INFORMATION TO USERS

The most advanced technology has been used to photo­ graph and reproduce this manuscript from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer.

The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction.

In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.

Oversize materials (e.g., maps, drawings, charts) are re­ produced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. These are also available as one exposure on a standard 35mm slide or as a 17" x 23" black and white photographic print for an additional charge.

Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photo^aphs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order.

UMI University Microfilms international A Bell & Howell Information Company 300 Nortfi Z eeb Road, Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600

Order Number 9011226

The effects of task order and function pattern on learning harmonic dictation

Murphy, Barbara Ann, Ph.D.

The Ohio State University, 1989

Copyright ©1989 by Miu-phy, Barbara Ann. All rights reserved.

UMI 300 N. Zeeb Rd. Ann Aibor, MI 48106

THE EFFECTS OF TASK ORDER AND FUNCTION PATTERN ON LEARNING HARMONIC DICTATION

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree Doctor of Philosphy in the Graduate

School of The Ohio State University

By

Barbara A. Muiphy, B.M., M.A.

*****

The Ohio State University

1989

Dissertation Committee Approved by Burdette L. Green Ann K. Blombach

A. Peter Costanza Adviser School of Music Copyright by

Barbara Ann Murphy

1989 ACKNOWLEDGEMENTS

I would like to thank all those students who participated in this study and their theory instructors for their assistance.

To the Department of Statistics at The Ohio State University, I would like to express my gratitude for their assistance. In particular, I would like to thank Dr. William Notz and Mr. Panickos Palettas for their assistance in the design of this study. I would also like to thank graduate students Ms. Jane Chang and Mr. S T. Wang for their help with the analysis of the data.

I would like to thank Dr. James Talley for his help with the programming of the computer-assisted instructional programs and with his help in uploading of the data from Experiment 1.

1 wish to extend my appreciation to the members of my reading committee. Dr. Ann Blombach and Dr. Peter Costanza, for their critical comments and suggestions which led to greater clarity and organization in this study.

To my advisor. Dr. Burdette Green, 1 am particularly indebted for all his assistance and encouragement in the design and implementation of this study. 1 am grateful

ii for his comments, suggestions, extreme patience and helpfulness in arranging meetings during the writing of this thesis.

The Ohio State University School of Music and Youngstown State University

Computer Center provided the use of their computers and facilities.

Ill VITA

July 11,1956 Bom - Youngstown, Ohio

1978 ...... B.M. Youngstown State University Youngstown, Ohio

1980 ...... M.A. The Ohio State University Columbus, Ohio

1982-1985 Systems Analyst/Programmer Goal Systems International, Inc. Columbus, Ohio

1985-1986 Systems Analyst, OCLC, Inc., Dublin, Ohio

1986-1987 Manager, CBT Goal Systems Australia, Pty. Ltd. Sydney, Australia

1987-present Adjunct Instructor Dana School of Music Youngstown State University Youngstown, Ohio

IV PUBLICATIONS

"Computerized Degree Audit at YSU," YSU/Online 16/2 (Winter 1988).

"Choosing the Right Training Method," Australian Computing October 1986, 66-67.

"Evaluation of Three Types of Instructional Strategies for Learner Acquisition of Intervals," with James Canelos, Ann K. Blombach and William Heck, Journal of Research in Music Education 28/4 (Winter 1980), 243-249.

HELDS OF STUDY

Major Field: Music Theory TABLE OF CONTENTS

PAGE

ACKNOWLEDGEMENTS ...... ii

VITA ...... iv LIST OF TABLES...... viii

LIST OF HGURES...... x PREFACE ...... '...... xii CHAPTER

L INTRODUCTION...... 1

Rationale ...... 1 Survey of Previous Studies, Methods and Programs ...... 3

n. EXPERIMENT 1: MATERIALS AND METHOD...... 18

Statistical M ethod ...... 18 Subjects...... 19 Computer Program ...... 20 Procedure ...... 40

m. EXPERIMENT 1: STATISTICAL ANALYSIS...... 42

Results ...... 42 Discussion ...... 74

VI IV. EXPERIMENT 2: MATERIALS AND METHOD...... 80

Statistical D esign ...... 81 Subjects...... 83 Computer Program ...... 84 Procedure ...... 94

