 8 outliers 5 parameters AR1 .4765 BPM CEN DBA MEL .0255 .0536 .0520 .0295 TEX
Pizzicato Valence R2 = 0.38 2 outliers 4 parameters AR1 .5006 BPM CEN DBA .0969 .0568 .0583 MEL TEX
Morning Valence R2 = 0.40 5 outliers 5 parameters AR1 .3928 BPM CEN DBA MEL TEX .0895 .1859 .2268 .1816
Analysis of Emotional Response with Each Musical Feature Time series analysis has been used to describe the relationship between emotional response and musical features for four separate pieces of music. In order to address the current research question specifically, the relationships between each emotional response dimension and the five musical features across all pieces were examined.
Statistically significant coefficients from the AR(1) regression models were collected, and a series of musical feature profiles were produced. The profiles required the collation of the regression coefficients for all pieces per emotional dimension. From this, a qualitative analysis can be used to
- 371 - determine if a relationship between each musical features and each emotional response exists. The profiles are reproduced in graphical form from Figure Chapter
7 -13 to Figure Chapter 7 -21. The following subsections are a discussion of the effect of each of the five musical features upon the two emotional dimensions.
Tempo
Changing tempo had a positive relationship with both valence gradient and arousal gradient. The positive relationship was found for all pieces except Slavonic Dance.
Based on further investigation and in light of previous research (Chapter 4), Slavonic
Dance was considered an anomalous finding. Its lacking relationship between tempo and arousal can be explained in terms of collinearity. Large changes in tempo occur only at the coda of the piece, where arousal increases. But loudness also increases in this section. Subsequently, tempo adds little or no extra information to the calculation; loudness is a sufficient predictor of arousal.
Valence was not affected by tempo with the exception of Slavonic Dance. The
Slavonic Dance finding can be explained in terms of interaction of features. The piece is based on a fast underlying tempo, short articulation and major mode.
Perhaps it is under these conditions that tempo affects valence rather than just arousal. The important aspect of this finding is that there is a strong interaction between tempo and other musical features with regard to the dimension of emotion which can be manipulated. The simple notion that tempo is related positively to arousal is, however, supported.
- 372 - Figure Chapter 7 -13 Tempo Profile for Arousal
0.09
0.08
0.07
0.06
0.05 0.04 Morning Coefficient 0.03 Pizzicato 0.02
0.01 Aranjuez 0 0 Slavonic Dance 1 2 3 Lag 4
Figure Chapter 7 -14Tempo Profile for Valence
0.06
0.05
0.04
0.03
Morning
Coefficient 0.02
Pizzicato
0.01
Aranjuez
0
0 Slavonic Dance 1 2 3 Lag 4
Centroid
The gradient of the frequency spectrum centroid has no significant effect on valence gradient for any of the four test pieces. There was a strong positive relationship between centroid for the arousal for Slavonic Dance. When mean spectral frequency
(brightness) gradient was rising, arousal gradient tended to rise. A small but opposite effect was observed in Morning, where an increasing centroid rate was correlated with decreasing arousal gradient. Again it could be that other variables such as loudness, texture, harmony and articulation act as confounding variables.
The following sequence might
- 373 - explain a possible chain that produced significant negative centroid gradient coefficients: The regions of high arousal occurred usually when the orchestra was playing loudly; loudness was enhanced by the use of a tutti orchestra; a tutti orchestra employed the lower instruments (celli, double basses, bassoons, trombones and timpani), and so the mean spectral frequency was, on average, lowered during these high arousal sections.
The findings suggest that centroid is not a useful variable in the investigation of music-emotion relationships. A risk involved with examining only four pieces of music is that they may not incorporate a sufficient variety of the pertinent emotion producing musical feature combinations. While this possibility looms, the frequency spectrum centroid variable should not be abandoned. Indeed, the fact that the results produce an unclear picture of the relationship between centroid and emotional response dimensions should signal the need for further research on this variable.
Figure Chapter 7 -15Centroid Profile for Arousal
0.007 0.006 0.005 0.004 0.003 0.002 0.001
0 Coefficient -0.001 -0.002 -0.003
Morning 0 Pizzicato 1 Lag 2 Aranjuez 3 4 Slavonic Dance
- 374 - Loudness The most conclusive results appear in loudness. Loudness is unambiguously positively correlated with arousal. The effect of loudness is particularly strong at lags one and two for all four test pieces. Loudness provides good explanatory power for the arousal changes in Slavonic Dance and Morning. This musical feature also effected valence, though not to the same degree. Increases in loudness in Pizzicato and Slavonic Dance tended to have a positive effect on valence. The finding that no tempo changes were effective on Aranjuez and Morning can be explained the same way as for loudness. Aranjuez and Morning are both legato articulation pieces with slow baseline tempi. This appears to fix the valence or make it less susceptible to manipulation by musical features such as tempo and loudness. Demonstrating these interactions is a issue for further investigation.
Figure Chapter 7 -16Loudness Profile for Arousal
0.5
0.4
0.3
0.2
Coefficient
0.1
0
Morning 0
Pizzicato 2 Lag Aranjuez 4 Slavonic Dance
- 375 - Figure Chapter 7 -17Loudness Profile for Valence
0.2
0.15
0.1 Morning
Coefficient 0.05 Pizzicato 0 Aranjuez 0 1 2 Slavonic Dance Lag 3 4
Melody
Melodic contour only significantly correlated with emotional response to one piece
— Aranjuez. Although there is a slight correlation between arousal gradient and melody gradient at lag 1, the relationship between melody gradient and changing valence is quite strong. Aranjuez is the only stimulus which contained a long melodic structure. The first melodic subject takes nearly 40 seconds to expose. It is an arch shaped melody, slowly rising, and then falling. The first subject is played twice, on the oboe and then on the solo guitar. The second subject is related to the first and takes around 25 seconds to expose. It consists of a downward melodic shape. This melodic structure provides a good opportunity to examine the relationship between emotional response and melodic movement. The finding is in agreement with the research of Gerardi and Gerken (1995) which posits that melodic contour is positively related to valence (but see Melodic Direction/Contour on page
235 in Chapter 4).
- 376 - Figure Chapter 7 -18Melody Profile for Arousal
0.03
0.025
0.02
0.015
Morning
Coefficient 0.01 Pizzicato 0.005 Aranjuez
0 Slavonic Dance 0 1 2 3 Lag 4
Figure Chapter 7 -19Melody Profile for Valence
0.06
0.04
Morning 0.02
Coefficient Pizzicato 0
0 Aranjuez 1 2 Slavonic Dance Lag 3 4
- 377 - Texture There are strong, though inconsistent, relationships between texture and emotional response. In Aranjuez, texture gradient is positively linked with the arousal dimension, while it is positively linked to the valence dimension in Morning.
Although there is no obvious explanation for why this is the case, the answer is likely to do with interactions and collinearity.
Interactions may act to facilitate a relationship between texture and valence in
Morning. For example, a relatively simple, diatonic mode within a slow tempo, legato articulation context may be sufficient to allow changes in texture to vary valence response. Conversely, Aranjuez, although sharing some characteristics with
Morning, is in a minor key. This means that more dissonant intervals are available
(Butler & Brown, 1994), and Rodrigo favoured chromatic dissonances as well.
Perhaps this use of dissonance opposed the positive relationship between valence and texture.
Regarding the issue of collinearity, texture may have been deprived of its chance to take part in relationships with emotional response. On several occasions texture is collinear with loudness, and one variable is often replaced in favour of another. The dominance of loudness gradient as a predictor of arousal may have suppressed an underlying relationship between texture and arousal. Due to its inconsistent, though significant effect, texture is a variable that may provide a rich area of future research.
- 378 - Figure Chapter 7 -20Texture Profile for Arousal
0.4
0.3
0.2
0.1
0 Coefficient 0 -0.1 2 Lag Morning 4 Pizzicato Aranjuez Slavonic Dance
Figure Chapter 7 -21Texture Profile for Valence
0.25
0.2
0.15
0.1 Morning Coefficient
Pizzicato 0.05 Aranjuez 0 0 Slavonic Dance 1 2 3 Lag 4
- 379 -
Chapter 8 Overview, Conclusions and Recommendations
This chapter begins with a summary of Chapters 1 to 7 and is followed by the conclusions and recommendations of the dissertation.
Overview of the Dissertation The aim of this dissertation was to examine the time varying relationship between emotion and musical features. The relationship between emotion and musical features is a question that can be traced back many centuries. The investigation of the time varying relationship is an attempt to make this question specific by imposing real experimental data which any postulated theory must explain.
In Chapter 1, a historical perspective of the problem was articulated. The Baroque era saw the formulation of theories pertaining to the expression of emotion in music, however the later movements of expressionism and formalism repressed this atomistic approach to the problem. It was not until the turn of this century that serious and systematic approaches to the question were re-asserted. There has since grown a rich but ununified body of literature of empirical work attempting to clarify the relationships between musical features and emotional response. Two problems that have
- 380 - fundamentally hindered past research are: (1) the lack of a unified definition and operationalising of emotion, and (2) the inability to record valid, continuous emotional responses and then to provide appropriate inferential analysis.
Chapter 2 reported a literature review of the techniques used for measuring self- report emotional responses to music. The techniques include open-ended measures, checklists and rating scales. Open-ended measures have the longest history in the music-emotion empirical literature and have the benefit for researchers of providing respondents with the freedom to report musical events that lead to strong emotional response (Gabrielsson & Lindström, 1993; Sloboda, 1991). However, they are generally inappropriate for measuring moment to moment responses. Checklists
(Hevner, 1936; Namba, Kuwano, Hatoh & Kato, 1991) and rating scales (Madsen,
Brittin & Capperella-Sheldon, 1993; Nielsen, 1983) have both been used for continuous measurement of emotion before the present study. However, these earlier studies have also lacked a solid, operational definition of emotion.
In Chapter 1, emotion was defined in terms of its important constituents — cognitive, physiological and motor; and operationalised in terms of its dimensional structure.
Past research, culminating in the work of Russell (1980), suggested that emotions could be adequately described along two bipolar dimensions: arousal (arousal- sleepiness) and valence (happiness-sadness). These dimensions were found to be orthogonal and meaningful. Happiness is closer in meaning to joy than anger because happiness and joy are both high arousal positive valence words, whereas happiness and anger
- 381 - have different arousal components. In Chapter 2 it was reported that this dimensional paradigm of emotion transferred well into emotion in music.
Numerous findings of a dimensional organisation of responses to music are spread throughout the literature especially after the influential work of Osgood, Suci and
Tannenbaum (1957). Empirical findings by Asmus (1985), Collins (1989), Nielzén and Cesarec (1982b), Thayer (1986) and Wedin (1972) and many others, provided evidence for the dimensional operationalisation of emotion. However, none of these studies measured the construct of arousal and valence directly.
In Chapter 3 a logical development of previous research was proposed as a solution to the problem of measuring and operationalised emotion. This chapter reported the development of a new instrument which could measure emotional responses meaningfully. This computer controlled instrument was referred to as the Two-
Dimensional Emotion Space (2DES). The main part of the software consisted of a screen containing a square (the emotion space). The square had two axes, with the vertical axis indicating valence and the horizontal axis indicating arousal (see Figure
Chapter 3 -1 on page 102). A response could be made by moving the cursor to the desired location within the square.
An experiment (Experiment II) was conducted to test the validity and reliability of the 2DES in a non-continuous mode. All aspects of the experiment were automated via a computer human interface, the EmotionSpace Lab. Responses made by 29 participants to a series of test words and pictures of faces were collected and analysed. The words
- 382 - consisted of three sets: (1) Words for which the arousal and valence was known in order to examine the external validity of the instrument, (2) Pictures of facial expressions to test the instrument as a measure of response to non-linguistic stimuli, and (3) A set of test words for which the valence and arousal components were not known. These words were taken from adjective lists used in past research on music- emotional response (Hevner, 1936; Farnsworth, 1969) and updated in a word usage survey (Experiment I). The instrument was found to be a reliable (test-retest r > 0.83, p = 0.01) and valid (external data set r > 0.84, p = 0.01) measure of expressed emotion.
It could also distinguish emotions that were approximately 12 points apart (on a scale of -100 to +100) with 95% confidence.
In Chapter 4 a second literature review was conducted in which the current state of research on the relationship between musical features and emotional response was ascertained. This provided information about the kinds of musical features that had been examined in the past, and how they were coded. For each of the pertinent musical features reported, emotional responses were mapped, where possible, onto a two-dimensional emotion space. Influential data were obtained from the work of earlier researchers such as Gundlach (1935), Hevner (1936), Rigg (1964), Scherer and
Oshinsky (1977), Sloboda (1991) and Watson (1942). Mapping these findings onto the
2DES helped to unify past research into a coherent framework. For example, the transformations demonstrated an unambiguous, positive relationship between arousal and tempo. Likewise, the contribution of mode was found to be reproduced across many studies, with minor mode shifting responses toward negative valence and major mode towards positive valence. In
- 383 - addition, the mapping summarised the effect of musical features on emotion suitably for the generation of hypotheses.
Music is a dynamic, time dependent phenomenon. It is music’s ability to express a variety of emotions temporally that provides enrichment and value to its admirer.
Studies investigating responses to short excerpts or isolated, controlled patterns can only hope to investigate this phenomenon in an indirect, perhaps cursory, manner.
However, none of the studies using continuous measures applied inferential statistical methods in order to extract relationships between musical features and emotional response. Subsequently, the second major problem in past research, of measuring and analysing continuous data, was addressed by modifying the 2DES so that it could measure responses to music at a rate of one sample per second. This was reported in Chapter 5.
Emotion judged to be expressed by four, entire, contrasting movements of music were collected continuously from 67 participants in Experiment III. Each piece was described in terms of five musical features which could be coded as multilevel variables for the purpose of analysis: frequency spectrum centroid, loudness, melodic pitch, tempo and texture (number of instruments playing). The experiment was repeated using 14 randomly selected participants from Experiment III in order to determine the test-retest reliability of the instrument (Experiment IV).
Collection of continuous data was relatively new in music-emotion research. The problem of modelling emotional response in terms of continuous musical features was even newer. In Chapter 6, a detailed investigation was
- 384 - undertaken into methods of analysing continuous data. After several exploratory exercises, a sequence of time series analysis steps was derived. Pertinent, lagged and first-order differenced musical feature variables were identified through ordinary least squares stepwise regression. The differencing transformation served to reduce the amount of serial correlation in the “musical feature-emotional response system”
(MF→ER) as well as eliminating the problem of using absolute locations on the emotion space. The model was then adjusted in order to explain the remaining serial correlation which violated each of the OLS regression models. The final, serially correlated models were evaluated according to how well they could fit the original data and an analysis of their outliers. Two kinds of outliers were identified: those generated by the participants responding in a manner not predicted by the model
(response driven outliers), and those produced by model mis-specification and coding errors (mis-specification outliers). The identification of either type of outlier were used to justify the relative simplicity of the models.
The research question could then be directly addressed by examining the coefficients of each model’s musical feature parameters. This was reported in Chapter 7. The findings were that musical features can be used to predict emotion expressed according to various complex interactions, however further research is required to ascertain the exact nature of the interactions. Loudness and tempo gradients have a strong, positive relationship with arousal gradient, while melodic pitch contour is related to valence response gradient (coefficients were significant at p = 0.01). The failure to find some of
- 385 - the hypothesised relationships was explained in terms of collinearity (the redundancy of multiple musical features) or interactions (other features of the music not facilitating the relationship). Importantly, I argued that the relationships found in the present study exhibit greater validity than in non-continuous, temporally static methodologies.
Interactions were described qualitatively in terms of the general characteristics of the music. For example, it was suggested that tempo variations in overall slow music with legato articulation appear to manipulate the arousal component, while faster music with more separated articulation tends to manipulate the valence component.
Such interactions require further investigation. An area for further research would be to expand the variables used to include other musical features such as articulation, rhythm and various aspects of harmony. Some examples of how harmony could be coded were provided, however further investigation into coding musical features in a objectively quantifiable manner was recommended. Further developing and checking the reliability and validity of the 2DES was also recommended.
Conclusions The major purpose of this dissertation was to examine the relationship between time varying musical features and emotional responses. My thesis was that combinations of musical features are causal (though not exclusive) determinants of emotional response. The findings of Experiment III support this thesis. Combinations of musical features were shown to explain 30% to
- 386 - 70% of response variance along the emotion dimensions of arousal or valence.
The analysis consisted of an examination of average responses to selections of
Western art music which were tonal, and mostly diatonic. The responses were made by people who were, on the whole, familiar with the styles of music used. All findings and conclusions are made bearing these important points in mind.
Measuring emotional response to music continuously provides a valid avenue for collecting data and is an overdue addition to the literature concerned with clarifying the relationship between music and emotion. The two-dimensional emotion space instrument (2DES) enables the collection of responses continuously along two meaningful dimensions of emotion.
In order to ascertain relationships between continuously judged response and musical features, time series analysis techniques can be used to model the data. Such models can deal with the problems of serial correlation and trending which otherwise can make analysis prohibitive. By using time series models, it was possible to analyse responses in a naturalistic setting with the aim of delving much deeper into the relationship between musical features and emotional response than has previously been possible. The exclusive focus upon musical stimuli which are highly controlled, synthetic and musically inferior is circumvented by the collection of continuous data and the application of time series analysis techniques.
- 387 - The models generated explained different amounts of variance in an emotional response dimension in terms of the five selected multilevel musical features of loudness, tempo, texture, melodic pitch and frequency spectrum centroid. As mentioned, model fit ranged from 30% to 70%. Low model fits can be explained in terms of the selection of musical features to use as predictors. Outliers can be explained in terms of either (1) changes in the dynamic (lag) structure of the MF→ER
(musical feature-emotional response) system, or (2) missing explanatory variables.
The former type of outliers were found more frequently and were exemplified by changes that were faster than the model predicted response (startle response), or slower than the model predicted response (inertia response). “Startle” changes commonly occurred in response to sudden loud passages. The scarcity of the latter type of outlier (missing variable) can be used to justify the validity of the proposed models. In fact, it is somewhat surprising that harmony, rhythm and articulation were rarely required to explain an outlier. The five variables chosen may therefore be an adequate representation of the musical signal. However, more research is required in order to identify the pertinent musical features that carry the emotional signal.
Regression model coefficients were collected and compared on a feature by feature basis. My “underlying rule” thesis suggests that the coefficients should be the same within each musical feature, but this was not what occurred. The reason is not necessarily because my thesis is false, but because the relationship between emotion and music is complex. The issue needs to be dealt with at various degrees of complexity. From the time series
- 388 - analysis of data collected in Experiment III, the simplest conclusion that can be drawn is that changes in loudness and tempo are each positively related to the gradient of the arousal dimension of emotion. Increasing loudness or tempo (or both) will tend to increase arousal within a lag of four seconds. This inferred causal chain provides evidence that musical features can be used to predict emotional response and that there are underlying principles that govern emotional response as a function of musical features.
However, apart from the finding of loudness (and to a lesser extent, tempo), a higher level of complexity is required to discover and understand the underlying principles.
The complexity arises through two key processes: (1) interactions, and (2) collinearity. Interactions provide a plausible explanation of several findings. For the musical examples chosen, the relationship between a musical feature and the emotional response was dependent, at least in part, on other musical features. For example, the articulation, the mode of the piece and the overall tempo appeared to have a controlling effect upon whether changes in either tempo, texture or loudness affected valence or whether they effect arousal. Minor mode, slow tempo and legato articulation appear to divert the effect of changing tempo to the arousal dimension and away from the valence dimension. For instance, a possible interaction between mode and loudness may be hypothesised as indicated in Figure Chapter 8 -1.
- 389 - Figure Chapter 8 -1 Hypothesised Interaction Between Tempo and Mode Minor mode Major mode
increasing increasing tempo tempo
Collinearity can be diagnosed by several statistical techniques. Tolerance (related to the variance inflation factor) was used in the present study. Collinearity could explain why some musical features did not provide predictive value in emotional response. Results demonstrated that loudness and texture gradients were collinear with one another in several sections of the four pieces. Loudness gradient dominated the contribution to arousal gradient for all pieces except Morning.
Changes in melodic pitch were related to changes in the valence dimension in one piece — Aranjuez. The other three pieces showed no necessary relationship between melodic pitch and valence. This suggests that the conditions necessary for the relationship between valence and melody may be dependent on other factors, such as the length of the melody. Aranjuez has a very long, flowing melodic line. These findings suggest that the relationship between melody and valence is not a simple one.
- 390 - It was demonstrated that valence and arousal responses are meaningful and constructive dimensions of emotion to examine. Participants were able to understand their meaning quite easily; the dimensions are meaningful but essentially independent, and; understanding the effect of musical features upon each dimension is of importance to musicologists, composers, psychologists and music educators.
Although certain musical features had an effect on both dimensions, there were some musical features that clearly affected one dimension more than another.
Consequently, investigating the relationships between musical features and the emotional response dimensions of valence and arousal is a meaningful and practical way of addressing the research question. This result suggests that a productive area for future research would be to perform bivariate analyses so that the construct of emotion is addressed more specifically rather than in terms of its (proposed) parts.
A major finding of this study supports the thesis that there are underlying principles which govern the relationship between musical features and emotional response. It is likely that the rules are bound by cultural norms, but whether the relationships be local or universal, a mass of relationships awaits discovery. It can therefore be proposed that the 2DES in tandem with time series analytic techniques provide efficient tools for explaining these relationships further.
In summary, time series analysis and the 2DES afford researchers new techniques which they can use to further our understanding of the underlying relationships between musical features and emotional response.
- 391 - The challenge is now to build upon the analytic and coding techniques introduced in this dissertation in order to add more complex variables such as harmony to the equation, and to continue addressing the question of interaction and collinearity.
Recommendations The findings of this study raise a series of important questions and concerns about past research and future directions. The discussion explores issues regarding the
2DES instrument, the spread of emotion in the stimuli, the coding of stimuli and suggestions for alternative and extended techniques of analysis and modelling.
The 2DES is not in a definitive state. Although it has served its purpose in enabling valuable continuous data to be collected, and appears to be valid and reliable, further work is needed to ensure that the instrument operates optimally. This means further research to ensure the reliability and validity of future testing. For example, different versions of the 2DES could be tested with the same pieces of music to determine the temporal stability of the instrument. A central question would be to ask: To what extent do responses change significantly when feedback devices are removed or altered?
Although a variety of moods of music were selected as test pieces, only the Aranjuez moved responses into quadrants two and three of the emotion space. The other three pieces tended to attract responses in the first quadrant. This raises the issue of semantic density. The issue is an important one, given the apparent subtlety and complexity of interactions.
- 392 - Music movements that attract responses at many points on the 2DES are required to gain a more complete picture of the instrument’s ability to measure emotional response.
Alternatively, the problem may be due to the topographical limits of the 2DES. For example, in Experiment II the lower portions of the 2DES were not used as frequently as the top portions. An emotion space with a unidimensional arousal axis, with origin at the centre bottom, rather than the centre middle, may be one solution. For testing any configuration of the instrument, the selection of stimuli, whether musical, linguistic or visual, must control for semantic density.
Determining a priori which pieces of music express a wide range of emotions would require a study in itself. Consequently, the subjective component of emotional response to music will be one of the limiting factors.
The choice of limiting musical examples to Western art music of a Romantic dialect was largely a pragmatic decision. Because the instrument appears to work well for such music, the next step is to test it with other kinds of music — ancient, popular, non-western and experimental to mention just a few. Whether it is appropriate to examine such music in this way is a matter for sociologists, anthropologists and philosophers. Nevertheless, emotion expressed by a variety of musical styles has and will continue to be of interest to music psychologists, music educators and musicologists. The 2DES and time series analysis technique provides a suitable basis for further research in this area.
- 393 - A mathematical extension of this research would be to search for alternative methods of analysing data. I argue that, although more sophisticated models may be available, the present technique provides a relatively simple procedure and a parsimonious result. However, one avenue that warrants detailed investigation is to model the various lag patterns with a single parameter. Take, for example the melody gradient profile for Aranjuez valence of Figure Chapter 7 -19 on page 377.
The coefficients rise and then fall as the lags increase, as though the coefficients were distributed according to some underlying distribution. By replacing the four lags with a single parameter, it may be possible to simplify the model further. Such an approach is formulated by Box and Jenkins (1976) and may lead to even more parsimonious modelling.
Another area worth considering is the use of neural networks to model the relationship between musical features and emotional response. One possibility is a simple backpropogation network (Todd & Loy, 1991) consisting of an input layer of musical feature codings and an output layer consisting of an arousal and a valence output. Data driven models such as these may help to explain more fully interactions through examination of weightings after the training period.
The reason for the omission of several important musical features from the analysis is that they could not be coded as multilevel variables. Multilevel variables are far easier to use than nominal or dichotomised data in regression models. Two possible approaches can be proposed to deal with the problem of non-multilevel musical feature variables. First, musical
- 394 - features may be dichotomised and added to the regression equation as dummy variables (Chatterjee & Price, 1991). This suggestion was expanded in the discussion of the valence response to Morning. Another alternative is to find perceptually valid, objectively codable ranked or ratio relationships among musical features.
Operationalising harmony poses a major concern in this respect. For example,
Krumhansl (1990) reported a perceptually valid method (according to distance) for coding the relationship of triadic harmonies along the cycle of fifths. However, there is no empirically supported relationship for explaining added dissonances such as sevenths and ninths, nor is there an established understanding about the perceptual detection and ranking of inverted chords. The problems in coding harmony are extensive, and there is much to be accomplished in this area alone.
Multilevel coding of elements related to rhythm and timbre are also problematic.
Some progress has been made in the coding of rhythm in terms of its perceived complexity by Pressing (1997), but more work is required. With regard to timbre, although the coding used to operationalise centroid did not support a clear relationship between timbre and emotion, the literature suggested that nominal categories of timbre are important. The problem is likely to be tied to our understanding of the dimensionality of timbre perception in addition to the problem of coding.
Once these questions are resolved and we have greater insight into musical features and their relationship with emotion, the next issue will be to combine the effects of musical features with those of individual differences and cultural conditioning.
Building a comprehensive model of the
- 395 - relationship between emotion and music is a long term goal for research of the kind presented here.
This list of recommendations may give the impression that there are more problems than solutions in understanding the relationships between emotion and music.
While there is a great deal more that needs to be achieved in order to understand these issues more fully, there is also every reason to be optimistic that advancement in technology and research methods will help to push the boundaries even further, and lead to new insights and understanding in this important area of human behaviour.
- 396 -
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- 419 -
Measurement and Time Series Analysis of Emotion in Music
Emery Schubert
BE, BA (Hons)
In Two Volumes
Volume 2
Glossary and Appendices
- 420 -
Glossary of Terms and Abbreviations
Italicised entries indicate emphasis or a separate glossary entry.
2DES Two-Dimensional Emotion Space. The abbreviated form refers specifically to the emotion space used for directly measuring response on a two- dimensional emotion space.
ACF Autocorrelation Function. See autocorrelation. anapaest A rhythmic pattern distinguished by the duration sequence short-short-long. ar Arousal.
AR Autoregressive component of a serially correlated process.
AR(1) A first order autoregressive model.
AR1 Coefficient of the first order autoregressive term in an autoregression model.
Aranjuez “Adagio” from Concierto de Aranjuez for guitar and orchestra by Joaquin Rodrigo performed by Gerald Garcia (guitar), CSSR State Philharmonic Orchestra, Peter Breiner (conductor), duration 10:52.
ARIM A Autoregressive Integrated M oving Average. arousal The aroused-sleepy dimension of emotion. attentional resources
See cognitive load. autocorrelation Serial correlation. The dependence, or correlation, of a time series on previous values of itself. autocorrelogram Correlogram of an autocorrelation.
- 421 - averaged response
The mathematical average of continuous responses made by a participant over the course of a piece of music. Compare with overall response. bar The collection of a group of beats of music as a means of measuring musical time. Time elapsed in a piece of music can be identified by the number of seconds that have elapsed or the number of bars that have elapsed. The latter has the advantage of being constant across different performances and is easily found on a musical score. When referring to a bar or range of bars I am using a pseudo decimal notation where the integer part is the bar number of the piece in question and the decimal place is the beat number within the bar. In the US bars are commonly referred to as measures, however, this term may be confused with the parameter or output of a measuring instrument (also referred to as a “measure”). The abbreviation for a bar number is m. and for several bars or a particular beat in a bar, mm. Examples: m.5 means bar five, m.5.3 (or mm.5.3) means the third beat of the fifth bar, and mm.4-8 means bars four to eight. bipolar scale A response format which consists of a label at either end of a one dimensional continuum. The labels usually have opposite meanings reflecting the poles of some psychological concept or phenomenon. A predetermined construct is assessed by responses made on such a scale or a collection of a variety of such scales. See also unipolar scale.