V. EXPERIMENT 2: STATISTICAL ANALYSIS ...... 96

Results ...... 96 Discussion ...... 141

VI. CONCLUSIONS ...... 150

Summary...... 160

APPENDICES

A. Progressions Used in Experiment .1...... 162 B. Macintosh Terminology ...... 171

C. Forms Used in Experiment 1 ...... 175

D. Progressions Used in Experiment 2 ...... 181

E. Forms Used in Experiment 2 ...... 194

F. Results of Student Survey used in Experiment 2 ...... 212 LIST OF REFERENCES...... 203

YU LIST OF TABLES

TABLE PAGE

1. Number of Progressions Completed by Each Student ...... 44

2. Frequency of Task Order Presentations ...... 47

3. Ranking for Orders by Mean Scores on Roman Numeral and Position Identifications ...... 48

4. Progressions Ranked by Means ...... 61

5. Progressions Ranked by Means with Spacing M arked ...... 63

6. Number of Correct and Incorrect Chord Identifications by Progression ...... 65

7. Number of Correct and Incorrect Identifications by Chord ...... 69

8. Chord Confusions: Experiment 1 ...... 71

9. Frequent Chord Confusions: Experiment 1...... 73

10. 6X6 Latin Square Design for Experiment 2 ...... 82

11. General Linear Models Procedure for Total Score ...... 99

12. General Linear Models Procedure for Total Score: Students Classified by Gender ...... 103

13. General Linear Models Procedure for Total Score YSU Students Classified by Gender ...... 104

V lll 14. General Linear Models Procedure for Total Score OSU Students Classified by Gender ...... 105

15. General Linear Models Procedure for Total Score: Students Classified by Instrument ...... 106

16. General Linear Models Procedure for Weighted Total ...... 108

17. General Linear Models Procedure for Total 1 ...... 112

18. General Linear Models Procedure for New Total ...... 116

19. General Linear Models Procedure for New Weighted Total ...... 117

20. General Linear Models Procedure for New Total 1 ...... 118

21. Progressions Ranked by Total Mean Score ...... 125

22. Number of Correct and Incorrect Identifications by Chord ...... 127

23. Ranked Progressions with Number of Difficult Chords Lidicated ...... 129

24. Mean and Total Number of Difficult Chords by Pattern ...... 130

25. Chord Confusions: Experiment 2 ...... 133

26. Frequent Chord Confusions: Experiment 2 ...... 136

27. Chords Listed by Types of Confusions ...... 139

28. Frequency of Positions of Chords by Pattern ...... 144

29. Mean Scores for Each Task by Student Gender and School ...... 146

IX LIST OF FIGURES

FIGURE PAGE

1. Experiment 1; Quality Identification Screen ...... 24

2. Experiment 1: Analysis Screen ...... 27

3. Experiment 1: Function Identification Screen ...... 28

4. Experiment 1: Bass Line Screen ...... 30

5. Experiment 1; Soprano Line Screen ...... 32

6. Experiment 1: Correct Answer Display ...... 33

7. Musical Sleuth Situation Screen ...... 35

8. Musical Sleuth Clue Screen ...... 36

9. Musical Sleuth Answer Screen...... 38

10. Mean and Mean +/- 2SE for Roman Numeral Scores on the Quality T ask...... 51

11. Mean and Mean +/- 2SE for Roman Numeral Scores on the Function T ask ...... 52

12. Mean and Mean +/- 2SE for Roman Numeral Scores on the Bass Task ...... 53

13. Mean and Mean +/- 2SE for Roman Numeral Scores on the Soprano Task ..... 54

14. Mean and Mean +/- 2SE for the Position Scores on the Quality Task...... 55

X 15. Mean and Mean +/- 2SE for, the Position Scores on the Function T a sk ...... 56

16. Mean and Mean +/- 2SE for the Position Scores on the Bass Task ...... 57

17. Mean and Mean +/- 2SE for the Position Scores on the Soprano Task ...... 58

18. Means and Mean +/- 2SD for Each Progression ...... 59

19. Experiment 2: Answer Screen ...... 89

20. Experiment 2: Correct Answer Display ...... 93

21. Interaction Between Order and Pattern Using Total Score ...... 101

22. Interaction Between Order and Pattern Using Weighted T otal ...... 110

23. Interaction Between Order and Pattern Using Totall ...... 114

24. Interaction Between Order and Pattern Using New Total ...... 120

25. Interaction Between Order and Pattern Using New Weighted Total ...... 121

26. Interaction Between Order and Pattern Using New Totall ...... 122

27. Mean and Mean +/- 2 Standard Deviations by Progression ...... 132

XI PREFACE

Learning to take harmonic dictation is a frustrating task for many music students.