BPM Tempo (beats per minute). brightness See CEN. card See stack.
CCF Cross correlation function.
CD Compact Disc.
CD-ROM Compact Disc - Read Only M emory. Storage device accessible to certain computers. With appropriate software, such devices can play audio CDs.
CEN Frequency spectrum centroid (Hz), related to the perceptual quality of the brightness or sharpness of tone colour. centroid The “centre of gravity”. In acoustics, the frequency above and below which the A-weighted (see dBA) intensity of the partials are balanced. See also frequency spectrum centroid. checklist A response format where an assessment is made by selecting a word or phrase from a predetermined list. Sometimes the participant is encouraged to add words or phrases not already on the list, making the format resemble a kind of open-ended measure. circumplex An approximately circular pattern or locus.
- 422 - cognitive load That which gives rise to a decrement in human performance caused by the need to process several tasks simultaneously. cognitivist The view that emotion in music is observed as being expressed by the music. See emotivist.; emotional response. collinearity The interdependence of predictor (regressor) variables. One method of diagnosing the existence of collinearity is by calculating tolerance. complex tone A sound (usually steady state) with energy emitted at several frequencies. The relationship among frequencies can be harmonic. content analysis A family of methods used for analysing qualitative data, where an attempt is made to extract and assess the content of the data. Usually the techniques involve sorting and reducing the data into predetermined categories using some relevant criteria. continuous response
A series of responses made over a period of time. Although the term continuous implies a train of uninterrupted responses, the measurement of such a response must be sampled, meaning that some information will be lost. Therefore, strictly speaking, the measurement of such responses should be referred to as “continual”. However, the surprising consistency with which the term continuous is used warrants its advocation. continuous variable
See multilevel variable. contour Shape or outline. correlogram A plot containing correlation coefficients on one axis and lag number on the other. Two common types of correlograms are the autocorrelogram, which is the correlogram of the autocorrelation of a time series, and the cross- correlogram, which is the correlogram of the cross-correlation of two series. cross-correlation
The correlation of two time series, repeat several times with one series shifted relative to the other series, by one lag each time. A cross-correlation can be produced by a CCF.
CSound Authoring software which enables sophisticated analysis of sound using the programming language of the same name. cursor A pointer on a computer screen indicating where the next action will take place. The position of the cursor is manipulated by the user via the computer’s mouse. d1 When added after a variable name, this indicates that the variable has been first order differenced. See also delta (∆).
- 423 - dBA A-weighed decibels (dB). A unit of sound intensity measurement of a pure tone weighted as a function of frequency so as to approximate human hearing response at relatively low sound levels. The dBA scale is used as a rough approximation of perceived loudness in this thesis.
∆ Delta. Used to denote first order differencing. See also difference transformation. Some texts use the del (∇). dependent variable
The response variable. For example, emotional response to music is a dependent variables in the present dissertation because it depends on musical feature variables (among other variables). The dependent variable is usually the one which a regression model tries to predict. deterministic Stable and predictable, in contrast to stochastic. df Degrees of freedom. The number of independent pieces of information. The number may be thought of as providing a “corrective weighting” to statistical calculation. dichotomisation
The division of a variable into two exclusive states or values. See also multilevel. difference transformation
The transformation of a numerical sequence obtained by subtracting each element of the sequence from the previous value. See also first order difference transform. drift A wandering time series pattern. It may be thought of as a trend which often changes direction. duration Usually, the amount of time taken to sound a note. emotion A multidimensional phenomenon that consists of physiological, cognitive and motor components. It serves a purpose in communicating and can therefore be detected by observers, whether the source is another sentient being or an object such as music. Emotion may be distinguished from other phenomena in terms of its dimensions which consist of arousal and valence at least. emotional response
An action or behaviour which can be observed or measured and which relates to emotional experience (emotivist response) or emotional judgement (cognitivist response). In the experimental work conducted in this dissertation emotional response refers exclusively to cognitivist response.
- 424 - EmotionSpace Lab
The name of the program or stack used to automatically control experiments using the 2DES. The program was developed and written by Emery Schubert for the purpose of this dissertation. emotivist The view that emotion in music is experienced by the listener. See cognitivist..
ER Emotional response variable. The time series that represents any single dimension of emotion, or some combination of emotional dimensions. Examples of emotional response are arousal and valence. expressionism The view that the value of music is in its ability to express or evoke irrational, indeterminate emotions and feelings. See also formalism.
Fechner’s Law An empirical law expressing the logarithmic relationship between the intensity of certain sensations and corresponding physical quantities. Sometimes referred to as Weber’s Law. first order difference transform
The modification of a series produced after subtracting from each element the one which precedes it. A first order difference variable is denoted by a ∆ (delta) prefix or a d1 suffix. fit Goodness of fit. formalism The view that the value in music is contained wholly within the musical structure. The contemplation of beauty in form. See also expressionism. frequency spectrum centroid
The centroid of the frequency spectrum. Measured in Hertz (Hz). This physical quantity is believed to be related to one aspect of timbre.
Gestalt A movement in Psychology, originating in Germany, where principles are described which explain the human tendency to perceive well organised wholes even when the source being perceived consists of separate, disjointed or isolated parts. goodness of fit An index indicating how well a regression model could explain actual data. The index is usually expressed as a percentage or a number less than or equal to one. gradient Rate of change. Moment to moment difference. A difference transformation. For example, “arousal response gradient” means the rate at which arousal response changes. The term infers that the original series, such as the arousal response, has been first order difference transformed. harmonic In acoustics (noun) related by a simple, whole number multiple; In music theory (adjective) the vertical combination of pitches.
- 425 - hemiola A mixture of rhythmic accents which emphasise different beat groupings. Usually the shifting emphasis is between two beats and three beats in triple of compound metre. For example, in compound 6/8 metre (six pulses per bar), a hemiola can be created by grouping pulses, through accent, into two sets of three and three sets of two.
Hypercard An authoring software package whose human-computer interface is based on the principle of the stack metaphor.
I The integrated process parameter of a serial correlation model. iambic A rhythmic pattern distinguished by the duration sequence short-long. impact intervention. inertial response
Alteration of the dynamic response pattern in a time dependent system where response occurs later than predicted. See also startle response. interrupted time series analysis
A method of analysing time series data which, at certain points or intervals, behaves in response to some kind of external intervention. interruption intervention. intervention In time series analysis, an external influence which has altered the general flow of a series. Different time series texts use impact or interruption to mean essentially the same thing. loudness The percept related primarily to the intensity of a sound signal (but also to frequency). In this thesis the term loudness is used to refer to A-weighted sound level. m./mm. See bar.
M A M oving average. masking The “drowning out” of sound components by a louder audio component, usually of similar frequency. measure See bar.
MEL Melodic pitch (MIDI pitch number or MIDI note number). melodic contour The contour of a melody. Can be expressed as the gradient of the melodic pitch sequence. Same as melodic gradient. melodic gradient The rate of change of melodic pitch. For example an increase in pitch constitutes a positive pitch contour and a downward movement in pitch constitutes a negative contour. Therefore, differencing a series of pitches produces a melodic gradient or melodic contour.
- 426 - Melodic pitch Melody. See MEL. melody A perceptually prominent and identifiable sequence of pitches, each of various durations.
MF Musical feature variable. The time series that represents some musical or psychoacoustic feature with appropriate coding. Examples of musical features are loudness, pitch and tempo.
MF→ER A system which consists of a range of musical feature inputs and an emotion response dimension (or combination of dimensions) output.
M IDI M usical Instrument Digital Interface. A standardised method of coding and communicating digital musical signals at the level of notes.
MIDI note number
The standardised system of numerically classifying pitch used by the MIDI system based on pitch category. mis-specified model outlier
see response driven outlier.
Morning “Morning Mood” from the incidental music to Peer Gynt by Edvard Grieg performed by CSSR State Philharmonic Orchestra, Stephen Gunzenhauser (conductor), duration 3:38. ms M illiseconds. multilevel variable
Used to describe a ratio or interval variable. Multilevel implies a variable that has ranked values. However, I am using it to mean continuous variables that comprise ratio and interval scales. Since continuous variable may be confused with the temporal process associated with continuous response, I have chosen this alternative terminology. musical features The musical (or acoustic) components that go into making music. For example, pitch, dynamics, tempo, rhythm, harmony, harmonic rhythm, appoggiatura and vibrato are musical features. For convenience, in this study, acoustic and psychoacoustic variables (such as loudness, duration and frequency spectrum) are also classified as musical features. The musical feature variables used for quantitative analysis are listed by the in this Glossary under the abbreviations used: dBA - loudness; MEL - melodic pitch; BPM - tempo; TEX - texture; CEN - frequency spectrum centroid. musometric An instrument that measures characteristics of music. The term, coined (to my knowledge) by Kate Stevens, contrasts the purpose of the instrument from the more traditional psychometric instrument, which measures characteristics of the individual. The terminology helps in distinguishing emotivist response from cognitivist response.
- 427 - nominal variable
Used to describe a variable whose values are not ordered with respect to one another. Compare with mulitlevel variable. null hypothesis A statistical assertion that there is no real difference between two or more groups or populations along a particular parameter of interest (such as their means). octave band A range of frequencies cover one octave. For example, 500Hz to 1000Hz is a one octave band. Perceptually, the range of an octave band can be heard as the interval of an octave.
OLS Ordinary least squares. open-ended measure
A measure in which the participant makes an assessment without being forced to respond according to predetermined answers. This self-report measure is in contrast to other formats such as checklists, unipolar scales and bipolar scales. operationalise The process of variable coding which facilitates quantification and further analysis. For example, converting a musical feature into a numerically coded variable. ordinary least squares
A technique for regressing predictor variables onto a variable of interest. It determines the coefficients which multiplies each predictor in such a way as to minimise the residual. The OLS technique assumes that each data point (or surface) is independent of other points (or surfaces). Partly because of this assumption, the OLS technique will not always work for time series data. overall response Response made by the participant as a single, overall judgement about an entire piece of music. Compare with averaged response. p Probability of Type I error of a statistical inference. That is, it indicates the probability of being wrong if rejecting the null hypothesis. For example, a p value of 0.01 means that the null hypothesis will be incorrectly rejected one in 100 times, on average. Sometimes referred to as the significance of a test.
PACF Partial autocorrelation function. partial (noun) An component of a sound which is usually derived from the breakdown of a complex tone into its components. Each component is a partial. physiognomic General appearance or character based on the interpretation of a combination of features. The metaphor is borrowed from the interpretation of human character based on the appearance of the human face.
- 428 - pitch The perceptual quality of a sound that is distinguished along a continuum of low-high. Pitch bears a fairly strong relationship with audio frequency of vibration of the fundamental partial of a harmonic tone. One unit of measurement of pitch is MIDI note number, which usually corresponds to the equal tempered pitch class sequence commonly used in Western tonal music. pitch category A system of coding pitch by simple, incremental number sequence moving from low pitch to high pitch.
Pizzicato “Pizzicato Polka” by Johann (Jr.) and Joseph Strauss, duration 2:30. predictor See regressor. primary V7-I See V7-I. pure tone A sound (usually steady state) with energy emitted at one frequency only. quad Quadrant. quadrant The division of a two-dimensional space by a pair of centred, orthogonal axes into four sections, numbered clockwise according to the convention where Quadrant 1 is the top right section (positive x and y, 0o-90o), Quadrant 2 is the top left section (negative x and positive y, 90o-180o), Quadrant 3 of the bottom left section (negative x and negative y, 180o-270o) and Quadrant 4 of the bottom right section (negative x and positive y, 270o-360o). For convenience, Quadrant 0 refers to the area around the origin. Reference to non-integer quadrants indicates a shared region between two adjacent quadrants. For example, Quadrant 1.5 indicates the region joining Quadrants 1 and 2. Quadrant 4.5 indicates a region joining Quadrants 4 and 1. regression model
A statistical model which infers an underlying mathematical relationship between regressors and a dependent variable based on a limited number of data points. One technique for calculating the weightings or coefficients of the regressor variables is called ordinary least squares. regressor A variable used as a component of a regression model. The variable should have some predictive ability for the dependent variable under investigation. For this reason, a regressor variable is sometimes referred to as a predictor variable. reliability The ability of a psychological instrument to measure responses consistently. residual In regression models, the difference between actual data and model predicted data.
Residual outliers Points where members of the residual series fall more than a predetermined distance away from the mean. A common range used for excluding outliers is the three sigma band, where 99.7% of values should fall within this range. Values falling well outside this range are usually outliers and require special attention and explanation.
- 429 - resilience I use this term to indicate an instrument’s ability to perform reliably when aspects of its appearance have been changed. For example, do responses to the 2DES change due to changes in the instruments layout? If not, then the instrument demonstrates resilience. response Any human action that can be measured or observed after or during the presentation of a stimulus. A response may also include a judgement, such as the judgement about the emotion being expressed by a piece of music. response dimension
The dimension along which response was made, for example the arousal dimension or the valence dimension. response driven outlier
An outlier that is explained in terms of the response changing the dynamic structure of the system. This type of outlier is distinct from a Mis-specified model outlier, which is an outlier caused by a coding error or a deficiency in the system model. s Seconds.
Schenkerian A highly formal approach to the analysis of music based on the methods of the Austrian musicologist, Heinrich Schenker (1868-1935). secondary V7-I See V7-I. self-report A means of gathering data where the participant is aware that he or she is making a responses to a given task. The response can be made verbally or non-verbally and may be mediated by some linguistic process.
SEM Strong Experiences of Music. A research project conducted by Alf Gabrielsson and Siv Lindström in which large amounts of data were collected from individuals’ experiences. semantic density The distribution of indicators of psychological or emotional meaning over the range of a psychological instrument. For example, checklist measures are particularly susceptible to an uneven semantic density because the instrument is often restricted to the words available in the list. sentograph A device developed by Manfred Clynes to measure inner emotion through small bodily movement, such as the movement of the finger, over a two- dimensional surface. serial correlation Autocorrelation. sig The significance of a test. Same as p. sigma Population standard deviation of a distribution. Not to be confused with the Greek symbol, sigma (Σ), which indicates a summing function.
- 430 - significance See p.
Slavonic Dance “Slavonic Dance”, Op. 46 No. 1 by Antonin Dvorak performed by Slovak Philharmonic Orchestra, Zdenek Kosler (conductor), duration 3:45.
SPSS Statistics Package for the Social Sciences. A statistics software package with the capability of performing time series analysis. Other such statistics software packages include SAS, S+ and TSP. stack Terminology used in a Hypercard software environment to denote a collection of information organised on a series of cards. Each card consists of a collection of programmable buttons and data storing fields in addition to graphics and scripts storing executable programs. For example, the EmotionSpace Lab software consists of a stack. The various experimental modules of the stack are interfaced and interlinked via the cards of the stack. startle response Alteration of the dynamic response pattern in a time dependent system where response occurs sooner than predicted. See also inertial response. stochastic Selected from a probability distribution, and therefore having the property of being predictable only within a range. Compare with deterministic. structural analysis of music
Analysis of the time varying aspect of the musical features of a musical stimulus, particularly those related to harmony. It usually examines how the piece fits together at a fairly high level. tempo The rate at which the underlying pulse of music is performed. It is often measured in beats per minute (bpm). See BPM .
TEX Texture (number of different musical voices sounding simultaneously as according to the musical score). texture See TEX. timbre The quality or tone colour of a sound. One aspect of timbre is believed to be frequency spectrum centroid which is related to the brightness of the sound. tolerance A statistic for diagnosing collinearity of a regressor variable with other regressor variables. It is given by 1-R2 where R2 refers to the strength of fit of the regressor with other regressors. A low tolerance (close to 0) indicates strong collinearity. A high tolerance (close to 1) indicates independence of the regressor from other regressor variables. trochaic A rhythmic pattern distinguished by the duration sequence long-short. trend An overall distinguishable time series pattern which may be slightly obscured by noise. The general movement of the time series tends to be in one direction (up or down). A series which
- 431 - changes direction frequently may be exhibiting drift behaviour instead of a trend.
Two-Dimensional Emotion Space
An instrument used to measure emotional response which consists of a square surface with two centred axes. The vertical axis is the arousal dimension of emotion and the horizontal dimension is the valence dimension of emotion. Participants respond by selecting a point on the emotion space as indicated by a requested task. See also 2DES and quadrant. unipolar scale A response format where a property related to a single concept or entity is made along a continuum. See also bipolar scale.
V7-I Dominant-seventh perfect cadence. A common harmonic progression in Western art music which occurs at the end of a phrase or piece of music. The chord built on the fifth degree of the scale (5, 7, 2 and 4, or the “dominant-seventh” chord) moves to the tonic chord (or chord I, the triad built on the first degree of the scale — 1, 3 and 5). When the first, dominant chord is actually the dominant of a foreign key, and the resolving chord is chord I of this foreign key, the progression is referred to as a secondary cadence. The secondary cadence is a simple technique composers employ to change the key of a piece. Otherwise, the progression is referred to as a primary cadence. The chord I resolution usually occurs on a strong beat. va Valence. valence The happiness-sadness dimension of emotion. validity In reference to a psychological instrument, the ability of that instrument to measure what it is purports to measure.
Weber’s Law See Fechner’s Law.
- 432 -
Appendices for Chapter 3
- 433 -
Appendix A: Word Usage Survey
Note: The survey which follows was one page long with narrow margins. In order to fit on the following page it required some reduction.
- 434 - WORD USAGE SURVEY Please indicate with a cross in the appropriate column whether, in your opinion, the following words are in low general usage (L), moderate general usage (M) or high general usage (H). Then indicate whether you think each word is useful in describing music (N - if not useful, M - if moderately useful or V- if very useful). General Usage Musical Usage General Usage Musical Usage L M H N M V L M H N M V afraid passionate agitated pathetic alarmed plaintive angry playful annoyed pleading aroused pleased astonished ponderous at ease quaint awe-inspiring quiet bored relaxed bright restless calm robust cheerful sacred content sad dark satisfied delicate satisfying delighted sensational depressed sentimental depressing serene dignified serious distressed sleepy doleful soaring dramatic sober dreamy solemn droopy soothing emphatic spiritual exalting sprightly excited surprised exciting tender exhilarated tense fanciful tired frustrated tragic gay tranquil glad triumphant gloomy vigorous graceful whimsical happy yearning heavy yielding humorous impetuous joyous leisurely light lofty longing lyrical majestic martial melancholic melancholy merry miserable mournful
- 435 -
Appendix B: Displays used in Experiments II, III and IV
This appendix consists of screen dumps of the EmotionSpace Lab computer-human interface displays used in Experiments II, III and IV. Additional displays used in
Experiment II are shown in Appendix C on page 482. Additional displays used in
Experiments III and IV can be found in the Appendices associated with Chapter 5
(Appendix D on page 488 and
Appendix J on page 566).
Three kinds of displays were used: cards, messages and dialogs. Most information was presented and collected using cards. A card is a Hypercard metaphor for a particular style of display screen. It is the most common and flexible form of interfacing implemented in EmotionSpace Lab. Cards with more than one line of instructions are usually displayed one line at a time, with a scrolling effect and a delay of about two seconds between lines. This makes reading and concentration somewhat easier. Dialogs are an alternative interface to cards and are presented “in front” of a card. They require the user to enter a piece of data using the “qwerty” keyboard or to make a selection from a small choice of alternatives. Fundamentally, a dialog is an interface which collects data from the participant and returns it to the computer. The participant then clicks the “OK” button which accompanies the dialog. A message is also a kind of dialog, except that no typing is
- 436 - required. Messages are simply used to remind the participant about something or to provide the participant with information. No information is required from the participant. For more detailed information about Hypercard interfacing and metaphors, see Goodman (1993).
Not all cards, dialogs and messages used in EmotionSpace Lab are shown in this appendix. Instead, a sample of important or relevant displays are shown for each experimental phase. For example, there are 24 verbal stimuli used in the Plain and
Anchor phases of Experiment II, but only a few examples are shown below. Consult the main text for a complete listing of the stimuli for each experiment.
Although an attempt has been made to show displays in sequence, some displays required the participant to make a response that required the program to branch to another display. Branching that was of little importance to the design of the experiment has been omitted for greater clarity. For example, questions asked of non-students have been omitted here.
The image quality of the screen dumps are degraded. This is because Hypercard saves images in bitmapped form, meaning that resizing distorts the original image.
Resizing was necessary to fit the images on the following pages. Words and images displayed by EmotionSpace Lab are not distorted.
- 437 - Opening Display and Opening Questionnaire
Display 1 Splash Screen
Display 2 Introduction
- 438 - Display 3 Enter Name Dialog
Display 4 Questionnaire Introduction Card
- 439 - Display 5 Help Demo Card
Display 6 Help Demo Message
- 440 - Display 7 Start Questions Card
Display 8 Gender Card
- 441 - Display 9 Age I Card
Display 10 Age II Card
- 442 - Display 11 Student Card
Display 12 Student Help Dialog
- 443 - Display 13 Enrolled Institution Card
Display 14 Year of Study Card
- 444 - Display 15 Field of Study Card
Display 16 Field of Study Help Message
- 445 - Display 17 Field of Study Other Dialog
Display 18 Used 2DES Before Card
- 446 - Display 19 Used 2DES Before Help Message
Display 20 Questionnaire End
- 447 - Valence Training
Display 21 Valence Training Introduction Card
Display 22 Valence Definition Card
- 448 - Display 23 Valence Demo I
Display 24 Valence Demo II
- 449 - Display 25 Valence Demo III
Display 26 Valence Demo IV
- 450 - Display 27 Valence Demo V
Display 28 Valence Demo VI
- 451 - Display 29 Valence Demo Your Turn Card
Display 30 Begin Next Valence Stimulus Card
- 452 - Display 31 Preparing Valence Trial Card
Display 32 Valence Trial I
- 453 - Display 33 Valence Trial II
Display 34 Valence Trial III
- 454 - Display 35 Valence Trial IV
Display 36 Valence Trial V
- 455 - Display 37 Valence Response Error Dialog
Display 38 Valence Help I Same as Display 22 on page 448, but with left arrow key (return to exercise option).
- 456 - Display 39 Valence Help Return To Exercise Dialog
Display 40 Return to Valence Trial
- 457 - Display 41 Preparing Next Valence Trial
Display 42 End of Valence Trial Card
- 458 - Arousal Training
Display 43 Arousal Training Introduction Card
Display 44 Arousal Definition Card
- 459 - Display 45 Arousal Demo I
Display 46 Arousal Demo II
- 460 - Display 47 Arousal Demo III
Display 48 Arousal Demo IV
- 461 - Display 49 Arousal Demo V
Display 50 Arousal Demo VI
- 462 - Display 51 Arousal Demo VII
Display 52 Arousal Demo Your Turn Card
- 463 - Display 53 Begin Next Arousal Stimulus Card
Display 54 Preparing Arousal Trial Card
- 464 - Display 55 Arousal Response Error Dialog
- 465 - 2DES Training
Display 56 2DES Training Introduction Card
Display 57 2DES Definition Card
- 466 - Display 58 2DES Demo I
Display 59 2DES Demo II
- 467 - Display 60 2DES Demo III
Display 61 2DES Demo IV
- 468 - Display 62 2DES Demo Thinking Card
Display 63 2DES Demo Your Turn Card
- 469 - Display 64 Begin Next 2DES Stimulus Card
Display 65 2DES Trial I
- 470 - Display 66 2DES Response Error Dialog
Display 67 2DES Help Menu
- 471 - Display 68 2DES Response Feedback
- 472 - Plain Phase
Display 69 Plain Phase Introduction Card when following Anchor Phase
Display 70 Plain Phase Information Card when followed by Anchor Phase
- 473 - Display 71 Plain Phase Information Card when preceding Anchor Phase
Display 72 Plain Phase Instruction Card when Preceding Anchor Phase
- 474 - Display 73 Ready to Begin Next Plain Phase Test Stimulus
Display 74 Response to a Facial Expression Stimulus Stimulus Source: Ekman and Friesen (1975), Photo No. 29, p. 189; Code: face22fb; Emotion: anger.
- 475 - Closing Questionnaire
Display 75 Closing Questionnaire Card
Display 76 Follow Up
- 476 - Display 77 Follow Up Help Message
Display 78 Follow Up
- 477 - Display 79 Follow Up Name Dialog
Display 80 Follow Up Phone Dialog
- 478 - Display 81 Follow Up Street Dialog
Display 82 Follow Up Suburb Dialog
- 479 - Display 83 Debrief
Display 84 Experiment Concluded
- 480 - Display 85 Experiment Concluded Message
- 481 -
Appendix C: Additional Displays used in Experiment II Only (Anchor Phase).
- 482 - Anchor Preparation This section of the experiment always preceded the Anchor phase.
Display 86 Anchor Phase Introduction Card
Display 87 Anchor Preparation Information Card
5
- 483 - Display 88 Anchor Preparation Card Initial position of anchors is taken from 2DES responses to trial stimuli. Left arrow enables return to the Anchor Preparation Information Card (Display 87).
Display 89 Dragging Anchor. Left arrow enables return to the Anchor Preparation Information Card (Display 87).
- 484 - Display 90 End of Anchor Preparation Dialog
Anchor Phase
Display 91 Anchor Phase Test Introduction
- 485 - Display 92 Anchor Phase Test Introduction Card
Display 93 Anchor Phase Test Stimulus Presentation
- 486 -
Appendices for Chapter 5
- 487 -
Appendix D: Additional Displays used in Experiments III and IV Only (Music Phase)
- 488 - Display 94 Music Phase Introduction Card
Display 95 Sound Check Card
- 489 - Display 96 Sound Check Help Message
Display 97 Sound Check Dialog
- 490 - Display 98 Music Phase Information Card
Display 99 Cognitivist Reminder Dialog
- 491 - Display 100 Prepare to Start Listening Card
Display 101 Recording Card
- 492 - Display 102 Post Listening Questionnaire Card
Display 103 Overall Response Card
- 493 - Display 104 Overall Response Dialog
Display 105 Word List Card
- 494 - Display 106 Non Word-List Dialog
Display 107 Word List Help Message
- 495 - Display 108 Word List Feedback Dialog
Display 109 End of Example Card
- 496 -
Appendix E: Musical Feature Time Plots
Notes:
For pitch and loudness, 0 indicates absence of the variable (no melodic line or silence respectively). These values were treated as missing for analysis.
Time (x-) axis is labelled with units of seconds elapsed (to the nearest second) and bar number (i.e., second/bar). Bar numbers are prefixed by m or mm (see Glossary). Y- axis units are indicated in the heading of each plot (in parentheses) and described in the Glossary under the unit name.
For more detailed arousal and valence plots see Appendix G from page 547.
- 497 - Plot 1 Morning Valence and Arousal
- 498 - Plot 2 Morning Tempo
- 499 - Plot 3 Morning Centroid
- 500 - Plot 4 Morning Loudness 10 20 30 40 50 60 70 80 0
1/m.1.1
11/m.14.2
21/m.28.1
31/m.42.1
41/m.56.1
51/m.70.1
61/m.84.1
71/m.96.1
81/m.108.1 Loudness (dBA) Morning
91/m.121.1
101/m.134.1
111/m.147.1
121/m.159.1
131/m.172.1
141/m.187.1
151/m.200.3
161/m.214.1
171/m.227.3
181/m.241.1
191/m.254.1
201/m.266.2
211/m.279.1
- 501 - Plot 5 Morning Melodic Pitch
- 502 - Plot 6 Morning Texture
- 503 - Plot 7 Pizzicato Arousal and Valence
- 504 - Plot 8 Pizzicato Tempo
- 505 - Plot 9 Pizzicato Centroid
- 506 - Plot 10 Pizzicato Loudness
- 507 - Plot 11 Pizzicato Melodic Pitch
- 508 - Plot 12 Pizzicato Texture 0 1 2 3 4 5
1/m.1.1
11/m.14.2
21/m.28.1
31/m.42.1
41/m.56.1
51/m.70.1 Texture (voices) Pizzicato 61/m.84.1
71/m.96.1
81/m.108.1
91/m.121.1
101/m.134.1
111/m.147.1
121/m.159.1
131/m.172.1
141/m.187.1
- 509 - Plot 13 Aranjuez Valence and Arousal
- 510 - Plot 14 Aranjuez Tempo
- 511 - Plot 15 Aranjuez Centroid
- 512 - Plot 16 Aranjuez Loudness
- 513 - Plot 17 Aranjuez Melodic Pitch
- 514 - Plot 18 Aranjuez Texture
- 515 - Plot 19 Slavonic Dance
- 516 - Plot 20 Slavonic Dance Tempo
- 517 - Plot 21 Slavonic Dance Centroid
- 518 - Plot 22 Slavonic Dance Loudness
- 519 - Plot 23 Slavonic Dance Melodic Pitch
- 520 - Plot 24 Slavonic Dance Texture 10 15 20 25 30 35 0 5
1/m.1.1
11/m.14.2
21/m.28.1
31/m.42.1
41/m.56.1
51/m.70.1
61/m.84.1
71/m.96.1 Texture (voices) Slavonic Dance 81/m.108.1
91/m.121.1
101/m.134.1
111/m.147.1
121/m.159.1
131/m.172.1
141/m.187.1
151/m.200.3
161/m.214.1
171/m.227.3
181/m.241.1
191/m.254.1
201/m.266.2
211/m.279.1
221/m.292.3
- 521 -
Appendix F: First Order Differenced Time Plots
Time (x-) axis is labelled with units of seconds elapsed (to the nearest second) and bar number (i.e., second/bar). Bar numbers are prefixed by m or mm (see Glossary). Y- axis units are indicated in the heading of each plot (in parentheses) and described in the Glossary under the unit name.