It is a very complex task. Students are typically asked to provide a complete harmonic analysis of a progression and to notate the soprano and bass lines as well. The students are thus required to attend to melodic structure, chord function and quality, and to identify the chords by means of Roman and Arabic numeral designations. Many students are overwhelmed by this complexity; they do not know what tasks to concentrate on first. Teachers, likewise, do not know what orders of presentation are best for chord types and function patterns. To make harmonic dictation easier for their students, they need to have experimental evidence to guide them.

The aim of this study is to discover which order of tasks best facilitates the accurate analysis of harmonic dictation exercises. This study also aims to discover whether patterns of tonic, subdominant and dominant function chords have an effect on analysis scores. The results of the this study will assist instructors by providing evidence about particular orderings of tasks and function patterns of the progressions. By knowing the effects of task orders and function patterns, instructors should be able to improve their methods of instruction. These findings

XU should also help students. If students follow a procedure that results in better scores, they will experience less fhistration in their aural training classes.

The study involves two experiments conducted in 1987 and 1989, The first experiment served an exploratory purpose and pointed the way to a more tightly controlled second experiment. The findings of the study are based on data gathered from both experiments. The study is presented as follows: Chapter I presents the rationale for the study and establishes its orientation by reviewing the existing literature about harmonic dictation. Chapter II explains the materials and method used in Experiment 1. The chapter details (1) the selection and description of the students who participated, (2) the instructional materials used, and (3) the procedure followed in conducting Experiment 1. Chapter III analyzes the results of Experiment 1 and discusses the implications of these results. Chapter IV explains the materials and method used in Experiment 2. This involves a description of (1) the subjects who participated, (2) the instructional materials used, and (3) the procedure followed. Chapter V analyzes the results of Experiment 2 and discusses

the implications of these results. Chapter VI presents a discussion of the results of the two experiments and their implications for learning and teaching, and ofiers some recommendations for further research in the area of harmonic dictation.

xiu CHAPTER I

INTRODUCTION

In recent years, music theorists and educators have undertaken a fair amount of research in the areas of perception and aural training skills. Some research has concentrated on the perception of tones and the combinations of two or more tones

(Jeffries, 1967; Deutsch and Roll, 1974; Killam, Lorton and Schubert, 1975; Fenner, 1976; Siegel and Siegel, 1977; Deutsch, 1978; 2^torre and Halpem, 1979; Blombach and Parrish, 1988; Gibson, 1988). Other research has concentrated on the perception of tone groups and melodies (Carlsen, 1964; Dowling, 1973). Little research, however, has focused on harmonic dictation, the concern of the present investigation.

Rationale

The probable reason for the small amount of research on harmonic dictation is that harmonic dictation is more complex than other types of dictation. In interval

dictation, students are asked only to provide the size and the quality of each interval. Students usually distinguish between 8 sizes of intervals—the prime through the octave-and 2 or 3 qualities for each interval, making a total of abouti 6 different combinations to be distinguished.

1 In the dictation of individual chords, students are asked only to provide the quality and position of each chord. If we limit the chords ItrGiads, there are four possible qualities and three positions. So, there are only 10 or 12 possible combinations to be distinguished.

Harmonic dictation, however, involves a much more complex set of tasks.

Harmonic dictation can be described as the process of listening to a short phrase of music and identifying the chords that are played. Training phrases are usually at least seven chords in length and written in four-part (SATB) texture.

To identify the chords played, the students must provide Roman and Arabic numeral designations for each chord. To provide the Roman numeral designation, the student must identify the root and the quality of the chord in both major and minor tonalities. If we limit the chord vocabulary to diatonic triads, there are still seven possible roots to be considered. Each triad may have one of four qualities: major, minor, diminished and augmented. To designate the quality of the chord, the student uses upper and lower case Roman numerals: upper case for a major chord, lower case for a minor chord, lower case with a small superscript 'o' for diminished and upper case with a superscript '+' for augmented chords.

To identify the chord position by Arabic numbers, the student must determine which of three chord members is in the bottom-most position. So far, there are 84 possible combinations ^ of qualities, positions and roots for each triad. If the six permutations of the notes in the upper three voices are also considered, there are 504 possible combinations for each of the seven chords in the progression. Recognizing that, in major and minor tonalities, each triad has only one quality, there are only 126 possible combinations^ for each of the seven chords in the progression. Even with this limitation, harmonic dictation is a much more complex set of tasks than other types of dictation.

And yet, the student may be asked to provide even more information. In addition to identifying the chords played, the student may also be asked to notate the top line of the progression, the soprano, and the bottom line, the bass. The student may also be asked to identify the general function of the chord; whether the chord has a tonic, subdominant and dominant function.

In all, students may be asked to complete six different tasks—the identirication of

the root, quality, position and function of each chord, and the notation of soprano and bass lines—involving a multitude of possible combinations.

Survev of Previous Studies, Methods and Programs

Despite the complexity of the task, a limited amount of research has been conducted on various aspects of harmonic dictation. Several studies pertinent to the present study require discussion.

14 qualities X 3 positions X 7 roots = 84. ^ 7 root and quality combinations X 3 positions X 6 permutations of the upper three voices = 126. Hamss (1974) compared an in-class, programmed instructional procedure with the traditional method of teaching nine types of aural training. Topics included sight- singing, error detection, chord identification, and melodic, rhythmic and harmonic dictation. Sixty freshmen music majors were divided into two groups. The control group received traditional in-class aural training for 2 hours each week for one academic year. The experimental group used a programmed instructional method featuring examples on tape. For the harmonic dictation examples, the students were expected to

Notate pulses of harmonic dictation by notating the chord symbols. The materials are selected from all primary triads [i.e. not secondary dominants or altered chords] in root position and fîrst inversion in one of the keys indicated above [with key signatures ranging from two flats to two sharps]; dictated in tempo (quarter = MM42) and in a single trial. (Harriss 1974, 218-219)

For the experimental group, the program began with just the I, IV and V chords

and gradually added first inversion as well as root position. The chords chosen for

each step in the program were presented randomly (Harriss 1974,219). However,

for the control group, the harmonic dictation presented "functional harmonies in their usual configuration" (Harriss 1974,219).

Students were tested in the fall, at midyear and at the end of the academic year on both experimental and control materials. When Harriss compared the mean gain

scores, he found that the programmed method of instruction was better overall. For harmonic dictation, he found that the experimental group performed better on experimental materials than control materials, and that the experimental group improved more on experimental examples than the control group improved on control materials. Despite these gains, Harriss concluded that the programmed harmonic examples were not useful since they were randomly generated. He stated

that in the exercises.

The vocabulary of functional harmony is used but the aural logic basic to the system is negated. If harmonic dictation is to be based on common practice vocabulary and content, it would be more appropriate for the harmonic dictation element of this program to be oriented toward a developmental exposition of this harmonic style. (Harriss 1974, 225)

Alvarez (1980) conducted an experiment to determine which of two harmonic

perception techniques would better assist seventh- and eighth-grade students in

identifying primary harmonic functions in progressions. The methods consisted of a scalar technique and a root technique. In the scalar method, the students were directed to identify the chord sounded by determining if the first or the seventh scale degree was part of the chord. For example, if tlie first scale degree was present, the chord was either a tonic (I) or subdominant (TV), and the choice could be made by

attending to the stability of the chord—the tonic would be the more stable. If the seventh scale degree was present, the chord was to be identified as the dominant (V). In the root method, the students were directed to determine the location of the chord root and identify the chord accordingly.

The subject pool for Alvarez’s experiment consisted of 106 seventh- and eighth- grade students in a New York middle school. After the subjects were taught for 10 30-minute periods, they were then given a test battery developed for the experiment. The battery consisted of two subtests: (1) Primary Harmonic Functions: Root and (2) Primary Harmonic Functions: Root/Inversion. Only root position chords were used in the rirst subtest whereas both root position and first inversion chords were used in the second subtest.

Based on data from 72 students, Alvarez found that subjects using the scalar method of identirication attained higher scores on both subtests. An analysis of variance indicated that the scalar method was the significantly better method (E(1.68) = 17.16, p < .05), but only on the Root/Inversion subtest. Alvarez

concluded that the scalar technique should be used in teaching the identification of primary harmonic functions.

In a follow-up study, Alvarez (1981) investigated the "effectiveness of scalar or root classification systems, inductive and deductive content sequences, and kinetic

or verbal coding processes on identifying harmonic functions" (Alvarez 1981,135).