- 522 - Plot 25 ∆Morning Valence and Arousal
- 523 - Plot 26 ∆Morning Tempo
- 524 - Plot 27 ∆Morning Centroid
- 525 - Plot 28 ∆Morning Loudness
- 526 - Plot 29 ∆Morning Melodic Pitch
- 527 - Plot 30 ∆Morning Texture
- 528 - Plot 31 ∆Pizzicato Valence and Arousal
- 529 - Plot 32 ∆Pizzicato Tempo
- 530 - Plot 33 ∆Pizzicato Centroid
- 531 - Plot 34 ∆Pizzicato Loudness
- 532 - Plot 35 ∆Pizzicato Melodic Pitch
- 533 - Plot 36 ∆Pizzicato Texture
- 534 - Plot 37 ∆Aranjuez Valence and Arousal
- 535 - Plot 38 ∆Aranjuez Tempo
- 536 - Plot 39 ∆Aranjuez Centroid
- 537 - Plot 40 ∆Aranjuez Loudness
- 538 - Plot 41 ∆Aranjuez Melodic Pitch
- 539 - Plot 42 ∆Aranjuez Texture
- 540 - Plot 43 ∆Slavonic Dance Valence and Arousal
- 541 - Plot 44 ∆Slavonic Dance Tempo
- 542 - Plot 45 ∆Slavonic Dance Centroid
- 543 - Plot 46 ∆Slavonic Dance Loudness
- 544 - Plot 47 ∆Slavonic Dance Melodic Pitch
- 545 - Plot 48 ∆Slavonic Dance Texture
- 546 -
Appendix G: Arousal and Valence Time Plots
The plots shown in this appendix are the mean responses collected from sixty-seven participants across the four test pieces used as stimuli in Experiment III. Plots are distributed over several pages for improved resolution. The top right hand corner of each plot indicates the time range of that plot. For each piece, mean valence response is plotted in the top half of the page, and mean arousal in the bottom half.
The horizontal x-axis is indicated in seconds and bar number. Bars are indicated every five seconds and are preceded by an m or mm (“measure” number — see
Glossary). The vertical y-axis is indicated in percentage units as read from the percentage box of the 2DES. The dotted line surrounding the mean response is the
95% confidence interval.
- 547 - Plot 49 Arousal and Valence Time Plots for Morning Thick line indicates mean response (N = 67). Region between dotted lines indicate 95% confidence interval.
- 548 -
- 549 - Plot 50 Arousal and Valence Time Plots for Aranjuez Thick line indicates mean response (N = 67). Region between dotted lines indicate 95% confidence interval.
- 550 -
- 551 -
- 552 -
- 553 - Plot 51 Arousal and Valence Time Plots for Slavonic Dance Thick line indicates mean response (N = 67). Region between dotted lines indicate 95% confidence interval.
- 554 -
- 555 - Plot 52 Arousal and Valence Time Plots for Pizzicato Polka Thick line indicates mean response (N = 67). Region between dotted lines indicate 95% confidence interval.
- 556 -
- 557 -
Appendix H: Scatterplots
The letters in each scatterplot denote the mean response at the opening seconds to the piece. The mean response to the first second of music occurred at A, the next second at B and so on. This allowed the investigation and control of the warm up period at the beginning of each piece. Point A was always near the origin because stimulus playing was initiated by movement to the centre of the 2DES.
The x-axis denotes valence and the y-axis denotes arousal, each in percentage units from -100% to +100%.
- 558 - Plot 53 Morning Scatterplot
Plot 54 Slavonic Dance Scatterplot
- 559 - Plot 55 Pizzicato Scatterplot
Plot 56 Aranjuez Scatterplot
- 560 -
Appendix I: Checklist Histograms, Pareto Charts and Tables
Checklist data were analysed in two ways. (1) Individual words were analysed graphically on Pareto charts, where the first 50% aggregate of frequency sorted response words was used as the cut off. (2) Checklist data were collapsed into nine clusters, as indicated in Table A - 1. An overall chi-square analysis was performed between clusters for each piece, as summarised in each Word Cluster Frequency table.
Table A - 1 Quadrant Mapping of Word Clusters Used in Experiment III See Glossary for a description of the Quadrants.
Group 1: bright Group 4: exalting Group 7: dreamy Quad 1 cheerful Quad 0 majestic Quad 3.5 sentimental happy ponderous tender joyous vigorous Group 8: calm merry Group 5: heavy Quad 4 leisurely Group 2: dramatic Quad 2.5 sacred lyrical Quad 1.5 exciting tragic serene passionate Group 6: dark soothing soaring Quad 3 melancholy tranquil triumphant mournful Group 9: delicate yearning sad Quad 4.5 graceful Group 3: agitated solemn Quad 2 restless tense
- 561 - Slavonic Dance Words
Figure A - 1 Pareto Chart for Slavonic Dance Words
80
70 100 60
50
40 50 30
20
10 17 10 0 88 0
Table A - 2 Word Cluster Frequency for Slavonic Dance
Category Observed Percent Expected Residual Group 1: Quad 1 1.00 16 23.9 9.05 6.95 Group 2: Quad 1.5 2.00 37 55.2 10.86 26.14 Group 3: Quad 2 3.00 1 1.5 5.43 -4.43 Group 4: Quad 0 4.00 13 19.4 7.24 5.76 Group 5: Quad 2.5 5.00 0 5.43 -5.43 Group 6: Quad 3 6.00 0 9.05 -9.05 Group 7: Quad 3.5 7.00 0 5.43 -5.43 Group 8: Quad 4 8.00 0 10.86 -10.86 Group 9: Quad 0.5 9.00 0 3.62 -3.62 Total 67 100 Chi-Square D.F. Significance 110.7933 8 .0000
Figure A - 2 Word Cluster Histogram for Slavonic Dance 40
30
20
10
0 Group 1: Quad 1 Group 3: Quad 2 Group 2: Quad 1.5 Group 4: Quad 0
Slavonic Dance Word Group
- 562 - Aranjuez Words
Figure A - 3 Pareto Chart for Aranjuez Words
70
100 60
50
40
50 30
20 23
10 8 6 0 45 0 melancholy dream y passionate solemn s o oth ing dram atic dark tranquil m ournful yearning sad sentimental bright tragic serene
Table A - 3 Word Cluster Frequency for Aranjuez Categor Cases Observed Percent Expected Residual y Group 1: Quad 1 1.00 1 1.6 8.38 -7.38 Group 2: Quad 1.5 2.00 10 16.1 10.05 -.05 Group 3: Quad 2 3.00 0 5.03 -5.03 Group 4: Quad 0 4.00 0 6.70 -6.70 Group 5: Quad 2.5 5.00 1 1.6 5.03 -4.03 Group 6: Quad 3 6.00 36 58.1 8.38 27.62 Group 7: Quad 3.5 7.00 10 16.1 5.03 4.97 Group 8: Quad 4 8.00 4 6.5 10.05 -6.05 Group 9: Quad 0.5 9.00 0 3.35 -3.35 Missing 5 7.5 Total 67 100 Chi-Square D.F. Significance 124.4323 8 .0000
Figure A - 4 Word Cluster Histogram for Aranjuez
40
30
20
10
0 Group 1: Quad 1 Group 5: Quad 2.5 Group 7: Quad 3.5
Group 2: Quad 1.5 Group 6: Quad 3 Group 8: Quad 4
- 563 - Pizzicato Words
Figure A - 5 Pareto Chart for Pizzicato Words
70
100 60
50
40
50 30 28 20
10 9 9 7 0 4 0 cheerful delicate happy joyous dream y bright m e rry lyrical restless graceful
Table A - 4 Word Cluster Frequency for Pizzicato Category Cases Observed Percent Expected Residual Group 1: Quad 1 1.00 49 73.1 8.92 40.08 Group 2: Quad 1.5 2.00 0 10.70 -10.70 Group 3: Quad 2 3.00 1 1.5 5.35 -4.35 Group 4: Quad 0 4.00 0 7.14 -7.14 Group 5: Quad 2.5 5.00 0 5.35 -5.35 Group 6: Quad 3 6.00 0 8.92 -8.92 Group 7: Quad 3.5 7.00 1 1.5 5.35 -4.35 Group 8: Quad 4 8.00 5 7.5 10.70 -5.70 Group 9: Quad 0.5 9.00 10 14.9 3.57 6.43 Missing 1 1.5 Total 67 100 Chi-Square D.F. Significance 233.9429 8 .0000
Figure A - 6 Word Cluster Histogram for Pizzicato
60
50
40
30
20
10
0 Group 1: Quad 1 Group 7: Quad 3.5 Group 9: Quad 0.5 Group 3: Quad 2 Group 8: Quad 4
- 564 - Morning Words
Figure A - 7 Pareto Chart for Morning Words
70 100 60
50
40
50 30
20
10 11 9 8 0 6 455 0
Table A - 5 Word Cluster Frequency for Morning Category Observed Percent Expected Residual Group 1: Quad 1 1.00 6 9.1 8.78 -2.78 Group 2: Quad 1.5 2.00 11 16.7 10.54 .46 Group 3: Quad 2 3.00 0 0 5.27 -5.27 Group 4: Quad 0 4.00 4 6.1 7.03 -3.03 Group 5: Quad 2.5 5.00 0 0 5.27 -5.27 Group 6: Quad 3 6.00 1 1.5 8.78 -7.78 Group 7: Quad 3.5 7.00 9 13.6 5.27 3.73 Group 8: Quad 4 8.00 32 48.5 10.54 21.46 Group 9: Quad 0.5 9.00 2 3.0 3.51 -1.51 Total 65 100 Chi-Square D.F. Significance 66.6251 8 .0000
Figure A - 8 Word Cluster Histogram for Morning
40
30
20
10
0
- 565 -
Appendix J: Additional Displays used in Experiment IV Only (Pretest)
- 566 - Display 110 Pretest Info Card
Display 111 Pretest Info Help Message
- 567 - Display 112 Skip Training Card
Display 113 Skip Training Help Dialog
- 568 -
Appendices for Chapter 6
- 569 -
Appendix K: SPSS Output for Lagged Loudness Regression Model of Arousal
SPSS conventions:
-> indicates a command
->* indicates a non-executable comment
Note: Underlined or bold text was added after SPSS output was produced, to indicate points of reference made in the chapter.
-> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 50 -> /FORMAT= WRAP NUMBERED . BAR 60 mm.025.3 110 mm.047.2 Number of cases read: 51 Number of cases listed: 2 -> * REGRESS. -> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA COLLIN TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT ar -> /METHOD=ENTER dba1 dba2 dba3 dba4 dba5 -> /RESIDUALS DURBIN -> /SAVE RESID (RESAR) . * * * * M U L T I P L E R E G R E S S I O N * * * * Listwise Deletion of Missing Data
- 570 - Equation Number 1 Dependent Variable.. AR Block Number 1. Method: Enter DBA1 DBA2 DBA3 DBA4 DBA5 Variable(s) Entered on Step Number 1.. DBA5 LAGS(DBA,5) 2.. DBA2 LAGS(DBA,2) 3.. DBA1 LAGS(DBA,1) 4.. DBA4 LAGS(DBA,4) 5.. DBA3 LAGS(DBA,3) Multiple R .92698 R Square .85930 Adjusted R Square .84331 Standard Error 3.32134 Analysis of Variance DF Sum of Squares Mean Square Regression 5 2964.36430 592.87286 Residual 44 485.37772 11.03131 F = 53.74455 Signif F = .0000 * * * * M U L T I P L E R E G R E S S I O N * * * * Equation Number 1 Dependent Variable.. AR ------Variables in the Equation ------Variable B SE B Beta Tolerance VIF T DBA1 .628130 .125441 .418966 .456773 2.189 5.007 DBA2 .269626 .145756 .180518 .335789 2.978 1.850 DBA3 .338923 .156504 .227245 .290405 3.443 2.166 DBA4 .312386 .144921 .210341 .335825 2.978 2.156 DBA5 .453040 .127913 .304778 .431837 2.316 3.542 (Constant) -89.842825 9.330134 -9.629 ------in ------Variable Sig T DBA1 .0000 DBA2 .0711 DBA3 .0358 DBA4 .0366 DBA5 .0010 (Constant) .0000 Collinearity Diagnostics Number Eigenval Cond Variance Proportions Index Constant DBA1 DBA2 DBA3 DBA4 DBA5 1 5.98129 1.000 .00007 .00008 .00006 .00005 .00006 .00008 2 .01017 24.248 .00004 .10795 .02955 .00007 .03012 .10097 3 .00416 37.933 .26251 .04099 .06987 .09286 .06103 .04481 4 .00194 55.522 .21870 .22904 .17922 .20411 .19952 .21465 5 .00129 68.019 .02101 .43012 .51985 .02002 .69091 .18925 6 .00114 72.352 .49767 .19182 .20145 .68289 .01837 .45024 End Block Number 1 All requested variables entered. * * * * M U L T I P L E R E G R E S S I O N * * * * Equation Number 1 Dependent Variable.. AR Residuals Statistics: Min Max Mean Std Dev N *PRED 31.9326 61.3932 47.0288 7.7780 50 *RESID -10.5523 5.0927 .0000 3.1473 50 *ZPRED -1.9409 1.8468 .0000 1.0000 50 *ZRESID -3.1771 1.5333 .0000 .9476 50 Total Cases = 51 Durbin-Watson Test = .67450 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * From Equation 1: 1 new variables have been created. Name Contents ------RESAR Residual -> * DIAGNOSTICS FOR RESIDUAL. -> *Sequence Charts .
- 571 - -> TSPLOT VARIABLES= RESAR -> /NOLOG -> /FORMAT NOFILL NOREFERENCE. MODEL: MOD_4. Hi-Res Chart # 4:Tsplot of residual -> ACF -> VARIABLES= RESAR -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF. MODEL: MOD_5. Variable: RESAR Missing cases: 1 Valid cases: 50 Some of the missing cases are imbedded within the series. Autocorrelations: RESAR Residual Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob.
1 .654 .136 . ****.******** 23.159 .000 2 .382 .134 . ****.*** 31.235 .000 3 .116 .134 . ** . 31.985 .000 4 -.091 .133 . ** . 32.452 .000 5 -.178 .132 .**** . 34.279 .000 6 -.308 .130 *.**** . 39.873 .000 7 -.395 .129 ***.**** . 49.318 .000 8 -.279 .127 *.**** . 54.131 .000 9 -.277 .126 *.**** . 58.988 .000 10 -.204 .124 .**** . 61.704 .000 Plot Symbols: Autocorrelations * Two Standard Error Limits . Total cases: 51 Computable first lags: 48 Hi-Res Chart # 5:Acf for residual Partial Autocorrelations: RESAR Residual Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1
1 .654 .141 . *****.******* 2 -.079 .141 . ** . 3 -.178 .141 . **** . 4 -.132 .141 . *** . 5 -.007 .141 . * . 6 -.224 .141 . **** . 7 -.176 .141 . **** . 8 .176 .141 . **** . 9 -.229 .141 .***** . 10 -.077 .141 . ** . Plot Symbols: Autocorrelations * Two Standard Error Limits . Total cases: 51 Computable first lags: 48 Hi-Res Chart # 6:Pacf for residual
- 572 -
Appendix L: Diagnosing Autocorrelation in (a) Loudness and (b) Arousal for Original Series and Differenced Transformations
See Appendix K on page 570 for notation conventions.
(a) -> * SELECT REGION OF INTEREST. -> USE 60 THRU 110. -> * CREATE REQUIRED VARIABLES (IF NECESSARY). -> * PLOT UNTRANSFORMED VARIABLE. -> *Sequence Charts . -> TSPLOT VARIABLES= dba -> /NOLOG -> /FORMAT NOFILL NOREFERENCE. MODEL: MOD_5. Hi-Res Chart # 5:Tsplot of loudness (dba)
80
70
60
50 60 66 72 78 84 90 96 102 108 63 69 75 81 87 93 99 105 -> * PLOT THE DIFFERENCED VARIABLE. -> TSPLOT VARIABLES= dba -> /NOLOG
- 573 - -> /DIFF=1 -> /FORMAT NOFILL NOREFERENCE. MODEL: MOD_6. Hi-Res Chart # 6:Tsplot of loudness (dba)
10
0
-1 0
-2 0 63 69 75 81 87 93 99 105 66 72 78 84 90 96 102 108
Sequence num ber -> * EXAMINE AUTOCORRELATION FUNCTION OF ORIGINAL LOUDNESS SERIES. -> ACF -> VARIABLES= dba -> /NOLOG -> /MXAUTO 16 -> /SERROR=IND. MODEL: MOD_7. Autocorrelations: DBA Loudness (dBA) Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob.
1 .688 .136 . ****.********* 25.560 .000 2 .459 .135 . ****.**** 37.180 .000 3 .069 .133 . * . 37.446 .000 4 -.175 .132 .**** . 39.217 .000 5 -.295 .130 *.**** . 44.321 .000 6 -.160 .129 . *** . 45.864 .000 7 -.003 .128 . * . 45.864 .000 8 .154 .126 . *** . 47.354 .000 9 .218 .125 . ****. 50.418 .000 10 .156 .123 . *** . 52.016 .000 11 -.034 .122 . * . 52.095 .000 12 -.235 .120 ***** . 55.920 .000 13 -.402 .119 ***.**** . 67.394 .000 14 -.392 .117 ***.**** . 78.600 .000 15 -.257 .115 ***** . 83.574 .000 16 -.034 .114 . * . 83.661 .000 Plot Symbols: Autocorrelations * Two Standard Error Limits . Total cases: 51 Computable first lags: 50 Hi-Res Chart # 7:Acf for loudness (dba)
- 574 - Loudness 1.0
.5
0.0
-.5 C onfidence Limits
-1 .0 C o e fficient 1 3 5 7 9 11 13 15 2 4 6 8 10 12 14 16 -> * AND OF FIRST ORDER DIFFERENCED LOUDNESS SERIES. -> ACF -> VARIABLES= dba -> /NOLOG -> /DIFF=1 -> /MXAUTO 16 -> /SERROR=IND. MODEL: MOD_8. 1 case(s) will be lost due to differencing. Autocorrelations: DBA Loudness (dBA) Transformations: difference (1) Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob.
1 -.130 .137 . *** . .890 .345 2 .261 .136 . ***** 4.592 .101 3 -.236 .134 ***** . 7.682 .053 4 -.204 .133 .**** . 10.031 .040 5 -.421 .132 ***.**** . 20.251 .001 6 -.044 .130 . * . 20.364 .002 7 -.001 .129 . * . 20.364 .005 8 .152 .127 . *** . 21.788 .005 9 .209 .126 . ****. 24.564 .003 10 .194 .124 . ****. 27.001 .003 11 .031 .122 . * . 27.064 .004 12 -.061 .121 . * . 27.317 .007 13 -.274 .119 ***** . 32.584 .002 14 -.186 .118 .**** . 35.082 .001 15 -.132 .116 . *** . 36.374 .002 16 .093 .114 . ** . 37.032 .002 Plot Symbols: Autocorrelations * Two Standard Error Limits . Total cases: 51 Computable first lags after differencing: 49 Hi-Res Chart # 8:Acf for loudness (dba)
- 575 - Loudness 1.0
.5
0.0
-.5 C onfidence Limits
-1 .0 C o e fficient 1 3 5 7 9 11 13 15 2 4 6 8 10 12 14 16
Lag Num ber -> *** END OF AUTOCORRELATION ANALYSIS.
(b) -> * SELECT REGION OF INTEREST. -> * CREATE REQUIRED VARIABLES (IF NECESSARY). -> * PLOT UNTRANSFORMED SIGNIFICANT AROUSAL RESPONSE VARIABLE. -> *Sequence Charts . -> TSPLOT VARIABLES= ar -> /NOLOG -> /FORMAT NOFILL NOREFERENCE. MODEL: MOD_9. Hi-Res Chart # 9:Tsplot ar = arousal
arousal
70
60
50
40
30
20 60 66 72 78 84 90 96 102 108 63 69 75 81 87 93 99 105 -> * PLOT DIFFERENCED VARIABLE. -> TSPLOT VARIABLES= ar -> /NOLOG -> /DIFF=1 -> /FORMAT NOFILL NOREFERENCE.
- 576 - MODEL: MOD_10. Hi-Res Chart # 10:Tsplot of ar = arousal
² arousal
20
10
0
-1 0 63 69 75 81 87 93 99 105
66 72 78 84 90 96 102 108
Sequence num ber -> * EXAMINE AUTOCORRELATION FUNCTION OF ORIGINAL SIGNIFICANT AROUSAL RESPONSE VARIABLE. -> ACF -> VARIABLES= ar -> /NOLOG -> /MXAUTO 16 -> /SERROR=IND. MODEL: MOD_11. Variable: AR Missing cases: 1 Valid cases: 50 Some of the missing cases are imbedded within the series. Autocorrelations: AR ar = arousal Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob.
1 .884 .136 . ****.************* 42.330 .000 2 .700 .134 . ****.********* 69.416 .000 3 .463 .134 . ****.**** 81.265 .000 4 .243 .133 . ***** 84.594 .000 5 .098 .132 . ** . 85.144 .000 6 -.003 .130 . * . 85.145 .000 7 -.046 .129 . * . 85.273 .000 8 -.072 .127 . * . 85.595 .000 9 -.138 .126 . *** . 86.800 .000 10 -.218 .124 .**** . 89.879 .000 11 -.319 .122 *.**** . 96.646 .000 12 -.376 .121 ***.**** . 106.307 .000 13 -.346 .119 **.**** . 114.734 .000 14 -.266 .118 ***** . 119.840 .000 15 -.126 .116 . *** . 121.025 .000 16 .012 .114 . * . 121.036 .000 Plot Symbols: Autocorrelations * Two Standard Error Limits . Total cases: 51 Computable first lags: 48 Hi-Res Chart # 11:Acf for ar = arousal
- 577 - arousal
1.0
.5
0.0
-.5 C onfidence Limits
-1 .0 C o e fficient 1 3 5 7 9 11 13 15 2 4 6 8 10 12 14 16 -> * AND OF FIRST ORDER DIFFERENCED SIGNIFICANT AROUSAL RESPONSE VARIABLE. -> ACF -> VARIABLES= ar -> /NOLOG -> /DIFF=1 -> /MXAUTO 16 -> /SERROR=IND. MODEL: MOD_12. 1 case(s) will be lost due to differencing. Variable: AR Missing cases: 1 Valid cases: 50 Some of the missing cases are imbedded within the series. Autocorrelations: AR AR = arousal Transformations: difference (1) Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob.
1 .350 .136 . ****.** 6.658 .010 2 .294 .134 . ****.* 11.466 .003 3 -.063 .134 . * . 11.689 .009 4 -.323 .133 *.**** . 17.610 .001 5 -.199 .131 .**** . 19.922 .001 6 -.300 .130 *.**** . 25.279 .000 7 -.053 .128 . * . 25.452 .001 8 .130 .127 . *** . 26.509 .001 9 .087 .125 . ** . 26.994 .001 10 .083 .123 . ** . 27.452 .002 11 -.184 .122 .**** . 29.746 .002 12 -.321 .120 *.**** . 36.909 .000 13 -.251 .118 ***** . 41.389 .000 14 -.312 .117 *.**** . 48.538 .000 15 -.023 .115 . * . 48.576 .000 16 .088 .113 . ** . 49.182 .000 Plot Symbols: Autocorrelations * Two Standard Error Limits . Total cases: 51 Computable first lags after differencing: 46 Hi-Res Chart # 12:Acf for ar = arousal
- 578 - ² arousal
1.0
.5
0.0
-.5 C onfidence Limits
-1 .0 C o e fficient 1 3 5 7 9 11 13 15 2 4 6 8 10 12 14 16
Lag Num ber
- 579 -
Appendix M: OLS Regression Using Differenced Variables
See Appendix K on page 570 for notation conventions.
-> * SELECT REQUIRED TIME WINDOW. -> FILTER OFF. -> use 60 thru 110 . -> EXECUTE . -> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 50 -> /FORMAT= WRAP NUMBERED . BAR 60 mm.025.3 110 mm.047.2 Number of cases read: 51 Number of cases listed: 2 -> * REGRESS. -> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA COLLIN TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT d1ar -> /METHOD=ENTER d1dba1 d1dba2 d1dba3 d1dba4 d1dba5 -> /RESIDUALS DURBIN -> /SAVE RESID (RES1) . * * * * M U L T I P L E R E G R E S S I O N * * * * Listwise Deletion of Missing Data Equation Number 1 Dependent Variable.. D1AR DIFF(AR,1) Block Number 1. Method: Enter D1DBA1 D1DBA2 D1DBA3 D1DBA4 D1DBA5 Variable(s) Entered on Step Number 1.. D1DBA5 LAGS(D1DBA,5) 2.. D1DBA4 LAGS(D1DBA,4) 3.. D1DBA3 LAGS(D1DBA,3) 4.. D1DBA2 LAGS(D1DBA,2) 5.. D1DBA1 LAGS(D1DBA,1) Multiple R .80086 R Square .64137 Adjusted R Square .60153 Standard Error 2.39231 Analysis of Variance
- 580 - DF Sum of Squares Mean Square Regression 5 460.59079 92.11816 Residual 45 257.54095 5.72313 F = 16.09576 Signif F = .0000 * * * * M U L T I P L E R E G R E S S I O N * * * * Equation Number 1 Dependent Variable.. D1AR DIFF(AR,1) ------Variables in the Equation ------Variable B SE B Beta Tolerance VIF T D1DBA1 .384019 .080962 .467316 .821014 1.218 4.743 D1DBA2 .170541 .078183 .206945 .885424 1.129 2.181 D1DBA3 .459086 .079308 .556910 .861028 1.161 5.789 D1DBA4 .257842 .078617 .312021 .880499 1.136 3.280 D1DBA5 .168819 .081688 .203933 .818432 1.222 2.067 (Constant) .167124 .335151 .499 ------in ------Variable Sig T D1DBA1 .0000 D1DBA2 .0344 D1DBA3 .0000 D1DBA4 .0020 D1DBA5 .0446 (Constant) .6205 Collinearity Diagnostics Number Eigenval Cond Variance Proportions Index Constant D1DBA1 D1DBA2 D1DBA3 D1DBA4 D1DBA5 1 1.67585 1.000 .00001 .05958 .13129 .12724 .13326 .06274 2 1.19231 1.186 .00061 .34585 .00132 .00001 .00217 .33780 3 1.00234 1.293 .98243 .00211 .00175 .00377 .00464 .00008 4 .85462 1.400 .01369 .00892 .22420 .58057 .18302 .00827 5 .76332 1.482 .00078 .00191 .56524 .00104 .58418 .00307 6 .51155 1.810 .00248 .58163 .07620 .28738 .09272 .58804 End Block Number 1 All requested variables entered. * * * * M U L T I P L E R E G R E S S I O N * * * * Equation Number 1 Dependent Variable.. D1AR DIFF(AR,1) Residuals Statistics: Min Max Mean Std Dev N *PRED -5.5887 5.7967 .1034 3.0351 51 *RESID -4.3199 5.1233 .0000 2.2695 51 *ZPRED -1.8754 1.8758 .0000 1.0000 51 *ZRESID -1.8058 2.1416 .0000 .9487 51 Total Cases = 51 Durbin-Watson Test = 1.67525 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * From Equation 1: 1 new variables have been created. Name Contents ------RES1 Residual -> ** DIAGNOSTICS FOR RESIDUAL. -> *Sequence Charts . -> *TSPLOT VARIABLES= RES1 -> * /NOLOG -> * /FORMAT NOFILL NOREFERENCE. -> ACF -> VARIABLES= RES1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF. MODEL: MOD_16. Autocorrelations: RES1 Residual Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob.
- 581 - 1 .125 .136 . ** . .839 .360 2 .100 .135 . ** . 1.395 .498 3 -.095 .133 . ** . 1.900 .593 4 -.149 .132 . *** . 3.177 .529 5 .154 .130 . *** . 4.576 .470 6 -.186 .129 .**** . 6.664 .353 7 -.116 .128 . ** . 7.488 .380 8 .042 .126 . * . 7.600 .473 9 -.222 .125 .**** . 10.762 .292 10 .090 .123 . ** . 11.298 .335 Plot Symbols: Autocorrelations * Two Standard Error Limits . Total cases: 51 Computable first lags: 50 Hi-Res Chart # 19:Acf for residual
Residual 1.0
.5
0.0
-. Confidence Limits
-1. Coefficient 987654321 10 Par tial Autocorrelations: RES1 Residual Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1
1 .125 .140 . ** . 2 .086 .140 . ** . 3 -.120 .140 . ** . 4 -.137 .140 . *** . 5 .221 .140 . **** . 6 -.234 .140 .***** . 7 -.150 .140 . *** . 8 .186 .140 . **** . 9 -.268 .140 .***** . 10 .009 .140 . * . Plot Symbols: Autocorrelations * Two Standard Error Limits . Total cases: 51 Computable first lags: 50 Hi-Res Chart # 20:Pacf for residual
- 582 - Residual 1.0
.5
0.0
-. Confidence Lim
-1. Coefficient 987654321 10
- 583 -
Appendices for Chapter 7
- 584 -
Appendix N: Time Series Analysis SPSS Output
The following appendices contain the complete output for the valence and arousal analysis of each of the four pieces used in Experiment III. These appendices are provided in a separate volume so that they may be easily referenced whilst reading the Time Series Analysis Chapter (which starts on page 339 in Volume 1).
All commands are included in the output with the exception of commands for opening files and generating differenced and lagged variables.
SPSS conventions -> indicates a command
->* indicates a non-executable comment
Note: Underlined or bold text was added after SPSS output was produced, to indicate points of reference made in the chapter.
- 585 - Steps of Analysis To make analyses easier to follow I have generated output per analysis in three steps.
Before commencing the steps, assume that all variables, their differences and lags have been generated and are present. The Table A - 6 describes each step.
Capitalised words in parentheses indicate the SPSS command used. There are a total of eight analysis: four movements of music with two emotional dimensions per piece.
Contents: • Slavonic Dance Arousal Model • Slavonic Dance Valence Model • Aranjuez Arousal Model • Aranjuez Valence Model • Pizzicato Arousal Model • Pizzicato Valence Model • Morning Arousal Model • Morning Valence Model
Table A - 6 Steps of Analysis
Step 1: Stepwise This shows the output of stepwise regression using all five variables and Regression their five lags (25 variables) as potential predictors. (REGRESSION) This is followed by: • a plot of the residual (CASEPLOT) • autocorrelation and partial autocorrelation plots (ACF) Step 2: Model Serial The variables accepted in the regression model in STEP 1 are used as the Correlation With predictor variables in the autoregression command (AREG) AREG This is followed by: • a plot of the residual (CASEPLOT) • autocorrelation and partial autocorrelation plots (ACF) • a simple regression command of the AREG model with the actual emotional response data in order to generate a crude estimate of model fit. Only the “R Square” output is of interest (REGRESSION) Step 3: AR(1) The final step involves calculating the standard deviation of the AREG Model Outlier model residual, and three times this value in order to demarcate outliers. Analysis Of Error This requires a series of COMPUTE commands followed by: • a plot of the AREG model residual with outlier regions indicated (CASEPLOT) • a table of outlier locations and values (FILTER and LIST)
- 586 - Appendix O: Slavonic Dance Arousal Model
-> TITLE -> 'SLAVONIC DANCE AROUSAL MODEL'.
-> SUBTITLE -> 'STEP 1: STEPWISE REGRESSION.'.
-> FILTER OFF.
-> use 1 thru 225 .
-> EXECUTE .
-> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 224 -> /FORMAT= WRAP NUMBERED .
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
BAR
1 m.001.1 225
Number of cases read: 225 Number of cases listed: 2
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA END TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT ard1 -> /METHOD=STEPWISE -> BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 -> CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 -> DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 -> MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 -> TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1 -> /RESIDUALS DURBIN -> /SAVE RESID (res1).
••• SLAVONIC DANCE AROUSAL MODEL
- 587 - +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Block Number 1. Method: Stepwise Criteria PIN .0500 POUT .1000 BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1
Step MultR Rsq F(Eqn) SigF Variable BetaIn 1 .5732 .3286 105.209 .000 In: DBA1D1 .5732 2 .7453 .5555 133.721 .000 In: DBA0D1 .4771 3 .7970 .6353 123.659 .000 In: DBA2D1 .2861 4 .8268 .6836 114.510 .000 In: DBA3D1 .2238 5 .8542 .7297 113.944 .000 In: CEN1D1 .2526 6 .8667 .7512 105.676 .000 In: DBA4D1 .1538 7 .8730 .7621 95.648 .000 In: CEN2D1 .1231 8 .8767 .7685 86.327 .000 In: CEN0D1 .1022
Variable(s) Entered on Step Number 8.. CEN0D1 DIFF(CEN,1)
Multiple R .87666 R Square .76853 Adjusted R Square .75963 Standard Error 2.35629
Analysis of Variance DF Sum of Squares Mean Square Regression 8 3834.37233 479.29654 Residual 208 1154.83610 5.55210
F = 86.32713 Signif F = .0000
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
------Variables in the Equation ------
Variable B SE B Beta Tolerance VIF T
CEN0D1 .002515 .001046 .102241 .615000 1.626 2.404 CEN1D1 .006293 .001059 .251797 .620291 1.612 5.945 CEN2D1 .003636 9.9996E-04 .147726 .674077 1.484 3.636 DBA0D1 .608686 .053653 .476334 .631248 1.584 11.345 DBA1D1 .551864 .052576 .431218 .659347 1.517 10.496
- 588 - DBA2D1 .277610 .051177 .215563 .704697 1.419 5.425 DBA3D1 .288785 .044760 .225456 .911297 1.097 6.452 DBA4D1 .146355 .040426 .129372 .871446 1.148 3.620 (Constant) .067891 .160075 .424
------in ------
Variable Sig T
CEN0D1 .0171 CEN1D1 .0000 CEN2D1 .0003 DBA0D1 .0000 DBA1D1 .0000 DBA2D1 .0000 DBA3D1 .0000 DBA4D1 .0004 (Constant) .6719
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
------Variables not in the Equation ------
Variable Beta In Partial Tolerance VIF Min Toler T Sig T
BPM0D1 -.017659 -.035758 .949100 1.054 .609035 -.515 .6072 BPM1D1 .008756 .016532 .825150 1.212 .561360 .238 .8122 BPM2D1 .030477 .055094 .756412 1.322 .550901 .794 .4282 BPM3D1 .049270 .092238 .811217 1.233 .612186 1.333 .1841 BPM4D1 .037678 .072777 .863587 1.158 .599988 1.050 .2950 CEN3D1 .058057 .098149 .661523 1.512 .573837 1.419 .1574 CEN4D1 .072328 .126713 .710430 1.408 .611255 1.838 .0675 MEL0D1 .030810 .063605 .986492 1.014 .614654 .917 .3602 MEL1D1 .030484 .062613 .976485 1.024 .614659 .903 .3678 MEL2D1 .041420 .081286 .891439 1.122 .596149 1.173 .2420 MEL3D1 -.002934 -.005773 .895766 1.116 .605251 -.083 .9339 MEL4D1 .046860 .091735 .887036 1.127 .604607 1.325 .1865 TEX0D1 .038646 .077528 .931502 1.074 .613330 1.119 .2645 TEX1D1 .002038 .003287 .602248 1.660 .525586 .047 .9623 TEX2D1 .054795 .084401 .549178 1.821 .530631 1.219 .2244 TEX3D1 -.043328 -.065790 .533669 1.874 .533669 -.949 .3439 TEX4D1 .038567 .062527 .608408 1.644 .602735 .901 .3684
End Block Number 1 PIN = .050 Limits reached.
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
- 589 - Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Residuals Statistics:
Min Max Mean Std Dev N
*PRED -31.0890 20.3840 -.1100 4.8524 219 *RESID -7.7358 25.6114 .1693 2.9801 219 *ZPRED -7.4064 4.8105 -.0537 1.1517 219 *ZRESID -3.2831 10.8694 .0719 1.2647 219
Total Cases = 225
Durbin-Watson Test = .95136
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
From Equation 1: 1 new variables have been created.
Name Contents ------
RES1 Residual
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> CASEPLOT VARIABLES= res1 -> /ID= seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_57.
Hi-Res Chart # 67:Caseplot of residual
- 590 - 1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 -10 0 10 20 30
Residual
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> ACF -> VARIABLES= res1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_58.
Variable: RES1 Missing cases: 6 Valid cases: 219
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
Autocorrelations: RES1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 .353 .067 . |**.**** 27.740 .000 2 .161 .067 . |*** 33.515 .000 3 .133 .067 . |*** 37.471 .000 4 .134 .067 . |*** 41.536 .000 5 .072 .066 . |* . 42.708 .000 6 -.029 .066 . *| . 42.904 .000 7 -.008 .066 . * . 42.917 .000 8 -.065 .066 . *| . 43.900 .000 9 -.076 .066 .**| . 45.244 .000 10 -.029 .066 . *| . 45.443 .000
- 591 - Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 225 Computable first lags: 218
Hi-Res Chart # 68:Acf for residual
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
Partial Autocorrelations: RES1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 .353 .068 . |**.**** 2 .041 .068 . |* . 3 .073 .068 . |* . 4 .071 .068 . |* . 5 -.009 .068 . * . 6 -.082 .068 .**| . 7 .011 .068 . * . 8 -.080 .068 .**| . 9 -.033 .068 . *| . 10 .031 .068 . |* .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 225 Computable first lags: 218
Hi-Res Chart # 69:Pacf for residual
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> SUBTITLE -> '* STEP 2: MODEL SERIAL CORRELATION WITH AREG.' -> *Autoregression.
-> TSET PRINT=DEFAULT CNVERGE=.001 CIN=95 NEWVAR=CURRENT .
-> PREDICT THRU END.
-> AREG ard1 WITH -> DBA1D1 -> DBA0D1 -> DBA2D1 -> DBA3D1 -> CEN1D1 -> DBA4D1 -> CEN2D1 -> CEN0D1 -> /METHOD=ML -> /CONSTANT -> /RHO=0 -> /MXITER=10.
MODEL: MOD_59
- 592 - Model Description:
Variable: ARD1 Regressors: DBA1D1 DBA0D1 DBA2D1 DBA3D1 CEN1D1 DBA4D1 CEN2D1 CEN0D1
95.00 percent confidence intervals will be generated.
Split group number: 1 Series length: 219 Number of cases skipped at beginning because of missing values: 5 Number of cases skipped at end because of missing values: 1 Melard's algorithm will be used for estimation.
••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Termination criteria: Parameter epsilon: .001 Maximum Marquardt constant: 1.00E+09 SSQ Percentage: .001 Maximum number of iterations: 10
Initial values:
AR1 .00000 DBA1D1 .40519 DBA0D1 .35572 DBA2D1 .26137 DBA3D1 .26005 CEN1D1 .00708 DBA4D1 .08804 CEN2D1 .00364 CEN0D1 .00513 CONSTANT .19066
Marquardt constant = .001 Adjusted sum of squares = 1647.7211
Iteration History:
Iteration Adj. Sum of Squares Marquardt Constant
1 1355.2583 .00100000 2 1353.8290 .00010000
••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Conclusion of estimation phase. Estimation terminated at iteration number 3 because: Sum of squares decreased by less than .001 percent.
FINAL PARAMETERS:
- 593 - Number of residuals 219 Standard error 2.5435148 Log likelihood -510.32559 AIC 1040.6512 SBC 1074.5419
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 209 1353.8175 6.4694673
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .49031947 .06885055 7.1215036 .00000000 DBA1D1 .35655623 .05333215 6.6855782 .00000000 DBA0D1 .39623285 .04898701 8.0885295 .00000000 DBA2D1 .18986165 .05603853 3.3880558 .00084113 DBA3D1 .20237397 .05097285 3.9702305 .00009875 CEN1D1 .00699403 .00116990 5.9783208 .00000000 DBA4D1 .04784117 .04309899 1.1100300 .26826162 CEN2D1 .00303114 .00104432 2.9025180 .00409867 CEN0D1 .00407423 .00106594 3.8221809 .00017450 CONSTANT .26695587 .33622673 .7939758 .42811010
Covariance Matrix:
AR1
AR1 .00474040
Correlation Matrix:
AR1
AR1 1.0000000
••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Regressor Covariance Matrix:
DBA1D1 DBA0D1 DBA2D1 DBA3D1 CEN1D1
DBA1D1 .00284432 .00093469 .00128465 .00067906 -.00003388 DBA0D1 .00093469 .00239973 .00069149 .00056114 -.00002150 DBA2D1 .00128465 .00069149 .00314032 .00106828 -.00001296 DBA3D1 .00067906 .00056114 .00106828 .00259823 .00000015 CEN1D1 -.00003388 -.00002150 -.00001296 .00000015 .00000137 DBA4D1 .00060134 .00060007 .00060052 .00086370 -.00001323 CEN2D1 -.00002077 -.00001264 -.00002634 -.00000121 .00000065 CEN0D1 -.00001366 -.00002732 -.00000442 -.00000761 .00000068 CONSTANT .00052310 .00060429 .00024341 .00004200 -.00000308
DBA4D1 CEN2D1 CEN0D1 CONSTANT
DBA1D1 .00060134 -.00002077 -.00001366 .00052310
- 594 - DBA0D1 .00060007 -.00001264 -.00002732 .00060429 DBA2D1 .00060052 -.00002634 -.00000442 .00024341 DBA3D1 .00086370 -.00000121 -.00000761 .00004200 CEN1D1 -.00001323 .00000065 .00000068 -.00000308 DBA4D1 .00185752 -.00000456 -.00001115 -.00022679 CEN2D1 -.00000456 .00000109 .00000045 -.00000441 CEN0D1 -.00001115 .00000045 .00000114 -.00000258 CONSTANT -.00022679 -.00000441 -.00000258 .11304841
Regressor Correlation Matrix:
DBA1D1 DBA0D1 DBA2D1 DBA3D1 CEN1D1
DBA1D1 1.0000000 .3577666 .4298418 .2497911 -.5429400 DBA0D1 .3577666 1.0000000 .2518938 .2247254 -.3752265 DBA2D1 .4298418 .2518938 1.0000000 .3739892 -.1976369 DBA3D1 .2497911 .2247254 .3739892 1.0000000 .0024644 CEN1D1 -.5429400 -.3752265 -.1976369 .0024644 1.0000000 DBA4D1 .2616163 .2842213 .2486395 .3931501 -.2624123 CEN2D1 -.3728838 -.2471745 -.4500771 -.0227647 .5356631 CEN0D1 -.2401994 -.5232186 -.0740556 -.1400454 .5423346 CONSTANT .0291720 .0366885 .0129185 .0024506 -.0078323
DBA4D1 CEN2D1 CEN0D1 CONSTANT
DBA1D1 .2616163 -.3728838 -.2401994 .0291720 DBA0D1 .2842213 -.2471745 -.5232186 .0366885 DBA2D1 .2486395 -.4500771 -.0740556 .0129185 DBA3D1 .3931501 -.0227647 -.1400454 .0024506 CEN1D1 -.2624123 .5356631 .5423346 -.0078323 DBA4D1 1.0000000 -.1014241 -.2426924 -.0156507 CEN2D1 -.1014241 1.0000000 .4050652 -.0125490 CEN0D1 -.2426924 .4050652 1.0000000 -.0072049 CONSTANT -.0156507 -.0125490 -.0072049 1.0000000
••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
The following new variables are being created:
Name Label
FIT#1 Fit for ARD1 from AREG, MOD_59 ERR#1 Error for ARD1 from AREG, MOD_59 LCL#1 95% LCL for ARD1 from AREG, MOD_59 UCL#1 95% UCL for ARD1 from AREG, MOD_59 SEP#1 SE of fit for ARD1 from AREG, MOD_59
••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Diagnose Residual.
-> VARIABLE LABEL ERR#1 'Residual'.
-> ACF
- 595 - -> VARIABLES= ERR#1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_60.
Variable: ERR#1 Missing cases: 6 Valid cases: 219
••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Autocorrelations: ERR#1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 -.030 .067 . *| . .204 .652 2 .051 .067 . |* . .774 .679 3 .001 .067 . * . .774 .856 4 .049 .067 . |* . 1.305 .861 5 .095 .066 . |**. 3.342 .647 6 -.086 .066 .**| . 5.022 .541 7 .029 .066 . |* . 5.220 .633 8 -.084 .066 .**| . 6.853 .553 9 -.052 .066 . *| . 7.477 .588 10 -.051 .066 . *| . 8.082 .621
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 225 Computable first lags: 218
Hi-Res Chart # 70:Acf for residual
••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Partial Autocorrelations: ERR#1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 -.030 .068 . *| . 2 .050 .068 . |* . 3 .004 .068 . * . 4 .046 .068 . |* . 5 .098 .068 . |**. 6 -.086 .068 .**| . 7 .015 .068 . * . 8 -.079 .068 .**| . 9 -.070 .068 . *| . 10 -.048 .068 . *| .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 225 Computable first lags: 218
Hi-Res Chart # 71:Pacf for residual
- 596 - ••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Since AREG does not produce an R estimate, generate one.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS R -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT ard1 -> /METHOD=ENTER fit#1 .
••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Block Number 1. Method: Enter FIT#1
Variable(s) Entered on Step Number 1.. FIT#1 Fit for ARD1 from AREG, MOD_59
Multiple R .85636 R Square .73335 Adjusted R Square .73212 Standard Error 2.49524
F = 596.79574 Signif F = .0000
End Block Number 1 All requested variables entered.
••• SLAVONIC DANCE AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> SUBTITLE -> 'STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR'.
-> * Determine the standard deviation of the error series.
-> DESCRIPTIVES -> VARIABLES=err#1 -> /FORMAT=NOLABELS NOINDEX -> /STATISTICS=MEAN STDDEV -> /SORT=MEAN (A) .
- 597 - ••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
Number of valid observations (listwise) = 219.00
Valid Variable Mean Std Dev N
ERR#1 .00 2.49 219
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> * Use the MN and SD of error series to determine outliers.
-> * Create upper and lower 3*SD lines for plotting.
-> COMPUTE U3Stdev = 0 + 3 * 2.49 .
-> COMPUTE L3Stdev = 0 - 3 * 2.49 .
-> VARIABLE LABEL L3Stdev '3 SDs below'.
-> VARIABLE LABEL U3Stdev '3 SDs above'.
-> EXECUTE.
-> * Now plot the error overlayed with 3*SD lines.
-> *Sequence Charts .
-> CASEPLOT VARIABLES= err#1 U3Stdev L3Stdev -> /ID = Seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_61.
Hi-Res Chart # 72:Caseplot of err#1, u3stdev, l3stdev
- 598 - 1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 Residual 181 193 3 SDs above 205 217 3 SDs below -20 -10 0 10 20
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> * And list the actual outlier values.
-> COMPUTE Outliers = 0 .
-> IF (err#1 > U3STDEV | err#1 < L3STDEV ) Outliers = 1 .
-> USE ALL.
-> VALUE LABELS Outliers 0 'OK' 1 'Outlier'.
-> COMPUTE filter_$=(Outliers = 1).
-> VARIABLE LABEL filter_$ 'res1 = 1 (FILTER)'.
-> VALUE LABELS filter_$ 0 'unselected' 1 'selected'.
-> FORMAT filter_$ (f1.0).
-> FILTER BY filter_$.
-> LIST -> VARIABLES=seconds outliers l3stdev err#1 u3stdev -> /CASES= BY 1 -> /FORMAT= SINGLE UNNUMBERED .
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
SECONDS OUTLIERS L3STDEV ERR#1 U3STDEV
- 599 - 64 1.00 -7.47 14.52569 7.47 142 1.00 -7.47 -9.56588 7.47 160 1.00 -7.47 -10.66486 7.47 223 1.00 -7.47 7.57682 7.47 224 1.00 -7.47 12.12758 7.47
Number of cases read: 5 Number of cases listed: 5
••• SLAVONIC DANCE AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> EXECUTE .
- 600 -
Appendix P: Slavonic Dance Valence Model
-> TITLE -> 'SLAVONIC DANCE VALENCE MODEL'.
-> SUBTITLE -> 'STEP 1: STEPWISE REGRESSION.'.
-> FILTER OFF.
-> use 1 thru 225 .
-> EXECUTE .
-> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 224 -> /FORMAT= WRAP NUMBERED .
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
BAR
1 m.001.1 225
Number of cases read: 225 Number of cases listed: 2
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA END TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT vad1 -> /METHOD=STEPWISE -> BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 -> CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1
- 601 - -> DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 -> MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 -> TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1 -> /RESIDUALS DURBIN -> /SAVE RESID (res2).
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Block Number 1. Method: Stepwise Criteria PIN .0500 POUT .1000 BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1
Step MultR Rsq F(Eqn) SigF Variable BetaIn 1 .4675 .2186 60.138 .000 In: DBA0D1 .4675 2 .6213 .3860 67.264 .000 In: DBA1D1 .4098 3 .6660 .4435 56.585 .000 In: BPM1D1 .2501 4 .6913 .4779 48.516 .000 In: BPM2D1 .1930 5 .6998 .4897 40.492 .000 In: BPM3D1 .1094 6 .7092 .5030 35.417 .000 In: TEX4D1 -.1190
Variable(s) Entered on Step Number 6.. TEX4D1 LAGS(TEX0D1,4)
Multiple R .70920 R Square .50296 Adjusted R Square .48876 Standard Error 1.36441
Analysis of Variance DF Sum of Squares Mean Square Regression 6 395.60194 65.93366 Residual 210 390.94186 1.86163
F = 35.41721 Signif F = .0000
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
------Variables in the Equation ------
- 602 - Variable B SE B Beta Tolerance VIF T
BPM1D1 .051249 .009186 .286669 .896538 1.115 5.579 BPM2D1 .033502 .008445 .201775 .914908 1.093 3.967 BPM3D1 .021508 .008382 .127437 .959504 1.042 2.566 DBA0D1 .184937 .025658 .364500 .925527 1.080 7.208 DBA1D1 .155862 .026245 .306732 .887246 1.127 5.939 TEX4D1 -.061834 .026094 -.118957 .939217 1.065 -2.370 (Constant) .211147 .092689 2.278
------in ------
Variable Sig T
BPM1D1 .0000 BPM2D1 .0001 BPM3D1 .0110 DBA0D1 .0000 DBA1D1 .0000 TEX4D1 .0187 (Constant) .0237
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
------Variables not in the Equation ------
Variable Beta In Partial Tolerance VIF Min Toler T Sig T
BPM0D1 .077735 .107714 .954336 1.048 .877634 1.566 .1188 BPM4D1 -.051159 -.068672 .895552 1.117 .860490 -.995 .3208 CEN0D1 .062397 .070565 .635693 1.573 .635693 1.023 .3076 CEN1D1 .050081 .057315 .650996 1.536 .650996 .830 .4075 CEN2D1 -.080720 -.099745 .758939 1.318 .758939 -1.449 .1488 CEN3D1 -.037677 -.043642 .666882 1.500 .666156 -.632 .5284 CEN4D1 -.049373 -.068299 .951124 1.051 .884017 -.990 .3235 DBA2D1 -.012215 -.015646 .815442 1.226 .815442 -.226 .8213 DBA3D1 -.048954 -.059189 .726599 1.376 .718242 -.857 .3923 DBA4D1 -.013013 -.018040 .955147 1.047 .875408 -.261 .7945 MEL0D1 -.012628 -.017878 .996156 1.004 .884495 -.259 .7963 MEL1D1 -.042300 -.059391 .979797 1.021 .886615 -.860 .3907 MEL2D1 -.035939 -.048594 .908711 1.100 .868978 -.703 .4826 MEL3D1 .043377 .058882 .915852 1.092 .840604 .853 .3948 MEL4D1 .009970 .013867 .961574 1.040 .887229 .200 .8413 TEX0D1 .020061 .027946 .964500 1.037 .865572 .404 .6865 TEX1D1 .038308 .046388 .728809 1.372 .728809 .671 .5027 TEX2D1 .034903 .040539 .670520 1.491 .670520 .587 .5581 TEX3D1 -.073007 -.092841 .803793 1.244 .803793 -1.348 .1791
End Block Number 1 PIN = .050 Limits reached.
- 603 - ••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Residuals Statistics:
Min Max Mean Std Dev N
*PRED -7.6366 5.3191 .1360 1.4978 219 *RESID -3.4531 4.7262 .0232 1.3769 219 *ZPRED -5.7892 3.7841 -.0458 1.1068 219 *ZRESID -2.5308 3.4639 .0170 1.0091 219
Total Cases = 225
Durbin-Watson Test = 1.00306
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
From Equation 1: 1 new variables have been created.
Name Contents ------
RES2 Residual
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> CASEPLOT VARIABLES= res2 -> /ID= seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_62.
Hi-Res Chart # 73:Caseplot of residual
- 604 - 1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 -4 -2 0 2 4 6
Residual
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> ACF -> VARIABLES= res2 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_63.
Variable: RES2 Missing cases: 6 Valid cases: 219
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
Autocorrelations: RES2 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 .465 .067 . |**.****** 48.013 .000 2 .272 .067 . |**.** 64.470 .000 3 .179 .067 . |**.* 71.655 .000 4 .105 .067 . |**. 74.130 .000 5 .034 .066 . |* . 74.389 .000 6 .066 .066 . |* . 75.388 .000 7 .103 .066 . |**. 77.813 .000 8 .140 .066 . |*** 82.323 .000
- 605 - 9 .089 .066 . |**. 84.165 .000 10 .089 .066 . |**. 86.016 .000
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 225 Computable first lags: 218
Hi-Res Chart # 74:Acf for residual
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
Partial Autocorrelations: RES2 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 .465 .068 . |**.****** 2 .071 .068 . |* . 3 .037 .068 . |* . 4 -.005 .068 . * . 5 -.038 .068 . *| . 6 .068 .068 . |* . 7 .069 .068 . |* . 8 .079 .068 . |**. 9 -.030 .068 . *| . 10 .026 .068 . |* .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 225 Computable first lags: 218
Hi-Res Chart # 75:Pacf for residual
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> SUBTITLE -> '* STEP 2: MODEL SERIAL CORRELATION WITH AREG.' -> *Autoregression.
-> TSET PRINT=DEFAULT CNVERGE=.001 CIN=95 NEWVAR=CURRENT .
-> PREDICT THRU END.
-> AREG vad1 WITH -> DBA0D1 -> DBA1D1 -> BPM1D1 -> BPM2D1 -> BPM3D1 -> TEX4D1 -> /METHOD=ML -> /CONSTANT -> /RHO=0 -> /MXITER=10.
MODEL: MOD_64
- 606 - Model Description:
Variable: VAD1 Regressors: DBA0D1 DBA1D1 BPM1D1 BPM2D1 BPM3D1 TEX4D1
95.00 percent confidence intervals will be generated.
Split group number: 1 Series length: 219 Number of cases skipped at beginning because of missing values: 5 Number of cases skipped at end because of missing values: 1 Melard's algorithm will be used for estimation.
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Termination criteria: Parameter epsilon: .001 Maximum Marquardt constant: 1.00E+09 SSQ Percentage: .001 Maximum number of iterations: 10
Initial values:
AR1 .00000 DBA0D1 .15886 DBA1D1 .12678 BPM1D1 .05523 BPM2D1 .03618 BPM3D1 .02297 TEX4D1 -.06989 CONSTANT .22793
Marquardt constant = .001 Adjusted sum of squares = 407.02446
Iteration History:
Iteration Adj. Sum of Squares Marquardt Constant
1 312.65496 .00100000 2 312.39891 .00010000
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Conclusion of estimation phase. Estimation terminated at iteration number 3 because: Sum of squares decreased by less than .001 percent.