In this study, the scalar-method subjects used three scale degrees to classify the chords: scale degree 1 for chords in the tonic class (I, IV, vi), scale degree 7 for chords in the dominant class (V, vii°, and iii), and scale degree 2 for the pre­

dominant chord, ii. Subjects employing the root method classified chords according to 5 categories: 1. mediant (iii)) 2. submediant (vi) 3. subdominant (IV, ii) 4. dominant (V, vii®) 5. tonic (I)

Deductive groups learned to identify the functional class of the chord before attempting to distinguish the particular chord. Inductive groups learned to identify the speciHc chord before attempting to determine its functional class. Subjects following a kinetic coding process used instrumental fingerings to help them identify the chords, whereas those following a verbal coding process learned to identify the chords by means of the movable "do" solfege syllables.

The subjects for this study consisted of 48 music students at the Hartt School of

Music. They were randomly assigned to a scalar or root method group, a deductive or inductive content sequence group and a kinetic or verbal coding process group. After 10 50-minute instructional sessions, the students were tested using the Harmonic Functions Test Battery described above. In addition, each subtest included "48 multiple choice items, major and minor tonalities, duple and triple meters, homophonie and polyphonic textures, and progressions in varying expectation" (Alvarez 1981,137).

The analysis of the data collected from the tests indicated that subjects using the scalar method scored higher than those using the root method, regardless of whether deductive or inductive and kinetic or verbal processes were used. But it also 8 indicated that the inductive and kinetic processes resulted in higher scores than the deductive and verbal processes.

The superiority of the scalar method could be attributed to its simplicity-it involved distinguishing among only 3 groups whereas the root method involved distinguishing among 5 groups. Therefore, subjects using the scalar method had a

33% chance of guessing the correct answer, whereas those using the root method had only a 20% chance of guessing correctly.

Questions arise concerning the claimed superiority of the inductive process. Indeed, the scalar method and inductive process of identifying chords seem to be contradictory. In reality, students following the scalar method provide a more general functional identitication of the chord prior to identifying the chord itself. By identifying the scale tone present in the chord, the students categorize the chord into one of 3 groups. However, when using the inductive process, they are taught

to identify the chord before providing its general function. It seems impossible that subjects could follow both methods if one asks for a general category first while the other asks for a specific identification first.

Rahn and McKay (1988) advocated the use of the scalar method (or "guide-tone method") over more traditional "reductive" or "holistic" methods. In the reductive

method, subjects attend to small parts of the progression, e.g., the notes in each of the voices, and then provide the analysis based on their identification of the parts. In the holistic method, they listen for the overall sound of the chord and analyze it accordingly.

Rahn and McKay's guide-tone method is basically the same as the scalar method discussed in Alvarez's 1980 article. Subjects fîrst leam to attend to whether the first or seventh scale degree is in the chord. This is just a first step, however. When subjects master this step, they proceed to chordal identification. For chordal identification, they are instructed to sing the triads using various vocal patterns, for example, "do-mi-sol-mi-do" for tonic and "ti-re-ti-sol-ti" for dominant. A different pattern is provided for each chord.

Although Rahn and McKay claim that their method has been used for twenty years with some success, it presents several evident problems. First, students in aural training classes are usually not adept at singing chords. Second, students lacking a strong scalar sense must identify the chord (i.e., provide Roman numeral or quality and position designations) mentally before they can sing it—so the singing merely confirms that the identification is correct. Students having a strong scalar sense can sing the notes without identifying the chord, but then must identify it in order to provide Roman numeral and position designations. In either case, the singing just adds a step to the identification process. Third, in order to sing each chord of the progression, the students must sing the notes quickly or the progression must be played slowly. Singing the notes quickly requires rapid identification of the notes in the chords, whereas playing the progressions very slowly creates an artificial musical situation. 10

The small amount of research in the area of harmonic dictation is matched by little development of computer-assisted instructional lessons for harmonic dictation. Of the 119 music CAT programs reviewed by Battle (1987), Hofstetter (1988), and the Association for Technology in Music Instruction Courseware Directory 89-90

(Boody, 1989), only 12 programs listed have modules concerning harmony:

Advanced Ear Training Tutorial Diatonic Chords Ear Eye GUIDO Harmonize Harmony Drills Harmonious Dictator Jazz Dictator MacGAMUT Practical Music Theory A Technique for Listening Voice

Three of these programs do not deal with dictation. "Harmonize" (Boody 1989, 60) deals with the harmonization of melodies. "Practical Music Theory" (Boody

1989, 41-42) and "Voice" (Boody 1989, 58) deal with written skills in chord progression and voice leading. Ann Blombach, the author of the "MacGAMUT" program (Boody 1989, 55), states that the module on harmonic dictation is planned. To sum up, only 8 programs currently contain drills on harmonic dictation.