FINAL PARAMETERS:
Number of residuals 219 Standard error 1.2159795
- 607 - Log likelihood -349.7124 AIC 715.4248 SBC 742.53737
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 211 312.39823 1.4786061
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .50118037 .06072319 8.2535247 .00000000 DBA0D1 .16944021 .01931264 8.7735390 .00000000 DBA1D1 .13737751 .02022991 6.7908100 .00000000 BPM1D1 .05072394 .00776246 6.5345220 .00000000 BPM2D1 .03563932 .00813589 4.3805071 .00001865 BPM3D1 .02581937 .00721480 3.5786665 .00042843 TEX4D1 -.03964408 .02002823 -1.9794102 .04906999 CONSTANT .25707470 .16415690 1.5660305 .11883998
Covariance Matrix:
AR1
AR1 .00368731
Correlation Matrix:
AR1
AR1 1.0000000
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Regressor Covariance Matrix:
DBA0D1 DBA1D1 BPM1D1 BPM2D1 BPM3D1
DBA0D1 .00037298 .00006620 -.00002579 .00000037 -.00000298 DBA1D1 .00006620 .00040925 -.00001812 -.00002520 .00000252 BPM1D1 -.00002579 -.00001812 .00006026 .00003029 .00001553 BPM2D1 .00000037 -.00002520 .00003029 .00006619 .00002867 BPM3D1 -.00000298 .00000252 .00001553 .00002867 .00005205 TEX4D1 .00001058 .00009315 .00000043 .00000961 .00000051 CONSTANT .00011994 .00010030 .00000263 -.00000804 .00000142
TEX4D1 CONSTANT
DBA0D1 .00001058 .00011994 DBA1D1 .00009315 .00010030 BPM1D1 .00000043 .00000263 BPM2D1 .00000961 -.00000804 BPM3D1 .00000051 .00000142 TEX4D1 .00040113 .00001436 CONSTANT .00001436 .02694749
- 608 - Regressor Correlation Matrix:
DBA0D1 DBA1D1 BPM1D1 BPM2D1 BPM3D1
DBA0D1 1.0000000 .1694325 -.1720139 .0023861 -.0213989 DBA1D1 .1694325 1.0000000 -.1154029 -.1531327 .0172739 BPM1D1 -.1720139 -.1154029 1.0000000 .4796426 .2772871 BPM2D1 .0023861 -.1531327 .4796426 1.0000000 .4884663 BPM3D1 -.0213989 .0172739 .2772871 .4884663 1.0000000 TEX4D1 .0273474 .2299157 .0027850 .0589783 .0034961 CONSTANT .0378332 .0302042 .0020673 -.0060213 .0012007
TEX4D1 CONSTANT
DBA0D1 .0273474 .0378332 DBA1D1 .2299157 .0302042 BPM1D1 .0027850 .0020673 BPM2D1 .0589783 -.0060213 BPM3D1 .0034961 .0012007 TEX4D1 1.0000000 .0043691 CONSTANT .0043691 1.0000000
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
The following new variables are being created:
Name Label
FIT#1 Fit for VAD1 from AREG, MOD_64 ERR#1 Error for VAD1 from AREG, MOD_64 LCL#1 95% LCL for VAD1 from AREG, MOD_64 UCL#1 95% UCL for VAD1 from AREG, MOD_64 SEP#1 SE of fit for VAD1 from AREG, MOD_64
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Diagnose Residual.
-> VARIABLE LABEL ERR#1 'Residual'.
-> ACF -> VARIABLES= ERR#1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_65.
Variable: ERR#1 Missing cases: 6 Valid cases: 219
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
- 609 - Autocorrelations: ERR#1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 -.021 .067 . * . .097 .756 2 .006 .067 . * . .106 .949 3 .038 .067 . |* . .434 .933 4 .034 .067 . |* . .701 .951 5 -.047 .066 . *| . 1.199 .945 6 .018 .066 . * . 1.270 .973 7 .039 .066 . |* . 1.617 .978 8 .097 .066 . |**. 3.757 .878 9 .014 .066 . * . 3.802 .924 10 -.023 .066 . * . 3.922 .951
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 225 Computable first lags: 218
Hi-Res Chart # 76:Acf for residual
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Partial Autocorrelations: ERR#1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 -.021 .068 . * . 2 .006 .068 . * . 3 .039 .068 . |* . 4 .036 .068 . |* . 5 -.046 .068 . *| . 6 .014 .068 . * . 7 .038 .068 . |* . 8 .101 .068 . |**. 9 .020 .068 . * . 10 -.030 .068 . *| .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 225 Computable first lags: 218
Hi-Res Chart # 77:Pacf for residual
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Since AREG does not produce an R estimate, generate one.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS R -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN
- 610 - -> /DEPENDENT vad1 -> /METHOD=ENTER fit#1 .
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Block Number 1. Method: Enter FIT#1
Variable(s) Entered on Step Number 1.. FIT#1 Fit for VAD1 from AREG, MOD_64
Multiple R .78819 R Square .62125 Adjusted R Square .61950 Standard Error 1.19995
F = 355.93199 Signif F = .0000
End Block Number 1 All requested variables entered.
••• SLAVONIC DANCE VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> SUBTITLE -> 'STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR'.
-> * Determine the standard deviation of the error series.
-> DESCRIPTIVES -> VARIABLES=err#1 -> /FORMAT=NOLABELS NOINDEX -> /STATISTICS=MEAN STDDEV -> /SORT=MEAN (A) .
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
Number of valid observations (listwise) = 219.00
Valid Variable Mean Std Dev N
ERR#1 .00 1.20 219
- 611 - ••• SLAVONIC DANCE VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> * Use the MN and SD of error series to determine outliers.
-> * Create upper and lower 3*SD lines for plotting.
-> COMPUTE U3Stdev = 0 + 3 * 1.20 .
-> COMPUTE L3Stdev = 0 - 3 * 1.20 .
-> VARIABLE LABEL L3Stdev '3 SDs below'.
-> VARIABLE LABEL U3Stdev '3 SDs above'.
-> EXECUTE.
-> * Now plot the error overlayed with 3*SD lines.
-> *Sequence Charts .
-> CASEPLOT VARIABLES= err#1 U3Stdev L3Stdev -> /ID = Seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_66.
Hi-Res Chart # 78:Caseplot of err#1, u3stdev, l3stdev 1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 Residual 181
193 3 SDs above 205 217 3 SDs below -6 -4 -2 0 2 4 6
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
- 612 - -> * And list the actual outlier values.
-> COMPUTE Outliers = 0 .
-> IF (err#1 > U3STDEV | err#1 < L3STDEV ) Outliers = 1 .
-> USE ALL.
-> VALUE LABELS Outliers 0 'OK' 1 'Outlier'.
-> COMPUTE filter_$=(Outliers = 1).
-> VARIABLE LABEL filter_$ 'res1 = 1 (FILTER)'.
-> VALUE LABELS filter_$ 0 'unselected' 1 'selected'.
-> FORMAT filter_$ (f1.0).
-> FILTER BY filter_$.
-> LIST -> VARIABLES=seconds outliers l3stdev err#1 u3stdev -> /CASES= BY 1 -> /FORMAT= SINGLE UNNUMBERED .
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
SECONDS OUTLIERS L3STDEV ERR#1 U3STDEV
143 1.00 -3.60 4.10229 3.60 168 1.00 -3.60 4.38398 3.60 224 1.00 -3.60 3.97155 3.60
Number of cases read: 3 Number of cases listed: 3
••• SLAVONIC DANCE VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> EXECUTE .
-> ******** END OF SLAVONIC DANCE ANALYSIS **********.
- 613 -
Appendix Q: Aranjuez Arousal Model
-> TITLE -> 'ARANJUEZ AROUSAL MODEL'.
-> SUBTITLE -> 'STEP 1: STEPWISE REGRESSION.'.
-> FILTER OFF.
-> use 1 thru 654.
-> EXECUTE .
-> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 653 -> /FORMAT= WRAP NUMBERED .
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
BAR
1 m. 1.1 654 m. 101.4
Number of cases read: 654 Number of cases listed: 2
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA END TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT ard1 -> /METHOD=STEPWISE -> BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 -> CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1
- 614 - -> DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 -> MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 -> TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1 -> /RESIDUALS DURBIN -> /SAVE RESID (res1).
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Block Number 1. Method: Stepwise Criteria PIN .0500 POUT .1000 BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1
Step MultR Rsq F(Eqn) SigF Variable BetaIn 1 .3037 .0922 54.144 .000 In: TEX3D1 .3037 2 .3980 .1584 50.078 .000 In: TEX2D1 .2573 3 .4486 .2012 44.589 .000 In: TEX4D1 .2069 4 .4783 .2288 39.306 .000 In: DBA2D1 .1690 5 .5105 .2606 37.286 .000 In: DBA1D1 .1821 6 .5325 .2836 34.836 .000 In: DBA3D1 .1552 7 .5518 .3044 32.952 .000 In: BPM3D1 .1454 8 .5636 .3176 30.600 .000 In: MEL3D1 .1168 9 .5727 .3280 28.477 .000 In: MEL2D1 .1048 10 .5808 .3374 26.678 .000 In: DBA4D1 .1001 11 .5879 .3457 25.118 .000 In: MEL1D1 .0934 12 .5941 .3529 23.727 .000 In: BPM2D1 .0876 13 .5997 .3596 22.505 .000 In: DBA0D1 .0872 14 .6041 .3649 21.339 .000 In: CEN1D1 .0752 15 .6089 .3707 20.386 .000 In: CEN3D1 .0792
Variable(s) Entered on Step Number 15.. CEN3D1 LAGS(CEN0D1,3)
Multiple R .60889 R Square .37075 Adjusted R Square .35256 Standard Error 1.28425
Analysis of Variance DF Sum of Squares Mean Square Regression 15 504.33428 33.62229 Residual 519 855.98128 1.64929
F = 20.38592 Signif F = .0000
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
- 615 - * * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
------Variables in the Equation ------
Variable B SE B Beta Tolerance VIF T
BPM2D1 .042551 .015088 .101409 .937667 1.066 2.820 BPM3D1 .063625 .017219 .130207 .976462 1.024 3.695 CEN1D1 7.38952E-04 3.1879E-04 .084204 .918773 1.088 2.318 CEN3D1 6.32394E-04 2.8739E-04 .079181 .936379 1.068 2.200 DBA0D1 .029103 .013541 .080068 .873610 1.145 2.149 DBA1D1 .081548 .013767 .223229 .853726 1.171 5.924 DBA2D1 .074388 .013794 .204191 .845647 1.183 5.393 DBA3D1 .063190 .012705 .184906 .877144 1.140 4.973 DBA4D1 .037268 .012429 .109075 .916272 1.091 2.999 MEL1D1 .030642 .012419 .088545 .941373 1.062 2.467 MEL2D1 .032326 .012988 .091014 .906645 1.103 2.489 MEL3D1 .032514 .013137 .091126 .894331 1.118 2.475 TEX2D1 .322894 .055530 .212998 .903601 1.107 5.815 TEX3D1 .396660 .055524 .261658 .903795 1.106 7.144 TEX4D1 .254396 .055307 .168655 .901838 1.109 4.600 (Constant) -.013575 .055826 -.243
------in ------
Variable Sig T
BPM2D1 .0050 BPM3D1 .0002 CEN1D1 .0208 CEN3D1 .0282 DBA0D1 .0321 DBA1D1 .0000 DBA2D1 .0000 DBA3D1 .0000 DBA4D1 .0028 MEL1D1 .0139 MEL2D1 .0131 MEL3D1 .0136 TEX2D1 .0000 TEX3D1 .0000 TEX4D1 .0000 (Constant) .8080
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
------Variables not in the Equation ------
- 616 - Variable Beta In Partial Tolerance VIF Min Toler T Sig T
BPM0D1 .006121 .007397 .918751 1.088 .845276 .168 .8664 BPM1D1 -.005276 -.006412 .929337 1.076 .845627 -.146 .8840 BPM4D1 .063157 .077576 .949382 1.053 .845646 1.771 .0772 CEN0D1 .071063 .084525 .890255 1.123 .845305 1.931 .0541 CEN2D1 .071261 .083761 .869379 1.150 .840834 1.913 .0563 CEN4D1 .034550 .040836 .879060 1.138 .845065 .930 .3527 MEL0D1 .020270 .025096 .964559 1.037 .845284 .571 .5680 MEL4D1 .055927 .067136 .906773 1.103 .844170 1.531 .1263 TEX0D1 -.035395 -.043996 .972224 1.029 .845606 -1.002 .3167 TEX1D1 -.037911 -.046780 .958102 1.044 .840668 -1.066 .2870
End Block Number 1 PIN = .050 Limits reached.
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Residuals Statistics:
Min Max Mean Std Dev N
*PRED -3.8798 4.4371 .0594 .9872 568 *RESID -4.3648 10.0117 -.0373 1.2911 568 *ZPRED -4.0316 4.5264 .0218 1.0158 568 *ZRESID -3.3987 7.7957 -.0290 1.0054 568
Total Cases = 654
Durbin-Watson Test = .86795
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
From Equation 1: 1 new variables have been created.
Name Contents ------
RES1 Residual
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> CASEPLOT VARIABLES= res1 -> /ID= seconds -> /NOLOG
- 617 - -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_67.
Hi-Res Chart # 79:Caseplot of residual 1 34 67 100 133 166 199 232 265 298 331 364 397 430 463 496 529 562 595 628
-10 0 10 20
Residual
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> ACF -> VARIABLES= res1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_68.
Variable: RES1 Missing cases: 86 Valid cases: 568 Some of the missing cases are imbedded within the series.
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
Autocorrelations: RES1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 .547 .041 . |*.********* 176.030 .000 2 .339 .041 . |*.***** 245.780 .000 3 .251 .040 . |*.*** 284.801 .000 4 .192 .040 . |*.** 308.142 .000 5 .080 .040 . |** 312.178 .000
- 618 - 6 .008 .040 . * . 312.215 .000 7 .001 .040 . * . 312.215 .000 8 -.017 .040 . * . 312.402 .000 9 -.036 .040 .*| . 313.212 .000 10 -.005 .040 . * . 313.228 .000
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 654 Computable first lags: 551
Hi-Res Chart # 80:Acf for residual
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
Partial Autocorrelations: RES1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 .547 .042 . |*.********* 2 .057 .042 . |*. 3 .064 .042 . |*. 4 .029 .042 . |*. 5 -.081 .042 **| . 6 -.044 .042 .*| . 7 .015 .042 . * . 8 -.016 .042 . * . 9 -.012 .042 . * . 10 .046 .042 . |*.
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 654 Computable first lags: 551
Hi-Res Chart # 81:Pacf for residual
••• ARANJUEZ AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> SUBTITLE -> '* STEP 2: MODEL SERIAL CORRELATION WITH AREG.' -> *Autoregression.
-> TSET PRINT=DEFAULT CNVERGE=.001 CIN=95 NEWVAR=CURRENT .
-> PREDICT THRU END.
-> AREG ard1 WITH -> TEX3D1 -> TEX2D1 -> TEX4D1 -> DBA2D1 -> DBA1D1 -> DBA3D1 -> BPM3D1 -> MEL3D1 -> MEL2D1
- 619 - -> DBA4D1 -> MEL1D1 -> BPM2D1 -> DBA0D1 -> CEN1D1 -> CEN3D1 -> /METHOD=ML -> /CONSTANT -> /RHO=0 -> /MXITER=10.
MODEL: MOD_69
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Model Description:
Variable: ARD1 Regressors: TEX3D1 TEX2D1 TEX4D1 DBA2D1 DBA1D1 DBA3D1 BPM3D1 MEL3D1 MEL2D1 DBA4D1 MEL1D1 BPM2D1 DBA0D1 CEN1D1 CEN3D1
95.00 percent confidence intervals will be generated.
Split group number: 1 Series length: 637 Number of cases skipped at beginning because of missing values: 9 Number of cases skipped at end because of missing values: 8 Number of cases containing missing values: 69 Kalman filtering will be used for estimation.
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Termination criteria: Parameter epsilon: .001 Maximum Marquardt constant: 1.00E+09 SSQ Percentage: .001 Maximum number of iterations: 10
Initial values:
AR1 .00000 TEX3D1 .38364 TEX2D1 .32381 TEX4D1 .26020 DBA2D1 .05355
- 620 - DBA1D1 .07942 DBA3D1 .05942 BPM3D1 .04366 MEL3D1 .03630 MEL2D1 .02525 DBA4D1 .04468 MEL1D1 .03310 BPM2D1 .04936 DBA0D1 .03190 CEN1D1 .00069 CEN3D1 .00053 CONSTANT -.04141
Marquardt constant = .001 Adjusted sum of squares = 930.47025
Iteration History:
Iteration Adj. Sum of Squares Marquardt Constant
1 602.26283 .00100000 2 597.49360 .00010000 3 597.45322 .00001000
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Conclusion of estimation phase. Estimation terminated at iteration number 4 because: Sum of squares decreased by less than .001 percent.
FINAL PARAMETERS:
Number of residuals 568 Standard error 1.0337047 Log likelihood -820.34944 AIC 1674.6989 SBC 1748.515
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 551 597.45293 1.0685454
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .62555161 .03227649 19.381031 .00000000 TEX3D1 .32745765 .04799424 6.822853 .00000000 TEX2D1 .32379982 .04250487 7.617946 .00000000 TEX4D1 .13163808 .04244188 3.101608 .00202325 DBA2D1 .05975439 .01201929 4.971541 .00000089 DBA1D1 .07130162 .01202764 5.928148 .00000000 DBA3D1 .05346296 .01138138 4.697407 .00000333 BPM3D1 .03047106 .01162162 2.621929 .00898509 MEL3D1 .01852453 .00992206 1.867004 .06243182 MEL2D1 .01842517 .01100627 1.674062 .09468590 DBA4D1 .02396324 .00957526 2.502619 .01261631
- 621 - MEL1D1 .02768813 .00949835 2.915047 .00370097 BPM2D1 .03889084 .01150667 3.379852 .00077659 DBA0D1 .03123530 .01022692 3.054223 .00236550 CEN1D1 .00028974 .00019867 1.458411 .14529713 CEN3D1 .00017526 .00016621 1.054439 .29214427 CONSTANT -.07163614 .11197508 -.639751 .52260057
Covariance Matrix:
AR1
AR1 .00104177
Correlation Matrix:
AR1
AR1 1.0000000
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Regressor Covariance Matrix:
TEX3D1 TEX2D1 TEX4D1 DBA2D1 DBA1D1
TEX3D1 .00230345 .00105311 .00102234 -.00011201 -.00012282 TEX2D1 .00105311 .00180666 .00041335 -.00007461 -.00008730 TEX4D1 .00102234 .00041335 .00180131 -.00008701 -.00004947 DBA2D1 -.00011201 -.00007461 -.00008701 .00014446 .00009127 DBA1D1 -.00012282 -.00008730 -.00004947 .00009127 .00014466 DBA3D1 -.00007554 -.00005440 -.00006320 .00008826 .00006744 BPM3D1 -.00000080 .00000288 .00003356 -.00000554 .00000724 MEL3D1 .00003758 .00002866 .00006475 -.00001684 -.00001236 MEL2D1 .00009870 .00004295 .00005961 -.00001728 -.00001530 DBA4D1 -.00004433 -.00002141 -.00003490 .00005238 .00004058 MEL1D1 .00006249 .00006174 .00001164 -.00001166 -.00000986 BPM2D1 .00002122 -.00001578 .00001392 -.00000130 .00000082 DBA0D1 -.00005345 -.00006994 -.00000871 .00005202 .00006944 CEN1D1 .00000006 -.00000081 -.00000007 .00000009 .00000014 CEN3D1 .00000033 .00000021 -.00000042 -.00000016 -.00000009 CONSTANT .00008523 .00005025 .00005836 -.00011694 -.00008881
DBA3D1 BPM3D1 MEL3D1 MEL2D1 DBA4D1
TEX3D1 -.00007554 -.00000080 .00003758 .00009870 -.00004433 TEX2D1 -.00005440 .00000288 .00002866 .00004295 -.00002141 TEX4D1 -.00006320 .00003356 .00006475 .00005961 -.00003490 DBA2D1 .00008826 -.00000554 -.00001684 -.00001728 .00005238 DBA1D1 .00006744 .00000724 -.00001236 -.00001530 .00004058 DBA3D1 .00012954 -.00000121 -.00001157 -.00001222 .00006161 BPM3D1 -.00000121 .00013506 .00000468 .00000851 .00000036 MEL3D1 -.00001157 .00000468 .00009845 .00005647 -.00000974 MEL2D1 -.00001222 .00000851 .00005647 .00012114 -.00000474 DBA4D1 .00006161 .00000036 -.00000974 -.00000474 .00009169 MEL1D1 -.00000504 -.00000233 .00002835 .00005767 -.00000365 BPM2D1 .00000221 .00006578 -.00001304 .00000739 .00000394 DBA0D1 .00004128 .00000641 -.00001159 -.00000887 .00002436 CEN1D1 .00000002 .00000004 -.00000006 -.00000023 -.00000005 CEN3D1 .00000026 -.00000006 .00000021 .00000007 .00000006
- 622 - CONSTANT -.00009505 -.00003157 -.00000283 -.00000491 -.00004192
MEL1D1 BPM2D1 DBA0D1 CEN1D1 CEN3D1
TEX3D1 .00006249 .00002122 -.00005345 .00000006 .00000033 TEX2D1 .00006174 -.00001578 -.00006994 -.00000081 .00000021 TEX4D1 .00001164 .00001392 -.00000871 -.00000007 -.00000042 DBA2D1 -.00001166 -.00000130 .00005202 .00000009 -.00000016 DBA1D1 -.00000986 .00000082 .00006944 .00000014 -.00000009 DBA3D1 -.00000504 .00000221 .00004128 .00000002 .00000026 BPM3D1 -.00000233 .00006578 .00000641 .00000004 -.00000006 MEL3D1 .00002835 -.00001304 -.00001159 -.00000006 .00000021 MEL2D1 .00005767 .00000739 -.00000887 -.00000023 .00000007
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
DBA4D1 -.00000365 .00000394 .00002436 -.00000005 .00000006 MEL1D1 .00009022 .00000191 -.00000848 .00000005 .00000004 BPM2D1 .00000191 .00013240 .00000875 .00000010 -.00000001 DBA0D1 -.00000848 .00000875 .00010459 -.00000011 -.00000012 CEN1D1 .00000005 .00000010 -.00000011 .00000004 .00000000 CEN3D1 .00000004 -.00000001 -.00000012 .00000000 .00000003 CONSTANT -.00000968 -.00000975 -.00003307 -.00000011 -.00000017
CONSTANT
TEX3D1 .00008523 TEX2D1 .00005025 TEX4D1 .00005836 DBA2D1 -.00011694 DBA1D1 -.00008881 DBA3D1 -.00009505 BPM3D1 -.00003157 MEL3D1 -.00000283 MEL2D1 -.00000491 DBA4D1 -.00004192 MEL1D1 -.00000968 BPM2D1 -.00000975 DBA0D1 -.00003307 CEN1D1 -.00000011 CEN3D1 -.00000017 CONSTANT .01253842
Regressor Correlation Matrix:
TEX3D1 TEX2D1 TEX4D1 DBA2D1 DBA1D1
TEX3D1 1.0000000 .5162323 .5018932 -.1941769 -.2127659 TEX2D1 .5162323 1.0000000 .2291293 -.1460448 -.1707635 TEX4D1 .5018932 .2291293 1.0000000 -.1705575 -.0969087 DBA2D1 -.1941769 -.1460448 -.1705575 1.0000000 .6313201 DBA1D1 -.2127659 -.1707635 -.0969087 .6313201 1.0000000 DBA3D1 -.1382846 -.1124461 -.1308401 .6451956 .4926554 BPM3D1 -.0014350 .0058283 .0680419 -.0396728 .0517781 MEL3D1 .0789247 .0679619 .1537593 -.1411743 -.1035994 MEL2D1 .1868548 .0918117 .1276038 -.1305963 -.1155669 DBA4D1 -.0964591 -.0526126 -.0858665 .4551614 .3523599 MEL1D1 .1370869 .1529235 .0288774 -.1021257 -.0862908
- 623 - BPM2D1 .0384234 -.0322623 .0284964 -.0093801 .0059559 DBA0D1 -.1088895 -.1608837 -.0200700 .4232258 .5645046 CEN1D1 .0062566 -.0962897 -.0081881 .0366136 .0583423 CEN3D1 .0417999 .0291825 -.0592295 -.0780790 -.0435803 CONSTANT .0158588 .0105581 .0122802 -.0868921 -.0659448
DBA3D1 BPM3D1 MEL3D1 MEL2D1 DBA4D1
TEX3D1 -.1382846 -.0014350 .0789247 .1868548 -.0964591
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
TEX2D1 -.1124461 .0058283 .0679619 .0918117 -.0526126 TEX4D1 -.1308401 .0680419 .1537593 .1276038 -.0858665 DBA2D1 .6451956 -.0396728 -.1411743 -.1305963 .4551614 DBA1D1 .4926554 .0517781 -.1035994 -.1155669 .3523599 DBA3D1 1.0000000 -.0091564 -.1024735 -.0975573 .5653736 BPM3D1 -.0091564 1.0000000 .0405665 .0665253 .0032598 MEL3D1 -.1024735 .0405665 1.0000000 .5170729 -.1024752 MEL2D1 -.0975573 .0665253 .5170729 1.0000000 -.0450127 DBA4D1 .5653736 .0032598 -.1024752 -.0450127 1.0000000 MEL1D1 -.0466369 -.0211389 .3008681 .5516748 -.0400906 BPM2D1 .0168740 .4919158 -.1142022 .0583811 .0357220 DBA0D1 .3546327 .0538969 -.1141890 -.0788306 .2487262 CEN1D1 .0086076 .0178070 -.0303540 -.1044869 -.0246813 CEN3D1 .1380985 -.0308782 .1280132 .0363290 .0357563 CONSTANT -.0745839 -.0242595 -.0025466 -.0039842 -.0390941
MEL1D1 BPM2D1 DBA0D1 CEN1D1 CEN3D1
TEX3D1 .1370869 .0384234 -.1088895 .0062566 .0417999 TEX2D1 .1529235 -.0322623 -.1608837 -.0962897 .0291825 TEX4D1 .0288774 .0284964 -.0200700 -.0081881 -.0592295 DBA2D1 -.1021257 -.0093801 .4232258 .0366136 -.0780790 DBA1D1 -.0862908 .0059559 .5645046 .0583423 -.0435803 DBA3D1 -.0466369 .0168740 .3546327 .0086076 .1380985 BPM3D1 -.0211389 .4919158 .0538969 .0178070 -.0308782 MEL3D1 .3008681 -.1142022 -.1141890 -.0303540 .1280132 MEL2D1 .5516748 .0583811 -.0788306 -.1044869 .0363290 DBA4D1 -.0400906 .0357220 .2487262 -.0246813 .0357563 MEL1D1 1.0000000 .0174775 -.0872976 .0291269 .0279160 BPM2D1 .0174775 1.0000000 .0743342 .0435279 -.0053865 DBA0D1 -.0872976 .0743342 1.0000000 -.0541997 -.0700255 CEN1D1 .0291269 .0435279 -.0541997 1.0000000 -.0190504 CEN3D1 .0279160 -.0053865 -.0700255 -.0190504 1.0000000 CONSTANT -.0091055 -.0075652 -.0288742 -.0050739 -.0092289
CONSTANT
TEX3D1 .0158588 TEX2D1 .0105581 TEX4D1 .0122802 DBA2D1 -.0868921 DBA1D1 -.0659448 DBA3D1 -.0745839 BPM3D1 -.0242595 MEL3D1 -.0025466
- 624 - MEL2D1 -.0039842 DBA4D1 -.0390941 MEL1D1 -.0091055 BPM2D1 -.0075652 DBA0D1 -.0288742 CEN1D1 -.0050739
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
CEN3D1 -.0092289 CONSTANT 1.0000000
The following new variables are being created:
Name Label
FIT#1 Fit for ARD1 from AREG, MOD_69 ERR#1 Error for ARD1 from AREG, MOD_69 LCL#1 95% LCL for ARD1 from AREG, MOD_69 UCL#1 95% UCL for ARD1 from AREG, MOD_69 SEP#1 SE of fit for ARD1 from AREG, MOD_69
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Diagnose Residual.
-> VARIABLE LABEL ERR#1 'Residual'.
-> ACF -> VARIABLES= ERR#1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_70.
Variable: ERR#1 Missing cases: 86 Valid cases: 568 Some of the missing cases are imbedded within the series.
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Autocorrelations: ERR#1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 -.033 .041 .*| . .646 .422 2 -.034 .041 .*| . 1.352 .509 3 .058 .040 . |*. 3.421 .331 4 .115 .040 . |** 11.761 .019 5 -.008 .040 . * . 11.801 .038 6 -.083 .040 **| . 16.120 .013
- 625 - 7 .000 .040 . * . 16.120 .024 8 -.022 .040 . * . 16.440 .037 9 -.011 .040 . * . 16.510 .057 10 -.063 .040 .*| . 19.014 .040
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 654 Computable first lags: 551
Hi-Res Chart # 82:Acf for residual
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Partial Autocorrelations: ERR#1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 -.033 .042 .*| . 2 -.035 .042 .*| . 3 .056 .042 . |*. 4 .118 .042 . |** 5 .004 .042 . * . 6 -.081 .042 **| . 7 -.020 .042 . * . 8 -.042 .042 .*| . 9 -.003 .042 . * . 10 -.046 .042 .*| .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 654 Computable first lags: 551
Hi-Res Chart # 83:Pacf for residual
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Since AREG does not produce an R estimate, generate one.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS R -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT ard1 -> /METHOD=ENTER fit#1 .
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
* * * * M U L T I P L E R E G R E S S I O N * * * *
- 626 - Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Block Number 1. Method: Enter FIT#1
Variable(s) Entered on Step Number 1.. FIT#1 Fit for ARD1 from AREG, MOD_69
Multiple R .75868 R Square .57560 Adjusted R Square .57485 Standard Error 1.03138
F = 767.65001 Signif F = .0000
End Block Number 1 All requested variables entered.
••• ARANJUEZ AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> SUBTITLE -> 'STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR'.
-> * Determine the standard deviation of the error series.
-> DESCRIPTIVES -> VARIABLES=err#1 -> /FORMAT=NOLABELS NOINDEX -> /STATISTICS=MEAN STDDEV -> /SORT=MEAN (A) .
••• ARANJUEZ AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
Number of valid observations (listwise) = 568.00
Valid Variable Mean Std Dev N
ERR#1 .01 1.03 568
••• ARANJUEZ AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> * Use the MN and SD of error series to determine outliers.
-> * Create upper and lower 3*SD lines for plotting.
-> COMPUTE U3Stdev = 0 + 3 * 1.03 .
- 627 - -> COMPUTE L3Stdev = 0 - 3 * 1.03 .
-> VARIABLE LABEL L3Stdev '3 SDs below'.
-> VARIABLE LABEL U3Stdev '3 SDs above'.
-> EXECUTE.
-> * Now plot the error overlayed with 3*SD lines.
-> *Sequence Charts .
-> CASEPLOT VARIABLES= err#1 U3Stdev L3Stdev -> /ID = Seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_71.
Hi-Res Chart # 84:Caseplot of err#1, u3stdev, l3stdev 1 34 67 100 133 166 199 232 265 298 331 364 397 430 463 496 Residual 529 562 3 SDs above 595 628 3 SDs below -10 0 10 20
••• ARANJUEZ AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> * And list the actual outlier values.
-> COMPUTE Outliers = 0 .
-> IF (err#1 > U3STDEV | err#1 < L3STDEV ) Outliers = 1 .
-> USE ALL.
-> VALUE LABELS Outliers 0 'OK' 1 'Outlier'.
- 628 - -> COMPUTE filter_$=(Outliers = 1).
-> VARIABLE LABEL filter_$ 'res1 = 1 (FILTER)'.
-> VALUE LABELS filter_$ 0 'unselected' 1 'selected'.
-> FORMAT filter_$ (f1.0).
-> FILTER BY filter_$.
-> LIST -> VARIABLES=seconds outliers l3stdev err#1 u3stdev -> /CASES= BY 1 -> /FORMAT= SINGLE UNNUMBERED .
••• ARANJUEZ AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
SECONDS OUTLIERS L3STDEV ERR#1 U3STDEV
213 1.00 -3.09 3.10828 3.09 220 1.00 -3.09 -3.62535 3.09 228 1.00 -3.09 10.48489 3.09 229 1.00 -3.09 -3.33980 3.09 233 1.00 -3.09 -4.26484 3.09 363 1.00 -3.09 3.67279 3.09 465 1.00 -3.09 -3.44393 3.09 501 1.00 -3.09 3.35323 3.09
Number of cases read: 8 Number of cases listed: 8
••• ARANJUEZ AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> EXECUTE .
-> ******************************** -> ********************************.
-> LIST -> VARIABLES=seconds outliers l3stdev err#1 u3stdev -> /CASES= BY 1 -> /FORMAT= SINGLE NUMBERED .
••• ARANJUEZ AROUSAL MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
SECONDS OUTLIERS L3STDEV ERR#1 U3STDEV
213 213 1.00 -3.09 3.10828 3.09 220 220 1.00 -3.09 -3.62535 3.09 228 228 1.00 -3.09 10.48489 3.09 229 229 1.00 -3.09 -3.33980 3.09 233 233 1.00 -3.09 -4.26484 3.09 363 363 1.00 -3.09 3.67279 3.09 465 465 1.00 -3.09 -3.44393 3.09
- 629 - 501 501 1.00 -3.09 3.35323 3.09
Number of cases read: 8 Number of cases listed: 8
••• ARANJUEZ AROUSAL MODEL
+++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> EXECUTE .
- 630 -
Appendix R: Aranjuez Valence Model
-> TITLE -> 'ARANJUEZ VALENCE MODEL'.
-> SUBTITLE -> 'STEP 1: STEPWISE REGRESSION.'.
-> FILTER OFF.
-> use 1 thru 654 .
-> EXECUTE .
-> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 653 -> /FORMAT= WRAP NUMBERED .
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
BAR
1 m. 1.1 654 m. 101.4
Number of cases read: 654 Number of cases listed: 2
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA END TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT vad1 -> /METHOD=STEPWISE -> BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 -> CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1
- 631 - -> DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 -> MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 -> TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1 -> /RESIDUALS DURBIN -> /SAVE RESID (res2).
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Block Number 1. Method: Stepwise Criteria PIN .0500 POUT .1000 BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1
Step MultR Rsq F(Eqn) SigF Variable BetaIn 1 .2049 .0420 23.347 .000 In: MEL3D1 .2049 2 .2822 .0796 23.018 .000 In: MEL2D1 .1944 3 .3305 .1092 21.704 .000 In: MEL4D1 .1734 4 .3557 .1266 19.198 .000 In: MEL1D1 .1323 5 .3746 .1403 17.266 .000 In: BPM3D1 .1184 6 .3833 .1469 15.154 .000 In: BPM4D1 .0816
Variable(s) Entered on Step Number 6.. BPM4D1 LAGS(BPM0D1,4)
Multiple R .38328 R Square .14690 Adjusted R Square .13721 Standard Error 1.11526
Analysis of Variance DF Sum of Squares Mean Square Regression 6 113.08911 18.84818 Residual 528 656.72400 1.24380
F = 15.15377 Signif F = .0000
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
------Variables in the Equation ------
- 632 - Variable B SE B Beta Tolerance VIF T
BPM3D1 .043368 .014925 .117978 .980118 1.020 2.906 BPM4D1 .029396 .014536 .081611 .992035 1.008 2.022 MEL1D1 .033721 .010546 .129533 .984556 1.016 3.198 MEL2D1 .058306 .010880 .218221 .974370 1.026 5.359 MEL3D1 .063925 .010857 .238163 .987522 1.013 5.888 MEL4D1 .043321 .011053 .160167 .967479 1.034 3.919 (Constant) -.001787 .048278 -.037
------in ------
Variable Sig T
BPM3D1 .0038 BPM4D1 .0437 MEL1D1 .0015 MEL2D1 .0000 MEL3D1 .0000 MEL4D1 .0001 (Constant) .9705
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
------Variables not in the Equation ------
Variable Beta In Partial Tolerance VIF Min Toler T Sig T
BPM0D1 .012896 .013596 .948338 1.054 .944327 .312 .7550 BPM1D1 .004076 .004288 .943742 1.060 .932631 .098 .9216 BPM2D1 .070629 .074583 .951283 1.051 .947775 1.717 .0866 CEN0D1 .037714 .039510 .936294 1.068 .936294 .908 .3644 CEN1D1 .027826 .029389 .951619 1.051 .945189 .675 .5000 CEN2D1 .070356 .074519 .957021 1.045 .954516 1.715 .0868 CEN3D1 .055492 .058612 .951719 1.051 .931560 1.348 .1783 CEN4D1 .046931 .050527 .988828 1.011 .961332 1.161 .2460 DBA0D1 -.009751 -.010519 .992637 1.007 .966484 -.241 .8093 DBA1D1 .041249 .044421 .989309 1.011 .964384 1.021 .3078 DBA2D1 .020872 .022476 .989302 1.011 .966540 .516 .6060 DBA3D1 .022730 .024461 .988017 1.012 .965607 .562 .5746 DBA4D1 -.009701 -.010434 .986840 1.013 .964085 -.240 .8108 MEL0D1 .040845 .043304 .958878 1.043 .944967 .995 .3202 TEX0D1 .029396 .031766 .996213 1.004 .967028 .730 .4660 TEX1D1 -.010197 -.011010 .994518 1.006 .966322 -.253 .8006 TEX2D1 .076769 .081715 .966584 1.035 .964235 1.882 .0604 TEX3D1 -.005789 -.006162 .966632 1.035 .952577 -.141 .8876 TEX4D1 .060066 .063968 .967545 1.034 .963890 1.472 .1418
End Block Number 1 PIN = .050 Limits reached.
- 633 - ••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Residuals Statistics:
Min Max Mean Std Dev N
*PRED -1.6947 3.1788 .0128 .4785 551 *RESID -3.2587 9.7664 -.0171 1.1069 551 *ZPRED -3.6968 6.8934 .0137 1.0398 551 *ZRESID -2.9219 8.7571 -.0153 .9926 551
Total Cases = 654
Durbin-Watson Test = 1.15525
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
From Equation 1: 1 new variables have been created.
Name Contents ------
RES2 Residual
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> CASEPLOT VARIABLES= res2 -> /ID= seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_72.
Hi-Res Chart # 85:Caseplot of residual
- 634 - 1 34 67 100 133 166 199 232 265 298 331 364 397 430 463 496 529 562 595 628 -4 -2 86420 10 12
Residual
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> ACF -> VARIABLES= res2 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_73.
Variable: RES2 Missing cases: 103 Valid cases: 551 Some of the missing cases are imbedded within the series.
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
Autocorrelations: RES2 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 .438 .042 . |*.******* 109.080 .000 2 .237 .041 . |*.*** 141.782 .000 3 .136 .041 . |*.* 152.873 .000 4 .138 .040 . |*.* 164.430 .000 5 .086 .040 . |** 169.074 .000 6 -.001 .040 . * . 169.074 .000 7 -.053 .040 .*| . 170.844 .000
- 635 - 8 -.072 .040 .*| . 174.112 .000 9 -.039 .040 .*| . 175.052 .000 10 .005 .040 . * . 175.071 .000
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 654 Computable first lags: 535
Hi-Res Chart # 86:Acf for residual
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
Partial Autocorrelations: RES2 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 .438 .043 . |*.******* 2 .056 .043 . |*. 3 .017 .043 . * . 4 .077 .043 . |** 5 -.008 .043 . * . 6 -.070 .043 .*| . 7 -.052 .043 .*| . 8 -.038 .043 .*| . 9 .018 .043 . * . 10 .047 .043 . |*.
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 654 Computable first lags: 535
Hi-Res Chart # 87:Pacf for residual
••• ARANJUEZ VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> SUBTITLE -> '* STEP 2: MODEL SERIAL CORRELATION WITH AREG.' -> *Autoregression.
-> TSET PRINT=DEFAULT CNVERGE=.001 CIN=95 NEWVAR=CURRENT .
-> PREDICT THRU END.
-> AREG vad1 WITH -> MEL3D1 -> MEL2D1 -> MEL4D1 -> MEL1D1 -> BPM3D1 -> BPM4D1 -> /METHOD=ML -> /CONSTANT -> /RHO=0 -> /MXITER=10.
- 636 - MODEL: MOD_74
Model Description:
Variable: VAD1 Regressors: MEL3D1 MEL2D1 MEL4D1 MEL1D1 BPM3D1 BPM4D1
95.00 percent confidence intervals will be generated.
Split group number: 1 Series length: 636 Number of cases skipped at beginning because of missing values: 10 Number of cases skipped at end because of missing values: 8 Number of cases containing missing values: 85 Kalman filtering will be used for estimation.
••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Termination criteria: Parameter epsilon: .001 Maximum Marquardt constant: 1.00E+09 SSQ Percentage: .001 Maximum number of iterations: 10
Initial values:
AR1 .00000 MEL3D1 .06281 MEL2D1 .06288 MEL4D1 .04456 MEL1D1 .03223 BPM3D1 .03349 BPM4D1 .02877 CONSTANT -.01909
Marquardt constant = .001 Adjusted sum of squares = 672.84665
Iteration History:
Iteration Adj. Sum of Squares Marquardt Constant
1 531.73062 .00100000 2 531.01362 .00010000
••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Conclusion of estimation phase. Estimation terminated at iteration number 3 because: Sum of squares decreased by less than .001 percent.
FINAL PARAMETERS:
- 637 - Number of residuals 551 Standard error .98520803 Log likelihood -771.66132 AIC 1559.3226 SBC 1593.8165
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 543 531.01000 .97063486
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .47652084 .03744277 12.726645 .00000000 MEL3D1 .05204845 .01051446 4.950180 .00000099 MEL2D1 .05364506 .01043562 5.140570 .00000038 MEL4D1 .02954247 .00939161 3.145623 .00174810 MEL1D1 .02553233 .00913012 2.796494 .00534911 BPM3D1 .02437528 .01106497 2.202923 .02801946 BPM4D1 .01145924 .01250298 .916521 .35980076 CONSTANT -.02366662 .07823905 -.302491 .76239354
Covariance Matrix:
AR1
AR1 .00140196
Correlation Matrix:
AR1
AR1 1.0000000
••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Regressor Covariance Matrix:
MEL3D1 MEL2D1 MEL4D1 MEL1D1 BPM3D1
MEL3D1 .00011055 .00005525 .00004267 .00002286 .00000352 MEL2D1 .00005525 .00010890 .00002315 .00004555 -.00000157 MEL4D1 .00004267 .00002315 .00008820 .00000479 -.00001439 MEL1D1 .00002286 .00004555 .00000479 .00008336 -.00000359 BPM3D1 .00000352 -.00000157 -.00001439 -.00000359 .00012243 BPM4D1 .00000606 -.00000422 .00000121 .00000530 .00004933 CONSTANT -.00002308 -.00002141 -.00001261 -.00001605 -.00000424
BPM4D1 CONSTANT
MEL3D1 .00000606 -.00002308 MEL2D1 -.00000422 -.00002141 MEL4D1 .00000121 -.00001261 MEL1D1 .00000530 -.00001605 BPM3D1 .00004933 -.00000424 BPM4D1 .00015632 -.00000081
- 638 - CONSTANT -.00000081 .00612135
Regressor Correlation Matrix:
MEL3D1 MEL2D1 MEL4D1 MEL1D1 BPM3D1
MEL3D1 1.0000000 .5035070 .4320955 .2381735 .0302834 MEL2D1 .5035070 1.0000000 .2361632 .4780757 -.0135677 MEL4D1 .4320955 .2361632 1.0000000 .0558660 -.1384499 MEL1D1 .2381735 .4780757 .0558660 1.0000000 -.0355112 BPM3D1 .0302834 -.0135677 -.1384499 -.0355112 1.0000000 BPM4D1 .0460767 -.0323499 .0102852 .0464094 .3565500 CONSTANT -.0280603 -.0262196 -.0171588 -.0224639 -.0048981
BPM4D1 CONSTANT
MEL3D1 .0460767 -.0280603 MEL2D1 -.0323499 -.0262196 MEL4D1 .0102852 -.0171588 MEL1D1 .0464094 -.0224639 BPM3D1 .3565500 -.0048981 BPM4D1 1.0000000 -.0008327 CONSTANT -.0008327 1.0000000
••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
The following new variables are being created:
Name Label
FIT#1 Fit for VAD1 from AREG, MOD_74 ERR#1 Error for VAD1 from AREG, MOD_74 LCL#1 95% LCL for VAD1 from AREG, MOD_74 UCL#1 95% UCL for VAD1 from AREG, MOD_74 SEP#1 SE of fit for VAD1 from AREG, MOD_74
••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Diagnose Residual.
-> VARIABLE LABEL ERR#1 'Residual'.
-> ACF -> VARIABLES= ERR#1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_75.
Variable: ERR#1 Missing cases: 103 Valid cases: 551 Some of the missing cases are imbedded within the series.
- 639 - ••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Autocorrelations: ERR#1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 -.036 .042 .*| . .753 .385 2 .034 .041 . |*. 1.444 .486 3 -.009 .041 . * . 1.496 .683 4 .091 .040 . |** 6.510 .164 5 .046 .040 . |*. 7.809 .167 6 -.013 .040 . * . 7.910 .245 7 -.038 .040 .*| . 8.812 .266 8 -.056 .040 .*| . 10.770 .215 9 -.027 .040 .*| . 11.227 .260 10 .066 .040 . |*. 13.932 .176
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 654 Computable first lags: 535
Hi-Res Chart # 88:Acf for residual
••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Partial Autocorrelations: ERR#1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 -.036 .043 .*| . 2 .033 .043 . |*. 3 -.007 .043 . * . 4 .089 .043 . |** 5 .053 .043 . |*. 6 -.015 .043 . * . 7 -.042 .043 .*| . 8 -.067 .043 .*| . 9 -.039 .043 .*| . 10 .068 .043 . |*.
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 654 Computable first lags: 535
Hi-Res Chart # 89:Pacf for residual
••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Since AREG does not produce an R estimate, generate one.
-> REGRESSION -> /MISSING LISTWISE
- 640 - -> /STATISTICS R -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT vad1 -> /METHOD=ENTER fit#1 .
••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Block Number 1. Method: Enter FIT#1
Variable(s) Entered on Step Number 1.. FIT#1 Fit for VAD1 from AREG, MOD_74
Multiple R .57240 R Square .32764 Adjusted R Square .32642 Standard Error .98676
F = 267.52743 Signif F = .0000
End Block Number 1 All requested variables entered.
••• ARANJUEZ VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> -> SUBTITLE -> 'STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR'.
-> * Determine the standard deviation of the error series.
-> DESCRIPTIVES -> VARIABLES=err#1 -> /FORMAT=NOLABELS NOINDEX -> /STATISTICS=MEAN STDDEV -> /SORT=MEAN (A) .
••• ARANJUEZ VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
Number of valid observations (listwise) = 551.00
Valid
- 641 - Variable Mean Std Dev N
ERR#1 .00 .99 551
••• ARANJUEZ VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> * Use the MN and SD of error series to determine outliers.
-> * Create upper and lower 3*SD lines for plotting.
-> COMPUTE U3Stdev = 0 + 3 * .99 .
-> COMPUTE L3Stdev = 0 - 3 * .99 .
-> VARIABLE LABEL L3Stdev '3 SDs below'.
-> VARIABLE LABEL U3Stdev '3 SDs above'.
-> EXECUTE.
-> * Now plot the error overlayed with 3*SD lines.
-> *Sequence Charts .
-> CASEPLOT VARIABLES= err#1 U3Stdev L3Stdev -> /ID = Seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_76.
Hi-Res Chart # 90:Caseplot of err#1, u3stdev, l3stdev
- 642 - 1 34 67 100 133 166 199 232 265 298 331 364 397 430 463 496 Residual 529 562 3 SDs above 595 628 3 SDs below -6 -4 -2 0 2 4 6 8 10
••• ARANJUEZ VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> * And list the actual outlier values.
-> COMPUTE Outliers = 0 .
-> IF (err#1 > U3STDEV | err#1 < L3STDEV ) Outliers = 1 .
-> USE ALL.
-> VALUE LABELS Outliers 0 'OK' 1 'Outlier'.
-> COMPUTE filter_$=(Outliers = 1).
-> VARIABLE LABEL filter_$ 'res1 = 1 (FILTER)'.
-> VALUE LABELS filter_$ 0 'unselected' 1 'selected'.
-> FORMAT filter_$ (f1.0).
-> FILTER BY filter_$.
-> LIST -> VARIABLES=seconds outliers l3stdev err#1 u3stdev -> /CASES= BY 1 -> /FORMAT= SINGLE UNNUMBERED .
••• ARANJUEZ VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
- 643 - SECONDS OUTLIERS L3STDEV ERR#1 U3STDEV
156 1.00 -2.97 3.70992 2.97 213 1.00 -2.97 -3.57254 2.97 342 1.00 -2.97 -3.60242 2.97 363 1.00 -2.97 8.70995 2.97 512 1.00 -2.97 -3.15577 2.97 513 1.00 -2.97 2.99518 2.97 519 1.00 -2.97 -3.84926 2.97 595 1.00 -2.97 3.18529 2.97
Number of cases read: 8 Number of cases listed: 8
••• ARANJUEZ VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> EXECUTE .
-> ***************** END OF ARANJUEZ ANALYSIS ******************.
- 644 -
Appendix S: Pizzicato Arousal Model
-> ***************** START OF PIZZICATO ANALYSIS ******************.
-> TITLE -> 'PIZZICATO AROUSAL MODEL'.
-> SUBTITLE -> 'STEP 1: STEPWISE REGRESSION.'.
-> FILTER OFF.
-> use 1 thru 150.
-> EXECUTE .
-> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 149 -> /FORMAT= WRAP NUMBERED .
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
BAR
1 mm.001.1 150 mm.110.2
Number of cases read: 150 Number of cases listed: 2
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA END TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT ard1 -> /METHOD=STEPWISE
- 645 - -> BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 -> CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 -> DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 -> MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 -> TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1 -> /RESIDUALS DURBIN -> /SAVE RESID (res1).
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Block Number 1. Method: Stepwise Criteria PIN .0500 POUT .1000 BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1
Step MultR Rsq F(Eqn) SigF Variable BetaIn 1 .3459 .1197 14.682 .000 In: DBA0D1 .3459 2 .4953 .2453 17.390 .000 In: DBA1D1 .3564 3 .6012 .3615 20.002 .000 In: DBA2D1 .3504 4 .6435 .4141 18.556 .000 In: BPM3D1 .2352 5 .6637 .4405 16.374 .000 In: TEX1D1 -.1702
Variable(s) Entered on Step Number 5.. TEX1D1 LAGS(TEX0D1,1)
Multiple R .66368 R Square .44047 Adjusted R Square .41357 Standard Error 1.54579
Analysis of Variance DF Sum of Squares Mean Square Regression 5 195.62994 39.12599 Residual 104 248.50453 2.38947
F = 16.37436 Signif F = .0000
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
------Variables in the Equation ------
- 646 - Variable B SE B Beta Tolerance VIF T
BPM3D1 .060593 .020137 .226487 .949615 1.053 3.009 DBA0D1 .229833 .037039 .483582 .885838 1.129 6.205 DBA1D1 .209830 .036044 .442578 .930832 1.074 5.821 DBA2D1 .151113 .036789 .318910 .892523 1.120 4.108 TEX1D1 -2.073823 .937404 -.170183 .909168 1.100 -2.212 (Constant) .311702 .149287 2.088
------in ------
Variable Sig T
BPM3D1 .0033 DBA0D1 .0000 DBA1D1 .0000 DBA2D1 .0001 TEX1D1 .0291 (Constant) .0392
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
------Variables not in the Equation ------
Variable Beta In Partial Tolerance VIF Min Toler T Sig T
BPM0D1 -.107525 -.142286 .979771 1.021 .875200 -1.459 .1476 BPM1D1 -.046680 -.060016 .924878 1.081 .867868 -.610 .5431 BPM2D1 -.006278 -.008055 .921288 1.085 .852867 -.082 .9350 BPM4D1 .105139 .139222 .981091 1.019 .875945 1.427 .1566 CEN0D1 -.073688 -.081509 .684603 1.461 .657330 -.830 .4085 CEN1D1 .051605 .065754 .908397 1.101 .848520 .669 .5051 CEN2D1 -.059030 -.077383 .961540 1.040 .879119 -.788 .4327 CEN3D1 .052036 .068868 .980038 1.020 .885659 .701 .4851 CEN4D1 -.057783 -.076502 .980755 1.020 .881588 -.779 .4379 DBA3D1 .129418 .168463 .948073 1.055 .873156 1.735 .0858 DBA4D1 .086341 .112305 .946632 1.056 .853549 1.147 .2540 MEL0D1 .066144 .086579 .958671 1.043 .865440 .882 .3798 MEL1D1 .079329 .096626 .830125 1.205 .773983 .985 .3268 MEL2D1 .015329 .018509 .815763 1.226 .787725 .188 .8513 MEL3D1 -.015041 -.018078 .808260 1.237 .766662 -.184 .8548 MEL4D1 .042155 .053559 .903196 1.107 .864441 .544 .5874 TEX0D1 -.077858 -.102217 .964403 1.037 .856581 -1.043 .2995 TEX2D1 -.022239 -.028496 .918676 1.089 .861888 -.289 .7729 TEX3D1 -.017553 -.022791 .943243 1.060 .848466 -.231 .8175 TEX4D1 .024787 .033001 .991758 1.008 .885424 .335 .7382
End Block Number 1 PIN = .050 Limits reached.
- 647 - ••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Residuals Statistics:
Min Max Mean Std Dev N
*PRED -3.5384 3.9162 .5501 1.5460 136 *RESID -5.8055 4.9905 -.2033 1.8415 136 *ZPRED -3.0019 2.5625 .0500 1.1540 136 *ZRESID -3.7557 3.2285 -.1315 1.1913 136
Total Cases = 150
Durbin-Watson Test = 1.28660
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
From Equation 1: 1 new variables have been created.
Name Contents ------
RES1 Residual
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> CASEPLOT VARIABLES= res1 -> /ID= seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_11.
Hi-Res Chart # 13:Caseplot of residual
- 648 - 1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 -8 -6 -4 -2 0 2 4 6
Residual
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> ACF -> VARIABLES= res1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_12.
Variable: RES1 Missing cases: 14 Valid cases: 136 Some of the missing cases are imbedded within the series.
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
Autocorrelations: RES1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 .397 .084 . |**.***** 22.566 .000 2 .181 .082 . |**.* 27.447 .000 3 -.080 .082 .**| . 28.393 .000 4 -.061 .082 . *| . 28.941 .000 5 -.155 .082 ***| . 32.571 .000 6 -.041 .081 . *| . 32.826 .000 7 -.123 .081 .**| . 35.123 .000 8 .011 .081 . * . 35.140 .000 9 .069 .080 . |* . 35.881 .000 10 .090 .080 . |**. 37.160 .000
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 150 Computable first lags: 131
- 649 - Hi-Res Chart # 14:Acf for residual
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
Partial Autocorrelations: RES1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 .397 .086 . |**.***** 2 .028 .086 . |* . 3 -.191 .086 *.**| . 4 .034 .086 . |* . 5 -.124 .086 .**| . 6 .056 .086 . |* . 7 -.120 .086 .**| . 8 .074 .086 . |* . 9 .090 .086 . |**. 10 -.032 .086 . *| .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 150 Computable first lags: 131
Hi-Res Chart # 15:Pacf for residual
••• PIZZICATO AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> SUBTITLE -> '* STEP 2: MODEL SERIAL CORRELATION WITH AREG.' -> *Autoregression.
-> TSET PRINT=DEFAULT CNVERGE=.001 CIN=95 NEWVAR=CURRENT .
-> PREDICT THRU END.
-> AREG ard1 WITH -> DBA0D1 -> DBA1D1 -> DBA2D1 -> BPM3D1 -> TEX1D1 -> /METHOD=ML -> /CONSTANT -> /RHO=0 -> /MXITER=10.
MODEL: MOD_13
Model Description:
Variable: ARD1 Regressors: DBA0D1 DBA1D1 DBA2D1 BPM3D1
- 650 - TEX1D1
95.00 percent confidence intervals will be generated.
Split group number: 1 Series length: 144 Number of cases skipped at beginning because of missing values: 4 Number of cases skipped at end because of missing values: 2 Number of cases containing missing values: 8 Kalman filtering will be used for estimation.
••• PIZZICATO AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Termination criteria: Parameter epsilon: .001 Maximum Marquardt constant: 1.00E+09 SSQ Percentage: .001 Maximum number of iterations: 10
Initial values:
AR1 .00000 DBA0D1 .12509 DBA1D1 .11744 DBA2D1 .10908 BPM3D1 .03955 TEX1D1 -.98961 CONSTANT .21057
Marquardt constant = .001 Adjusted sum of squares = 402.12699
Iteration History:
Iteration Adj. Sum of Squares Marquardt Constant
1 330.73539 .00100000 2 330.33558 .00010000
••• PIZZICATO AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Conclusion of estimation phase. Estimation terminated at iteration number 3 because: Sum of squares decreased by less than .001 percent.
FINAL PARAMETERS:
Number of residuals 136 Standard error 1.5940609 Log likelihood -253.39064 AIC 520.78128 SBC 541.16986
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 129 330.33531 2.5410301
- 651 - Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .44079518 .07997349 5.5117661 .00000019 DBA0D1 .13649463 .02953883 4.6208541 .00000914 DBA1D1 .11354078 .03028502 3.7490745 .00026681 DBA2D1 .08692198 .02908759 2.9882844 .00335958 BPM3D1 .04163222 .01556810 2.6742001 .00846029 TEX1D1 -.95513381 .73592081 -1.2978758 .19664589 CONSTANT .20603270 .24042485 .8569526 .39306026
Covariance Matrix:
AR1
AR1 .00639576
Correlation Matrix:
AR1
AR1 1.0000000
Regressor Covariance Matrix:
DBA0D1 DBA1D1 DBA2D1 BPM3D1 TEX1D1
DBA0D1 .00087254 .00038040 .00032190 .00002586 -.00241562 DBA1D1 .00038040 .00091718 .00032629 -.00002537 -.00240764 DBA2D1 .00032190 .00032629 .00084609 -.00014983 -.00111539 BPM3D1 .00002586 -.00002537 -.00014983 .00024237 .00029911 TEX1D1 -.00241562 -.00240764 -.00111539 .00029911 .54157943 CONSTANT -.00067995 -.00061613 -.00022735 -.00000835 .00250553
••• PIZZICATO AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
CONSTANT
DBA0D1 -.00067995 DBA1D1 -.00061613 DBA2D1 -.00022735 BPM3D1 -.00000835 TEX1D1 .00250553 CONSTANT .05780411
Regressor Correlation Matrix:
DBA0D1 DBA1D1 DBA2D1 BPM3D1 TEX1D1
DBA0D1 1.0000000 .4252235 .3746486 .0562234 -.1111229 DBA1D1 .4252235 1.0000000 .3703990 -.0538106 -.1080272 DBA2D1 .3746486 .3703990 1.0000000 -.3308755 -.0521060 BPM3D1 .0562234 -.0538106 -.3308755 1.0000000 .0261073 TEX1D1 -.1111229 -.1080272 -.0521060 .0261073 1.0000000 CONSTANT -.0957428 -.0846185 -.0325093 -.0022299 .0141608
CONSTANT
- 652 - DBA0D1 -.0957428 DBA1D1 -.0846185 DBA2D1 -.0325093 BPM3D1 -.0022299 TEX1D1 .0141608 CONSTANT 1.0000000
The following new variables are being created:
Name Label
FIT#1 Fit for ARD1 from AREG, MOD_13 ERR#1 Error for ARD1 from AREG, MOD_13 LCL#1 95% LCL for ARD1 from AREG, MOD_13 UCL#1 95% UCL for ARD1 from AREG, MOD_13 SEP#1 SE of fit for ARD1 from AREG, MOD_13
••• PIZZICATO AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Diagnose Residual.
-> VARIABLE LABEL ERR#1 'Residual'.
-> ACF -> VARIABLES= ERR#1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_14.
Variable: ERR#1 Missing cases: 14 Valid cases: 136 Some of the missing cases are imbedded within the series.
••• PIZZICATO AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Autocorrelations: ERR#1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 -.016 .084 . * . .035 .851 2 .085 .082 . |**. 1.106 .575 3 -.167 .082 ***| . 5.238 .155 4 -.035 .082 . *| . 5.420 .247 5 -.154 .082 ***| . 9.003 .109 6 .034 .081 . |* . 9.174 .164 7 -.099 .081 .**| . 10.683 .153 8 .049 .081 . |* . 11.054 .199 9 .155 .080 . |*** 14.792 .097 10 .070 .080 . |* . 15.561 .113
Plot Symbols: Autocorrelations * Two Standard Error Limits .
- 653 - Total cases: 150 Computable first lags: 131
Hi-Res Chart # 16:Acf for residual
••• PIZZICATO AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Partial Autocorrelations: ERR#1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 -.016 .086 . * . 2 .085 .086 . |**. 3 -.165 .086 ***| . 4 -.046 .086 . *| . 5 -.132 .086 ***| . 6 .011 .086 . * . 7 -.096 .086 .**| . 8 -.004 .086 . * . 9 .173 .086 . |*** 10 .025 .086 . |* .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 150 Computable first lags: 131
Hi-Res Chart # 17:Pacf for residual
••• PIZZICATO AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Since AREG does not produce an R estimate, generate one.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS R -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT ard1 -> /METHOD=ENTER fit#1 .
••• PIZZICATO AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Block Number 1. Method: Enter FIT#1
- 654 - Variable(s) Entered on Step Number 1.. FIT#1 Fit for ARD1 from AREG, MOD_13
Multiple R .59632 R Square .35560 Adjusted R Square .35079 Standard Error 1.58173
F = 73.94553 Signif F = .0000
End Block Number 1 All requested variables entered.
••• PIZZICATO AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> SUBTITLE -> 'STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR'.
-> * Determine the standard deviation of the error series.
-> DESCRIPTIVES -> VARIABLES=err#1 -> /FORMAT=NOLABELS NOINDEX -> /STATISTICS=MEAN STDDEV -> /SORT=MEAN (A) .
••• PIZZICATO AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
Number of valid observations (listwise) = 136.00
Valid Variable Mean Std Dev N
ERR#1 .01 1.58 136
••• PIZZICATO AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
-> * Use the MN and SD of error series to determine outliers.
-> * Create upper and lower 3*SD lines for plotting.
-> COMPUTE U3Stdev = 0 + 3 * 1.60 .
-> COMPUTE L3Stdev = 0 - 3 * 1.60 .
-> VARIABLE LABEL L3Stdev '3 SDs below'.
-> VARIABLE LABEL U3Stdev '3 SDs above'.
- 655 - -> EXECUTE.
-> * Now plot the error overlayed with 3*SD lines.
-> *Sequence Charts .
-> CASEPLOT VARIABLES= err#1 U3Stdev L3Stdev -> /ID = Seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_15.
Hi-Res Chart # 18:Caseplot of err#1, u3stdev, l3stdev
1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 Residual 121 129 3 SDs above 137 145 3 SDs below -6 -4 -2 86420
••• PIZZICATO AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
-> * And list the actual outlier values.
-> COMPUTE Outliers = 0 .
-> IF (err#1 > U3STDEV | err#1 < L3STDEV ) Outliers = 1 .
-> USE ALL.
-> VALUE LABELS Outliers 0 'OK' 1 'Outlier'.
-> COMPUTE filter_$=(Outliers = 1).
-> VARIABLE LABEL filter_$ 'res1 = 1 (FILTER)'.
-> VALUE LABELS filter_$ 0 'unselected' 1 'selected'.
-> FORMAT filter_$ (f1.0).
-> FILTER BY filter_$.
-> LIST -> VARIABLES=seconds outliers l3stdev err#1 u3stdev
- 656 - -> /CASES= BY 1 -> /FORMAT= SINGLE UNNUMBERED .
••• PIZZICATO AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
SECONDS OUTLIERS L3STDEV ERR#1 U3STDEV
70 1.00 -4.80 5.02863 4.80 79 1.00 -4.80 5.98357 4.80
Number of cases read: 2 Number of cases listed: 2
••• PIZZICATO AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
-> EXECUTE .
- 657 -
Appendix T: Pizzicato Valence Model
-> TITLE -> 'PIZZICATO VALENCE MODEL'.
-> SUBTITLE -> 'STEP 1: STEPWISE REGRESSION.'.
-> FILTER OFF.
-> use 1 thru 150 .
-> EXECUTE .
-> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 149 -> /FORMAT= WRAP NUMBERED .
••• PIZZICATO VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
BAR
1 mm.001.1 150 mm.110.2
Number of cases read: 150 Number of cases listed: 2
••• PIZZICATO VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA END TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT vad1 -> /METHOD=STEPWISE -> BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 -> CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1
- 658 - -> DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 -> MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 -> TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1 -> /RESIDUALS DURBIN -> /SAVE RESID (res2).
••• PIZZICATO VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Block Number 1. Method: Stepwise Criteria PIN .0500 POUT .1000 BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1
Step MultR Rsq F(Eqn) SigF Variable BetaIn 1 .3654 .1335 16.637 .000 In: DBA1D1 .3654 2 .4419 .1953 12.981 .000 In: BPM3D1 .2490 3 .4974 .2474 11.616 .000 In: DBA3D1 .2324 4 .5518 .3045 11.491 .000 In: DBA0D1 .2413 5 .5981 .3577 11.584 .000 In: DBA2D1 .2435
Variable(s) Entered on Step Number 5.. DBA2D1 LAGS(DBA0D1,2)
Multiple R .59809 R Square .35771 Adjusted R Square .32683 Standard Error .81199
Analysis of Variance DF Sum of Squares Mean Square Regression 5 38.18938 7.63788 Residual 104 68.57047 .65933
F = 11.58427 Signif F = .0000
••• PIZZICATO VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
------Variables in the Equation ------
Variable B SE B Beta Tolerance VIF T
- 659 - BPM3D1 .029101 .010596 .221864 .946349 1.057 2.746 DBA0D1 .068577 .018972 .294301 .931607 1.073 3.615 DBA1D1 .111221 .018851 .478478 .939039 1.065 5.900 DBA2D1 .056570 .019266 .243503 .898026 1.114 2.936 DBA3D1 .056839 .016645 .275332 .950031 1.053 3.415 (Constant) .091826 .079749 1.151
------in ------
Variable Sig T
BPM3D1 .0071 DBA0D1 .0005 DBA1D1 .0000 DBA2D1 .0041 DBA3D1 .0009 (Constant) .2522
••• PIZZICATO VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
------Variables not in the Equation ------
Variable Beta In Partial Tolerance VIF Min Toler T Sig T
BPM0D1 -.023364 -.028871 .980759 1.020 .897425 -.293 .7700 BPM1D1 .102100 .122577 .925743 1.080 .897887 1.253 .2129 BPM2D1 .055722 .066753 .921785 1.085 .859884 .679 .4987 BPM4D1 -.014596 -.017885 .964359 1.037 .895156 -.182 .8563 CEN0D1 -.015856 -.019251 .946776 1.056 .862565 -.195 .8455 CEN1D1 .005711 .006948 .950725 1.052 .896664 .071 .9439 CEN2D1 .044054 .054187 .971725 1.029 .887450 .551 .5830 CEN3D1 .017958 .021774 .944276 1.059 .895798 .221 .8255 CEN4D1 -.144044 -.176542 .964804 1.036 .897901 -1.820 .0716 DBA4D1 .099752 .120640 .939436 1.064 .856219 1.233 .2202 MEL0D1 -.033538 -.040870 .953856 1.048 .897333 -.415 .6789 MEL1D1 .076562 .087015 .829641 1.205 .810931 .886 .3774 MEL2D1 .083786 .093560 .800877 1.249 .782443 .954 .3425 MEL3D1 -.152643 -.167143 .770107 1.299 .770107 -1.721 .0883 MEL4D1 -.014991 -.017082 .833891 1.199 .833891 -.173 .8627 TEX0D1 -.001303 -.001599 .967120 1.034 .897393 -.016 .9871 TEX1D1 -.022383 -.026603 .907294 1.102 .873156 -.270 .7876 TEX2D1 .132424 .157933 .913566 1.095 .866232 1.623 .1076 TEX3D1 .036370 .043442 .916371 1.091 .847801 .441 .6599 TEX4D1 -.026106 -.031777 .951666 1.051 .895050 -.323 .7476
End Block Number 1 PIN = .050 Limits reached.
••• PIZZICATO VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
- 660 - * * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Residuals Statistics:
Min Max Mean Std Dev N
*PRED -2.4729 1.8340 .1019 .7556 144 *RESID -1.8229 5.0312 .1880 1.1064 144 *ZPRED -4.5230 2.7533 -.1731 1.2765 144 *ZRESID -2.2450 6.1961 .2315 1.3625 144
Total Cases = 150
Durbin-Watson Test = .98605
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
From Equation 1: 1 new variables have been created.
Name Contents ------
RES2 Residual
••• PIZZICATO VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> CASEPLOT VARIABLES= res2 -> /ID= seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_6.
Hi-Res Chart # 7:Caseplot of residual
- 661 - 1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 -4 -2 0 2 4 6
Residual
••• PIZZICATO VALENCE MODEL Page 38 +++ STEP 1: STEPWISE REGRESSION.
-> ACF -> VARIABLES= res2 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_7.
Variable: RES2 Missing cases: 6 Valid cases: 144
••• PIZZICATO VALENCE MODEL Page 39 +++ STEP 1: STEPWISE REGRESSION.
Autocorrelations: RES2 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 .425 .082 . |**.****** 26.569 .000 2 .345 .082 . |**.**** 44.220 .000 3 .187 .082 . |**.* 49.407 .000 4 .285 .082 . |**.*** 61.571 .000 5 .218 .081 . |**.* 68.735 .000 6 .287 .081 . |**.*** 81.319 .000 7 .151 .081 . |*** 84.821 .000 8 .120 .080 . |**. 87.039 .000 9 .157 .080 . |*** 90.866 .000 10 .210 .080 . |**.* 97.795 .000
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 150 Computable first lags: 143
Hi-Res Chart # 8:Acf for residual
- 662 - ••• PIZZICATO VALENCE MODEL Page 40 +++ STEP 1: STEPWISE REGRESSION.
Partial Autocorrelations: RES2 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 .425 .083 . |**.****** 2 .201 .083 . |**.* 3 -.021 .083 . * . 4 .200 .083 . |**.* 5 .044 .083 . |* . 6 .134 .083 . |*** 7 -.053 .083 . *| . 8 -.045 .083 . *| . 9 .110 .083 . |**. 10 .072 .083 . |* .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 150 Computable first lags: 143
Hi-Res Chart # 9:Pacf for residual
••• PIZZICATO VALENCE MODEL Page 41 +++ STEP 1: STEPWISE REGRESSION.
-> SUBTITLE -> '* STEP 2: MODEL SERIAL CORRELATION WITH AREG.' -> *Autoregression.
-> TSET PRINT=DEFAULT CNVERGE=.001 CIN=95 NEWVAR=CURRENT .
-> PREDICT THRU END.
-> AREG vad1 WITH -> DBA1D1 -> BPM3D1 -> DBA3D1 -> DBA0D1 -> DBA2D1 -> /METHOD=ML -> /CONSTANT -> /RHO=0 -> /MXITER=10.
MODEL: MOD_8
Model Description:
Variable: VAD1 Regressors: DBA1D1 BPM3D1 DBA3D1 DBA0D1 DBA2D1
- 663 - 95.00 percent confidence intervals will be generated.
Split group number: 1 Series length: 144 Number of cases skipped at beginning because of missing values: 4 Number of cases skipped at end because of missing values: 2 Melard's algorithm will be used for estimation.
Termination criteria: Parameter epsilon: .001 Maximum Marquardt constant: 1.00E+09 SSQ Percentage: .001 Maximum number of iterations: 10
Initial values:
AR1 .00000 DBA1D1 .09912 BPM3D1 .01342 DBA3D1 .05806 DBA0D1 .03481 DBA2D1 .04980 CONSTANT .28468
Marquardt constant = .001 Adjusted sum of squares = 166.69194
••• PIZZICATO VALENCE MODEL Page 42 +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Iteration History:
Iteration Adj. Sum of Squares Marquardt Constant
1 131.06971 .00100000 2 130.52473 .00010000 3 130.51356 .00001000
Conclusion of estimation phase. Estimation terminated at iteration number 4 because: Sum of squares decreased by less than .001 percent.
FINAL PARAMETERS:
Number of residuals 144 Standard error .97506178 Log likelihood -197.32786 AIC 408.65571 SBC 429.44441
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 137 130.51330 .95074548
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
- 664 - AR1 .50057603 .07444872 6.7237696 .00000000 DBA1D1 .09687106 .01713339 5.6539341 .00000009 BPM3D1 .01147902 .00769554 1.4916467 .13809085 DBA3D1 .05863138 .01603345 3.6568169 .00036309 DBA0D1 .04003898 .01564513 2.5591968 .01157693 DBA2D1 .05682414 .01784033 3.1851498 .00179160 CONSTANT .30449248 .16161667 1.8840413 .06167844
Covariance Matrix:
AR1
AR1 .00554261
Correlation Matrix:
AR1
AR1 1.0000000
••• PIZZICATO VALENCE MODEL Page 43 +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Regressor Covariance Matrix:
DBA1D1 BPM3D1 DBA3D1 DBA0D1 DBA2D1
DBA1D1 .00029355 .00001452 .00011433 .00010515 .00012852 BPM3D1 .00001452 .00005922 .00000365 .00000389 -.00003227 DBA3D1 .00011433 .00000365 .00025707 .00005227 .00010917 DBA0D1 .00010515 .00000389 .00005227 .00024477 .00011858 DBA2D1 .00012852 -.00003227 .00010917 .00011858 .00031828 CONSTANT -.00000883 -.00001301 -.00003257 -.00002915 .00001171
CONSTANT
DBA1D1 -.00000883 BPM3D1 -.00001301 DBA3D1 -.00003257 DBA0D1 -.00002915 DBA2D1 .00001171 CONSTANT .02611995
Regressor Correlation Matrix:
DBA1D1 BPM3D1 DBA3D1 DBA0D1 DBA2D1
DBA1D1 1.0000000 .1100902 .4161868 .3922667 .4204715 BPM3D1 .1100902 1.0000000 .0295996 .0322706 -.2350600 DBA3D1 .4161868 .0295996 1.0000000 .2083684 .3816638 DBA0D1 .3922667 .0322706 .2083684 1.0000000 .4248361 DBA2D1 .4204715 -.2350600 .3816638 .4248361 1.0000000 CONSTANT -.0031873 -.0104625 -.0125698 -.0115272 .0040603
CONSTANT
DBA1D1 -.0031873 BPM3D1 -.0104625
- 665 - DBA3D1 -.0125698 DBA0D1 -.0115272 DBA2D1 .0040603 CONSTANT 1.0000000
The following new variables are being created:
Name Label
FIT#1 Fit for VAD1 from AREG, MOD_8 ERR#1 Error for VAD1 from AREG, MOD_8 LCL#1 95% LCL for VAD1 from AREG, MOD_8 UCL#1 95% UCL for VAD1 from AREG, MOD_8 SEP#1 SE of fit for VAD1 from AREG, MOD_8
••• PIZZICATO VALENCE MODEL Page 44 +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Diagnose Residual.
-> VARIABLE LABEL ERR#1 'Residual'.
-> ACF -> VARIABLES= ERR#1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_9.
Variable: ERR#1 Missing cases: 6 Valid cases: 144
••• PIZZICATO VALENCE MODEL Page 45 +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Autocorrelations: ERR#1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 -.157 .082 ***| . 3.630 .057 2 .151 .082 . |*** 7.023 .030 3 -.072 .082 . *| . 7.790 .051 4 .145 .082 . |*** 10.951 .027 5 .055 .081 . |* . 11.408 .044 6 .183 .081 . |**.* 16.509 .011 7 .001 .081 . * . 16.510 .021 8 .028 .080 . |* . 16.627 .034 9 .037 .080 . |* . 16.835 .051 10 .106 .080 . |**. 18.611 .045
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 150 Computable first lags: 143
Hi-Res Chart # 10:Acf for residual
- 666 - ••• PIZZICATO VALENCE MODEL Page 46 +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Partial Autocorrelations: ERR#1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 -.157 .083 ***| . 2 .130 .083 . |*** 3 -.032 .083 . *| . 4 .116 .083 . |**. 5 .108 .083 . |**. 6 .182 .083 . |**.* 7 .050 .083 . |* . 8 -.015 .083 . * . 9 .028 .083 . |* . 10 .072 .083 . |* .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 150 Computable first lags: 143
Hi-Res Chart # 11:Pacf for residual
••• PIZZICATO VALENCE MODEL Page 47 +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Since AREG does not produce an R estimate, generate one.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS R -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT vad1 -> /METHOD=ENTER fit#1 .
••• PIZZICATO VALENCE MODEL Page 48 +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Block Number 1. Method: Enter FIT#1
Variable(s) Entered on Step Number 1.. FIT#1 Fit for VAD1 from AREG, MOD_8
- 667 - Multiple R .61874 R Square .38283 Adjusted R Square .37849 Standard Error .97477
F = 88.08410 Signif F = .0000
End Block Number 1 All requested variables entered.
••• PIZZICATO VALENCE MODEL Page 49 +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> SUBTITLE -> 'STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR'.
-> * Determine the standard deviation of the error series.
-> DESCRIPTIVES -> VARIABLES=err#1 -> /FORMAT=NOLABELS NOINDEX -> /STATISTICS=MEAN STDDEV -> /SORT=MEAN (A) .
••• PIZZICATO VALENCE MODEL Page 50 10:25:48 STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
Number of valid observations (listwise) = 144.00
Valid Variable Mean Std Dev N
ERR#1 -.02 .97 144
••• PIZZICATO VALENCE MODEL Page 51 10:25:48 STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
-> * Use the MN and SD of error series to determine outliers.
-> * Create upper and lower 3*SD lines for plotting.
-> COMPUTE U3Stdev = 0 + 3 * .98 .
-> COMPUTE L3Stdev = 0 - 3 * .98 .
-> VARIABLE LABEL L3Stdev '3 SDs below'.
-> VARIABLE LABEL U3Stdev '3 SDs above'.
-> EXECUTE.
-> * Now plot the error overlayed with 3*SD lines.
- 668 - -> *Sequence Charts .
-> CASEPLOT VARIABLES= err#1 U3Stdev L3Stdev -> /ID = Seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_10.
Hi-Res Chart # 12:Caseplot of err#1, u3stdev, l3stdev 1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 Residual 121 129 3 SDs above 137 145 3 SDs below -4 -2 0 2 4 6
••• PIZZICATO VALENCE MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
-> * And list the actual outlier values.
-> COMPUTE Outliers = 0 .
-> IF (err#1 > U3STDEV | err#1 < L3STDEV ) Outliers = 1 .
-> USE ALL.
-> VALUE LABELS Outliers 0 'OK' 1 'Outlier'.
-> COMPUTE filter_$=(Outliers = 1).
-> VARIABLE LABEL filter_$ 'res1 = 1 (FILTER)'.
-> VALUE LABELS filter_$ 0 'unselected' 1 'selected'.
-> FORMAT filter_$ (f1.0).
-> FILTER BY filter_$.
-> LIST -> VARIABLES=seconds outliers l3stdev err#1 u3stdev -> /CASES= BY 1 -> /FORMAT= SINGLE UNNUMBERED .
- 669 - ••• PIZZICATO VALENCE MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
SECONDS OUTLIERS L3STDEV ERR#1 U3STDEV
5 1.00 -2.94 4.48831 2.94 7 1.00 -2.94 3.07598 2.94
Number of cases read: 2 Number of cases listed: 2
••• PIZZICATO VALENCE MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
-> EXECUTE .
-> ************** END PIZZICATO ANLYSIS ******************.
- 670 -
Appendix U: Morning Arousal Model
-> TITLE -> 'MORNING AROUSAL MODEL'.
-> SUBTITLE -> 'STEP 1: STEPWISE REGRESSION.'.
-> FILTER OFF.
-> use 1 thru 216 .
-> EXECUTE .
-> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 215 -> /FORMAT= WRAP NUMBERED .
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
BAR
1 m. 1.30 216 m.87.40
Number of cases read: 216 Number of cases listed: 2
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA END TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT ard1 -> /METHOD=STEPWISE -> BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 -> CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1
- 671 - -> DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 -> MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 -> TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1 -> /RESIDUALS DURBIN -> /SAVE RESID (res1).
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Block Number 1. Method: Stepwise Criteria PIN .0500 POUT .1000 BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1
Step MultR Rsq F(Eqn) SigF Variable BetaIn 1 .4753 .2259 57.796 .000 In: DBA3D1 .4753 2 .5640 .3181 45.960 .000 In: DBA1D1 .3062 3 .6563 .4308 49.446 .000 In: DBA2D1 .3482 4 .7006 .4908 46.989 .000 In: DBA4D1 .2511 5 .7148 .5109 40.526 .000 In: TEX0D1 -.1451 6 .7259 .5270 35.838 .000 In: BPM3D1 .1325 7 .7370 .5432 32.621 .000 In: CEN4D1 -.1331 8 .7454 .5557 29.857 .000 In: CEN2D1 -.1216 9 .7524 .5661 27.540 .000 In: DBA0D1 .1065
Variable(s) Entered on Step Number 9.. DBA0D1 DIFF(DBA,1)
Multiple R .75238 R Square .56607 Adjusted R Square .54552 Standard Error 1.82919
Analysis of Variance DF Sum of Squares Mean Square Regression 9 829.32474 92.14719 Residual 190 635.72541 3.34592
F = 27.54014 Signif F = .0000
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
- 672 ------Variables in the Equation ------
Variable B SE B Beta Tolerance VIF T
BPM3D1 .132414 .042367 .158082 .892730 1.120 3.125 CEN2D1 -.002237 9.3869E-04 -.124244 .839959 1.191 -2.383 CEN4D1 -.002860 9.2285E-04 -.158968 .867971 1.152 -3.099 DBA0D1 .097613 .045722 .106483 .918051 1.089 2.135 DBA1D1 .352008 .045753 .385242 .910901 1.098 7.694 DBA2D1 .359475 .049574 .392889 .777946 1.285 7.251 DBA3D1 .543906 .047568 .593514 .847672 1.180 11.434 DBA4D1 .292288 .049061 .312576 .829665 1.205 5.958 TEX0D1 -.092933 .032335 -.141623 .940558 1.063 -2.874 (Constant) .055266 .129451 .427
------in ------
Variable Sig T
BPM3D1 .0021 CEN2D1 .0182 CEN4D1 .0022 DBA0D1 .0340 DBA1D1 .0000 DBA2D1 .0000 DBA3D1 .0000 DBA4D1 .0000 TEX0D1 .0045 (Constant) .6699
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
------Variables not in the Equation ------
Variable Beta In Partial Tolerance VIF Min Toler T Sig T
BPM0D1 .057144 .080271 .856221 1.168 .736935 1.107 .2697 BPM1D1 .053855 .071425 .763239 1.310 .762088 .984 .3262 BPM2D1 -.020190 -.028100 .840542 1.190 .710983 -.386 .6996 BPM4D1 .058960 .084750 .896558 1.115 .770151 1.169 .2437 CEN0D1 -.037404 -.052394 .851442 1.174 .772180 -.721 .4716 CEN1D1 .022142 .031744 .891873 1.121 .772608 .437 .6629 CEN3D1 -.022516 -.032469 .902361 1.108 .775964 -.447 .6557 MEL0D1 -.017270 -.024820 .896252 1.116 .776524 -.341 .7332 MEL1D1 -.030018 -.042715 .878661 1.138 .776934 -.588 .5574 MEL2D1 -.032279 -.047307 .932038 1.073 .777946 -.651 .5158 MEL3D1 .056231 .082247 .928341 1.077 .761018 1.135 .2580 MEL4D1 .039779 .058637 .942856 1.061 .777750 .808 .4204 TEX1D1 .019800 .023637 .618362 1.617 .618362 .325 .7455 TEX2D1 .023540 .031071 .755977 1.323 .755977 .427 .6696 TEX3D1 -.007262 -.009664 .768472 1.301 .689832 -.133 .8944 TEX4D1 .102723 .136601 .767338 1.303 .734404 1.896 .0595
- 673 - End Block Number 1 PIN = .050 Limits reached.
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Residuals Statistics:
Min Max Mean Std Dev N
*PRED -6.3888 7.3422 -.0121 2.0624 205 *RESID -4.5829 6.1239 .0180 1.7818 205 *ZPRED -3.1498 3.5764 -.0262 1.0103 205 *ZRESID -2.5055 3.3479 .0098 .9741 205
Total Cases = 216
Durbin-Watson Test = 1.04151
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
From Equation 1: 1 new variables have been created.
Name Contents ------
RES1 Residual
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> CASEPLOT VARIABLES= res1 -> /ID= seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_39.
Hi-Res Chart # 44:Caseplot of residual
- 674 - 1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 166 177 188 199 210 -6 -4 -2 0 2 4 6 8
Residual
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> ACF -> VARIABLES= res1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_40.
Variable: RES1 Missing cases: 11 Valid cases: 205 Some of the missing cases are imbedded within the series.
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
Autocorrelations: RES1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 .471 .069 . |**.****** 46.383 .000 2 .270 .069 . |**.** 61.753 .000 3 .126 .068 . |*** 65.156 .000 4 .109 .068 . |**. 67.699 .000 5 .194 .068 . |**.* 75.851 .000 6 -.041 .067 . *| . 76.214 .000 7 -.076 .067 .**| . 77.489 .000 8 -.044 .067 . *| . 77.919 .000 9 .021 .067 . * . 78.016 .000 10 .102 .067 . |**. 80.375 .000
Plot Symbols: Autocorrelations * Two Standard Error Limits .
- 675 - Total cases: 216 Computable first lags: 203
Hi-Res Chart # 45:Acf for residual
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
Partial Autocorrelations: RES1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 .471 .070 . |**.****** 2 .062 .070 . |* . 3 -.028 .070 . *| . 4 .059 .070 . |* . 5 .160 .070 . |*** 6 -.262 .070 **.**| . 7 -.019 .070 . * . 8 .076 .070 . |**. 9 .036 .070 . |* . 10 .054 .070 . |* .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 216 Computable first lags: 203
Hi-Res Chart # 46:Pacf for residual
••• MORNING AROUSAL MODEL +++ STEP 1: STEPWISE REGRESSION.
-> SUBTITLE -> '* STEP 2: MODEL SERIAL CORRELATION WITH AREG.' -> *Autoregression.
-> TSET PRINT=DEFAULT CNVERGE=.001 CIN=95 NEWVAR=CURRENT .
-> PREDICT THRU END.
-> AREG ard1 WITH -> DBA3D1 -> DBA1D1 -> DBA2D1 -> DBA4D1 -> TEX0D1 -> BPM3D1 -> CEN4D1 -> DBA0D1 -> CEN2D1 -> /METHOD=ML -> /CONSTANT -> /RHO=0 -> /MXITER=10.
MODEL: MOD_41
Model Description:
- 676 - Variable: ARD1 Regressors: DBA3D1 DBA1D1 DBA2D1 DBA4D1 TEX0D1 BPM3D1 CEN4D1 DBA0D1 CEN2D1
95.00 percent confidence intervals will be generated.
Split group number: 1 Series length: 211 Number of cases skipped at beginning because of missing values: 5 Number of cases containing missing values: 6 Kalman filtering will be used for estimation.
••• MORNING AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Termination criteria: Parameter epsilon: .001 Maximum Marquardt constant: 1.00E+09 SSQ Percentage: .001 Maximum number of iterations: 10
Initial values:
AR1 .00000 DBA3D1 .53360 DBA1D1 .34479 DBA2D1 .35410 DBA4D1 .28392 TEX0D1 -.08751 BPM3D1 .13300 CEN4D1 -.00278 DBA0D1 .09812 CEN2D1 -.00209 CONSTANT .07184
Marquardt constant = .001 Adjusted sum of squares = 647.14963
Iteration History:
Iteration Adj. Sum of Squares Marquardt Constant
1 490.65412 .00100000 2 487.55220 .00010000 3 487.49332 .00001000
••• MORNING AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Conclusion of estimation phase. Estimation terminated at iteration number 4 because: Sum of squares decreased by less than .001 percent.
- 677 - FINAL PARAMETERS:
Number of residuals 205 Standard error 1.5828161 Log likelihood -379.81146 AIC 781.62292 SBC 818.17603
Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 194 487.49221 2.5053067
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .51490540 .05894485 8.735375 .00000000 DBA3D1 .46819187 .04666036 10.034039 .00000000 DBA1D1 .34442808 .04593569 7.498049 .00000000 DBA2D1 .33171825 .04792987 6.920908 .00000000 DBA4D1 .19720829 .03962158 4.977295 .00000142 TEX0D1 -.09831105 .02134927 -4.604891 .00000745 BPM3D1 .11169469 .03234218 3.453530 .00067933 CEN4D1 -.00244869 .00067841 -3.609440 .00039053 DBA0D1 .09855920 .03900358 2.526927 .01230490 CEN2D1 -.00190897 .00068789 -2.775091 .00605848 CONSTANT .06243805 .22579706 .276523 .78244087
Covariance Matrix:
AR1
AR1 .00347450
Correlation Matrix:
AR1
AR1 1.0000000
••• MORNING AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Regressor Covariance Matrix:
DBA3D1 DBA1D1 DBA2D1 DBA4D1 TEX0D1
DBA3D1 .00217719 .00031361 .00121562 .00102026 .00003360 DBA1D1 .00031361 .00211009 .00109967 .00010950 .00004958 DBA2D1 .00121562 .00109967 .00229727 .00032444 -.00011939 DBA4D1 .00102026 .00010950 .00032444 .00156987 .00009462 TEX0D1 .00003360 .00004958 -.00011939 .00009462 .00045579 BPM3D1 .00038440 -.00005458 .00022316 .00026234 .00000247 CEN4D1 -.00000096 .00000226 -.00000104 -.00000644 -.00000071 DBA0D1 .00014429 .00099233 .00024177 .00014948 .00012430 CEN2D1 -.00000320 -.00000013 -.00000801 -.00000309 .00000097 CONSTANT .00016760 .00032089 .00040094 .00000285 -.00005971
- 678 - BPM3D1 CEN4D1 DBA0D1 CEN2D1 CONSTANT
DBA3D1 .00038440 -.00000096 .00014429 -.00000320 .00016760 DBA1D1 -.00005458 .00000226 .00099233 -.00000013 .00032089 DBA2D1 .00022316 -.00000104 .00024177 -.00000801 .00040094 DBA4D1 .00026234 -.00000644 .00014948 -.00000309 .00000285 TEX0D1 .00000247 -.00000071 .00012430 .00000097 -.00005971 BPM3D1 .00104602 -.00000225 .00002673 -.00000408 .00004293 CEN4D1 -.00000225 .00000046 .00000095 .00000007 -.00000015 DBA0D1 .00002673 .00000095 .00152128 -.00000091 .00013311 CEN2D1 -.00000408 .00000007 -.00000091 .00000047 -.00000181 CONSTANT .00004293 -.00000015 .00013311 -.00000181 .05098431
Regressor Correlation Matrix:
DBA3D1 DBA1D1 DBA2D1 DBA4D1 TEX0D1
DBA3D1 1.0000000 .1463157 .5435569 .5518605 .0337280 DBA1D1 .1463157 1.0000000 .4994674 .0601633 .0505555 DBA2D1 .5435569 .4994674 1.0000000 .1708403 -.1166783 DBA4D1 .5518605 .0601633 .1708403 1.0000000 .1118572 TEX0D1 .0337280 .0505555 -.1166783 .1118572 1.0000000 BPM3D1 .2547193 -.0367357 .1439583 .2047250 .0035761 CEN4D1 -.0303857 .0725427 -.0320394 -.2394822 -.0487246 DBA0D1 .0792854 .5538641 .1293276 .0967299 .1492719 CEN2D1 -.0997781 -.0042385 -.2430589 -.1133950 .0662208 CONSTANT .0159081 .0309378 .0370471 .0003187 -.0123872
BPM3D1 CEN4D1 DBA0D1 CEN2D1 CONSTANT
DBA3D1 .2547193 -.0303857 .0792854 -.0997781 .0159081 DBA1D1 -.0367357 .0725427 .5538641 -.0042385 .0309378 DBA2D1 .1439583 -.0320394 .1293276 -.2430589 .0370471 DBA4D1 .2047250 -.2394822 .0967299 -.1133950 .0003187 TEX0D1 .0035761 -.0487246 .1492719 .0662208 -.0123872 BPM3D1 1.0000000 -.1026514 .0211860 -.1832679 .0058780
••• MORNING AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
CEN4D1 -.1026514 1.0000000 .0359329 .1507106 -.0009910 DBA0D1 .0211860 .0359329 1.0000000 -.0340956 .0151148 CEN2D1 -.1832679 .1507106 -.0340956 1.0000000 -.0116392 CONSTANT .0058780 -.0009910 .0151148 -.0116392 1.0000000
The following new variables are being created:
Name Label
FIT#1 Fit for ARD1 from AREG, MOD_41 ERR#1 Error for ARD1 from AREG, MOD_41 LCL#1 95% LCL for ARD1 from AREG, MOD_41 UCL#1 95% UCL for ARD1 from AREG, MOD_41 SEP#1 SE of fit for ARD1 from AREG, MOD_41
••• MORNING AROUSAL MODEL
- 679 - +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Diagnose Residual.
-> VARIABLE LABEL ERR#1 'Residual'.
-> ACF -> VARIABLES= ERR#1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_42.
Variable: ERR#1 Missing cases: 11 Valid cases: 205 Some of the missing cases are imbedded within the series.
••• MORNING AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Autocorrelations: ERR#1 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 -.041 .069 . *| . .351 .554 2 .080 .069 . |**. 1.694 .429 3 -.045 .068 . *| . 2.119 .548 4 -.013 .068 . * . 2.155 .707 5 .272 .068 . |**.** 18.294 .003 6 -.133 .067 ***| . 22.170 .001 7 -.074 .067 . *| . 23.366 .001 8 -.022 .067 . * . 23.470 .003 9 -.007 .067 . * . 23.479 .005 10 .111 .067 . |**. 26.231 .003
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 216 Computable first lags: 203
Hi-Res Chart # 47:Acf for residual
••• MORNING AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Partial Autocorrelations: ERR#1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 -.041 .070 . *| . 2 .078 .070 . |**. 3 -.039 .070 . *| . 4 -.022 .070 . * . 5 .280 .070 . |**.*** 6 -.125 .070 .**| . 7 -.139 .070 ***| .
- 680 - 8 .034 .070 . |* . 9 .007 .070 . * . 10 .019 .070 . * .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 216 Computable first lags: 203
Hi-Res Chart # 48:Pacf for residual
••• MORNING AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Since AREG does not produce an R estimate, generate one.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS R -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT ard1 -> /METHOD=ENTER fit#1 .
••• MORNING AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. ARD1 DIFF(AR,1)
Block Number 1. Method: Enter FIT#1
Variable(s) Entered on Step Number 1.. FIT#1 Fit for ARD1 from AREG, MOD_41
Multiple R .82009 R Square .67254 Adjusted R Square .67093 Standard Error 1.54455
F = 416.92719 Signif F = .0000
End Block Number 1 All requested variables entered.
••• MORNING AROUSAL MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> SUBTITLE
- 681 - -> 'STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR'.
-> * Determine the standard deviation of the error series.
-> DESCRIPTIVES -> VARIABLES=err#1 -> /FORMAT=NOLABELS NOINDEX -> /STATISTICS=MEAN STDDEV -> /SORT=MEAN (A) .
••• MORNING AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
Number of valid observations (listwise) = 205.00
Valid Variable Mean Std Dev N
ERR#1 .01 1.55 205
••• MORNING AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
-> * Use the MN and SD of error series to determine outliers.
-> * Create upper and lower 3*SD lines for plotting.
-> COMPUTE U3Stdev = 0 + 3 * 1.55 .
-> COMPUTE L3Stdev = 0 - 3 * 1.55 .
-> VARIABLE LABEL L3Stdev '3 SDs below'.
-> VARIABLE LABEL U3Stdev '3 SDs above'.
-> EXECUTE.
-> * Now plot the error overlayed with 3*SD lines.
-> *Sequence Charts .
-> CASEPLOT VARIABLES= err#1 U3Stdev L3Stdev -> /ID = Seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_43.
Hi-Res Chart # 49:Caseplot of err#1, u3stdev, l3stdev
- 682 - 1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 Residual 166 177 188 3 SDs above 199 210 3 SDs below -6 -4 -2 0 2 4 6
••• MORNING AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
-> * And list the actual outlier values. -> COMPUTE Outliers = 0 . -> IF (err#1 > U3STDEV | err#1 < L3STDEV ) Outliers = 1 . -> USE ALL. -> VALUE LABELS Outliers 0 'OK' 1 'Outlier'. -> COMPUTE filter_$=(Outliers = 1). -> VARIABLE LABEL filter_$ 'res1 = 1 (FILTER)'. -> VALUE LABELS filter_$ 0 'unselected' 1 'selected'. -> FORMAT filter_$ (f1.0). -> FILTER BY filter_$. -> LIST -> VARIABLES=seconds outliers l3stdev err#1 u3stdev -> /CASES= BY 1 -> /FORMAT= SINGLE UNNUMBERED .
••• MORNING AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
SECONDS OUTLIERS L3STDEV ERR#1 U3STDEV
49 1.00 -4.65 4.72687 4.65 211 1.00 -4.65 4.94950 4.65
Number of cases read: 2 Number of cases listed: 2
••• MORNING AROUSAL MODEL +++ STEP 3. AR1 MODEL OUTLIER ANALYSIS OF ERROR
-> EXECUTE .
- 683 -
Appendix V: Morning Valence Model
-> TITLE -> 'MORNING VALENCE MODEL'.
-> SUBTITLE -> 'STEP 1: STEPWISE REGRESSION.'.
-> FILTER OFF.
-> use 1 thru 216 .
-> EXECUTE .
-> LIST -> VARIABLES=bar -> /CASES= FROM 1 BY 215 -> /FORMAT= WRAP NUMBERED .
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
BAR
1 m. 1.30 216 m.87.40
Number of cases read: 216 Number of cases listed: 2
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS COEFF OUTS R ANOVA END TOL -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT vad1 -> /METHOD=STEPWISE -> BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 -> CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1
- 684 - -> DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 -> MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 -> TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1 -> /RESIDUALS DURBIN -> /SAVE RESID (res2).
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Block Number 1. Method: Stepwise Criteria PIN .0500 POUT .1000 BPM0D1 BPM1D1 BPM2D1 BPM3D1 BPM4D1 CEN0D1 CEN1D1 CEN2D1 CEN3D1 CEN4D1 DBA0D1 DBA1D1 DBA2D1 DBA3D1 DBA4D1 MEL0D1 MEL1D1 MEL2D1 MEL3D1 MEL4D1 TEX0D1 TEX1D1 TEX2D1 TEX3D1 TEX4D1
Step MultR Rsq F(Eqn) SigF Variable BetaIn 1 .2751 .0757 16.289 .000 In: DBA3D1 .2751 2 .3638 .1323 15.100 .000 In: DBA2D1 .2430 3 .4154 .1726 13.694 .000 In: TEX4D1 .2222 4 .4532 .2053 12.662 .000 In: DBA1D1 .1856 5 .4988 .2488 12.918 .000 In: TEX3D1 .2559 6 .5353 .2865 12.985 .000 In: TEX2D1 .2451 7 .5539 .3068 12.202 .000 In: TEX1D1 .1737 8 .5485 .3009 13.917 .000 Out: DBA3D1
Variable(s) Removed on Step Number 8.. DBA3D1 LAGS(DBA0D1,3)
Multiple R .54855 R Square .30090 Adjusted R Square .27928 Standard Error 1.67675
Analysis of Variance DF Sum of Squares Mean Square Regression 6 234.76387 39.12731 Residual 194 545.43162 2.81150
F = 13.91687 Signif F = .0000
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
- 685 ------Variables in the Equation ------
Variable B SE B Beta Tolerance VIF T
DBA1D1 .080397 .045478 .121473 .763217 1.310 1.768 DBA2D1 .077496 .046133 .116473 .749578 1.334 1.680 TEX1D1 .093741 .034059 .195861 .711583 1.405 2.752 TEX2D1 .186536 .041489 .389749 .479551 2.085 4.496 TEX3D1 .241051 .039906 .503652 .518335 1.929 6.040 TEX4D1 .215045 .033049 .449315 .755724 1.323 6.507 (Constant) .113440 .118775 .955
------in ------
Variable Sig T
DBA1D1 .0787 DBA2D1 .0946 TEX1D1 .0065 TEX2D1 .0000 TEX3D1 .0000 TEX4D1 .0000 (Constant) .3407
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
------Variables not in the Equation ------
Variable Beta In Partial Tolerance VIF Min Toler T Sig T
BPM0D1 -.064326 -.075270 .957228 1.045 .479550 -1.049 .2956 BPM1D1 -.102516 -.116875 .908657 1.101 .468989 -1.635 .1037 BPM2D1 .015908 .018132 .908246 1.101 .470441 .252 .8014 BPM3D1 .097866 .115454 .972952 1.028 .478523 1.615 .1080 BPM4D1 .029403 .034640 .970285 1.031 .474523 .482 .6307 CEN0D1 -.068303 -.080277 .965708 1.036 .475937 -1.119 .2646 CEN1D1 -.004280 -.004853 .898869 1.113 .479378 -.067 .9463 CEN2D1 .026687 .030152 .892428 1.121 .468449 .419 .6756 CEN3D1 .024283 .028006 .929955 1.075 .471210 .389 .6975 CEN4D1 -.117934 -.139275 .975007 1.026 .479414 -1.954 .0522 DBA0D1 .053213 .056354 .784046 1.275 .478842 .784 .4339 DBA3D1 .091111 .091721 .708490 1.411 .446427 1.280 .2022 DBA4D1 .071753 .081838 .909414 1.100 .453941 1.141 .2554 MEL0D1 .007151 .008448 .975633 1.025 .479536 .117 .9067 MEL1D1 -8.212E-04 -.000931 .899262 1.112 .473826 -.013 .9897 MEL2D1 .019649 .022257 .897046 1.115 .458394 .309 .7574 MEL3D1 .114847 .130517 .902878 1.108 .479544 1.829 .0690 MEL4D1 .079536 .090769 .910503 1.098 .478322 1.266 .2070 TEX0D1 .007087 .007079 .697579 1.434 .429452 .098 .9218
End Block Number 1 PIN = .050 Limits reached.
- 686 - ••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Residuals Statistics:
Min Max Mean Std Dev N
*PRED -3.8959 3.2994 .1705 1.0901 211 *RESID -5.6515 5.6454 -.0441 1.6429 211 *ZPRED -3.7658 2.8754 -.0125 1.0062 211 *ZRESID -3.3705 3.3669 -.0263 .9798 211
Total Cases = 216
Durbin-Watson Test = 1.24467
* * * * * * * * * * * * * * * * * * * * * * * * * * * * *
From Equation 1: 1 new variables have been created.
Name Contents ------
RES2 Residual
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> CASEPLOT VARIABLES= res2 -> /ID= seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_5.
Hi-Res Chart # 6:Caseplot of residual
- 687 - 1 12 23 34 45 56 67 78 89 10 0 11 1 12 2 13 3 14 4 15 5 16 6 17 7 18 8 19 9 20 7 -8 -6 -4 -2 0 2 4 6 8
Residual
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> ACF -> VARIABLES= res2 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_6.
Variable: RES2 Missing cases: 5 Valid cases: 211
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
Autocorrelations: RES2 Residual
Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 .359 .068 . |**.**** 27.624 .000 2 .004 .068 . * . 27.627 .000 3 -.053 .068 . *| . 28.242 .000 4 .003 .068 . * . 28.245 .000 5 .106 .068 . |**. 30.693 .000 6 .058 .068 . |* . 31.439 .000 7 -.144 .067 ***| . 36.008 .000 8 -.154 .067 ***| . 41.256 .000 9 .007 .067 . * . 41.266 .000 10 -.031 .067 . *| . 41.482 .000
- 688 - Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 216 Computable first lags: 210
Hi-Res Chart # 7:Acf for residual
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
Partial Autocorrelations: RES2 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 .359 .069 . |**.**** 2 -.144 .069 ***| . 3 -.004 .069 . * . 4 .032 .069 . |* . 5 .101 .069 . |**. 6 -.025 .069 . * . 7 -.173 .069 ***| . 8 -.026 .069 . *| . 9 .080 .069 . |**. 10 -.118 .069 .**| .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 216 Computable first lags: 210
Hi-Res Chart # 8:Pacf for residual
••• MORNING VALENCE MODEL +++ STEP 1: STEPWISE REGRESSION.
-> SUBTITLE -> '* STEP 2: MODEL SERIAL CORRELATION WITH AREG.' -> *Autoregression.
-> TSET PRINT=DEFAULT CNVERGE=.001 CIN=95 NEWVAR=CURRENT .
-> PREDICT THRU END.
-> AREG vad1 WITH -> DBA2D1 -> TEX4D1 -> DBA1D1 -> TEX3D1 -> TEX2D1 -> TEX1D1 -> /METHOD=ML -> /CONSTANT -> /RHO=0 -> /MXITER=10.
MODEL: MOD_7
Model Description:
- 689 - Variable: VAD1 Regressors: DBA2D1 TEX4D1 DBA1D1 TEX3D1 TEX2D1 TEX1D1
95.00 percent confidence intervals will be generated.
Split group number: 1 Series length: 211 Number of cases skipped at beginning because of missing values: 5 Melard's algorithm will be used for estimation.
••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Termination criteria: Parameter epsilon: .001 Maximum Marquardt constant: 1.00E+09 SSQ Percentage: .001 Maximum number of iterations: 10
Initial values:
AR1 .00000 DBA2D1 .07717 TEX4D1 .21517 DBA1D1 .07192 TEX3D1 .24734 TEX2D1 .19406 TEX1D1 .08991 CONSTANT .06839
Marquardt constant = .001 Adjusted sum of squares = 566.40673
Iteration History:
Iteration Adj. Sum of Squares Marquardt Constant
1 487.34425 .00100000 2 486.23861 .00010000 3 486.22006 .00001000
••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Conclusion of estimation phase. Estimation terminated at iteration number 4 because: Sum of squares decreased by less than .001 percent.
FINAL PARAMETERS:
Number of residuals 211 Standard error 1.5470195 Log likelihood -387.54235 AIC 791.08469 SBC 817.89956
- 690 - Analysis of Variance:
DF Adj. Sum of Squares Residual Variance
Residuals 203 486.21973 2.3932693
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .39282191 .06313582 6.2218552 .00000000 DBA2D1 .04685175 .04040497 1.1595540 .24759251 TEX4D1 .18164289 .02970159 6.1155940 .00000000 DBA1D1 .05177515 .04062438 1.2744846 .20394870 TEX3D1 .22684042 .04034952 5.6218871 .00000006 TEX2D1 .18588640 .04189191 4.4372865 .00001493 TEX1D1 .08948949 .02991546 2.9914129 .00312080 CONSTANT .08188408 .17512817 .4675665 .64059613
Covariance Matrix:
AR1
AR1 .00398613
Correlation Matrix:
AR1
AR1 1.0000000
••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Regressor Covariance Matrix:
DBA2D1 TEX4D1 DBA1D1 TEX3D1 TEX2D1
DBA2D1 .00163256 .00006276 .00080788 -.00045842 -.00047224 TEX4D1 .00006276 .00088218 -.00010253 .00072572 .00047774 DBA1D1 .00080788 -.00010253 .00165034 -.00022174 -.00061944 TEX3D1 -.00045842 .00072572 -.00022174 .00162808 .00122939 TEX2D1 -.00047224 .00047774 -.00061944 .00122939 .00175493 TEX1D1 -.00017185 .00007526 -.00020414 .00050246 .00083034 CONSTANT .00012590 -.00017462 .00014314 -.00033902 -.00036535
TEX1D1 CONSTANT
DBA2D1 -.00017185 .00012590 TEX4D1 .00007526 -.00017462 DBA1D1 -.00020414 .00014314 TEX3D1 .00050246 -.00033902 TEX2D1 .00083034 -.00036535 TEX1D1 .00089493 -.00019178 CONSTANT -.00019178 .03066988
Regressor Correlation Matrix:
DBA2D1 TEX4D1 DBA1D1 TEX3D1 TEX2D1
- 691 - DBA2D1 1.0000000 .0522951 .4921797 -.2811842 -.2789967 TEX4D1 .0522951 1.0000000 -.0849744 .6055505 .3839557 DBA1D1 .4921797 -.0849744 1.0000000 -.1352765 -.3639854 TEX3D1 -.2811842 .6055505 -.1352765 1.0000000 .7273113 TEX2D1 -.2789967 .3839557 -.3639854 .7273113 1.0000000 TEX1D1 -.1421776 .0847022 -.1679746 .4162597 .6625639 CONSTANT .0177929 -.0335703 .0201198 -.0479767 -.0497995
TEX1D1 CONSTANT
DBA2D1 -.1421776 .0177929 TEX4D1 .0847022 -.0335703 DBA1D1 -.1679746 .0201198 TEX3D1 .4162597 -.0479767 TEX2D1 .6625639 -.0497995 TEX1D1 1.0000000 -.0366051 CONSTANT -.0366051 1.0000000
••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
The following new variables are being created:
Name Label
FIT#1 Fit for VAD1 from AREG, MOD_7 ERR#1 Error for VAD1 from AREG, MOD_7 LCL#1 95% LCL for VAD1 from AREG, MOD_7 UCL#1 95% UCL for VAD1 from AREG, MOD_7 SEP#1 SE of fit for VAD1 from AREG, MOD_7
••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Diagnose Residual.
-> VARIABLE LABEL ERR#1 'Residual'.
-> ACF -> VARIABLES= ERR#1 -> /NOLOG -> /MXAUTO 10 -> /SERROR=IND -> /PACF.
MODEL: MOD_8.
Variable: ERR#1 Missing cases: 5 Valid cases: 211
••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Autocorrelations: ERR#1 Residual
- 692 - Auto- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 Box-Ljung Prob. +----+----+----+----+----+----+----+----+ 1 .047 .068 . |* . .477 .490 2 -.121 .068 .**| . 3.630 .163 3 -.094 .068 .**| . 5.520 .137 4 -.016 .068 . * . 5.578 .233 5 .115 .068 . |**. 8.477 .132 6 .070 .068 . |* . 9.560 .144 7 -.134 .067 ***| . 13.503 .061 8 -.136 .067 ***| . 17.579 .025 9 .084 .067 . |**. 19.146 .024 10 .011 .067 . * . 19.172 .038
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 216 Computable first lags: 210
Hi-Res Chart # 9:Acf for residual
••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
Partial Autocorrelations: ERR#1 Residual
Pr-Aut- Stand. Lag Corr. Err. -1 -.75 -.5 -.25 0 .25 .5 .75 1 +----+----+----+----+----+----+----+----+ 1 .047 .069 . |* . 2 -.124 .069 .**| . 3 -.083 .069 .**| . 4 -.024 .069 . * . 5 .098 .069 . |**. 6 .051 .069 . |* . 7 -.122 .069 .**| . 8 -.100 .069 .**| . 9 .085 .069 . |**. 10 -.048 .069 . *| .
Plot Symbols: Autocorrelations * Two Standard Error Limits .
Total cases: 216 Computable first lags: 210
Hi-Res Chart # 10:Pacf for residual
••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> * Since AREG does not produce an R estimate, generate one.
-> REGRESSION -> /MISSING LISTWISE -> /STATISTICS R -> /CRITERIA=PIN(.05) POUT(.10) -> /NOORIGIN -> /DEPENDENT vad1 -> /METHOD=ENTER fit#1 .
- 693 - ••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
* * * * M U L T I P L E R E G R E S S I O N * * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. VAD1 DIFF(VA,1)
Block Number 1. Method: Enter FIT#1
Variable(s) Entered on Step Number 1.. FIT#1 Fit for VAD1 from AREG, MOD_7
Multiple R .63583 R Square .40428 Adjusted R Square .40143 Standard Error 1.52722
F = 141.83478 Signif F = .0000
End Block Number 1 All requested variables entered.
••• MORNING VALENCE MODEL +++ * STEP 2: MODEL SERIAL CORRELATION WITH AREG.
-> SUBTITLE -> 'STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR'.
-> * Determine the standard deviation of the error series.
-> DESCRIPTIVES -> VARIABLES=err#1 -> /FORMAT=NOLABELS NOINDEX -> /STATISTICS=MEAN STDDEV -> /SORT=MEAN (A) .
••• MORNING VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
Number of valid observations (listwise) = 211.00
Valid Variable Mean Std Dev N
ERR#1 -.01 1.53 211
- 694 - ••• MORNING VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> * Use the MN and SD of error series to determine outliers.
-> * Create upper and lower 3*SD lines for plotting.
-> COMPUTE U3Stdev = 0 + 3 * 1.53 .
-> COMPUTE L3Stdev = 0 - 3 * 1.53 .
-> VARIABLE LABEL L3Stdev '3 SDs below'.
-> VARIABLE LABEL U3Stdev '3 SDs above'.
-> EXECUTE.
-> * Now plot the error overlayed with 3*SD lines.
-> *Sequence Charts .
-> CASEPLOT VARIABLES= err#1 U3Stdev L3Stdev -> /ID = Seconds -> /NOLOG -> /FORMAT NOFILL NOREFERENCE -> /MARK gridline.
MODEL: MOD_9.
Hi-Res Chart # 11:Caseplot of err#1, u3stdev, l3stdev 1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 Residual 166 177 188 3 SDs above 199 207 3 SDs below -4-6-8 -2 86420
••• MORNING VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> * And list the actual outlier values.
-> COMPUTE Outliers = 0 .
- 695 - -> IF (err#1 > U3STDEV | err#1 < L3STDEV ) Outliers = 1 .
-> USE ALL.
-> VALUE LABELS Outliers 0 'OK' 1 'Outlier'.
-> COMPUTE filter_$=(Outliers = 1).
-> VARIABLE LABEL filter_$ 'res1 = 1 (FILTER)'.
-> VALUE LABELS filter_$ 0 'unselected' 1 'selected'.
-> FORMAT filter_$ (f1.0).
-> FILTER BY filter_$.
-> LIST -> VARIABLES=seconds outliers l3stdev err#1 u3stdev -> /CASES= BY 1 -> /FORMAT= SINGLE UNNUMBERED .
••• MORNING VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
SECONDS OUTLIERS L3STDEV ERR#1 U3STDEV
96 1.00 -4.59 -5.44357 4.59 99 1.00 -4.59 5.61925 4.59 109 1.00 -4.59 4.80645 4.59 172 1.00 -4.59 4.84381 4.59 221 1.00 -4.59 -6.19602 4.59
Number of cases read: 5 Number of cases listed: 5
••• MORNING VALENCE MODEL +++ STEP 3. AR(1) MODEL OUTLIER ANALYSIS OF ERROR
-> EXECUTE .
- 696 -