The harmonic dictation module of "Ear Eye" is described as follows: 11

Harmonie error perception and completion drills: Beginning with short progressions using the three triads and advancing to complete phrases which incorporate diatonic seventh chords, secondary dominants, Neopolitan sixths, borrowed chord, and modulation. (Boody 1989,61)

"Ear Eye" is written to run on GIGI terminals. The conversion to Macintosh computers, the author states, is projected.

Four programs are marketed by Temporal Acuity Products (TAP, Inc). They are: "Diatonic Chords," "Harmony Drills," Harmonious Dictator," and "Jazz Dictator."

"Diatonic Chords" presents harmonic dictation exercises containing all diatonic triads in root position, first and second inversions, and dominant seventh chords in all positions. For each exercise, the student is required to notate the soprano and the bass lines as well as provide Roman and Arabic numeral designations for each chord in the progression. The progressions of seven chords each are in four voices and are presented in major and minor keys from 4 flats to 4 sharps. The student may rehear the progression at any time. After all soprano and bass notes and

Roman numeral and position designations are coirectiy provided, the program plays each chord and notates the inner voices on the screen. No scores are given to the student (Bartle 1987, 31-32)

"Harmony Drills" contains five levels of harmonic dictation exercises, each containing 20 exercises. It covers all diatonic triads in root position and first inversion and the I^. Students are asked only to provide Roman numeral and 12 position designations for the five chords in the progressions. Answer Judging takes- place only when an answer has been provided for each chord. The students then see the correct Roman numeral and position identifications and the notes that were played. Students may move sequentially through the levels or choose the level on which they want to work. (Hofstetter 1988,178)

"Harmonious Dictator" is described as "a harmonic dictation program that automatically adjusts the length and the level of difficulty [i.e., from level 1 to 9] of the exercises according to student performance (Hofstetter 1989, 178).

Examples involve major keys up to 6 flats and sharps and minor keys up to 4 flats

and sharps and range from 3 to 6 chords in length. The progressions include all diatonic chords and their inversions, selected seventh chords and selected secondary dominants. In each exercise, the first chord is identified and notated for the students, the key is established (i.e., a scale is played ascending and descending), and the progression is played twice. When the student provides correct Roman numeral and position designations for a chord, it is notated on a staff and played.

The student may then rehear the progression or reestablish the key. When a progression is completed, the student is shown a "report card." The score is based on the number of errors and the number of additional hearings. (Bartle 1987, 59- 60)

"Jazz Dictator" introduces students to the sounds of jazz chords including major and minor seventh and ninth, dominant ninth and 13th, and fully- and half-diminished seventh chords in root position. Like "Harmonious Dictator," there are 9 levels of 13 difficulty from which the students may initially choose. As the student works on the program, the difficulty level will adjust to the student's ability. Exercises range

from 4 to 6 chords in length and involve major or minor keys from 4 flats to 4 sharps. In each exercise, the student must identify the quality of the triad and its seventh, disregarding any ninths and 13ths present. In later levels, the student must also indicate if the bass note is altered. The student may choose to rehear the progression or reestablish the tonal center. When the progression is completed, the program displays the level and the student's score, based on the number of errors and the number of rehearings the student required. (Bartle 1987,75)

The "Advanced Ear Training Tutorial Programs" include modules on chord recognition and harmonic dictation and are divided into 34 units. Of these, 12 units deal with harmonic dictation exercises. Three units deal with secondary dominants; in these, students are asked to provide the analysis of the second and third chords of a three chord progression where the second chord is the secondary dominant or leading-tone seventh chord of the third chord. In three other units, students are asked to identify the implied harmonies underlying two voice counteipoint exercises. Six units deal with chromatic harmony; in these, students are asked to identify the second of three chords. This second chord may be a

borrowed chord, 9th, 11th or 13th chord, Neopolitan 6 th, Augmented 6 th, altered dominant or a chromatic mediant chord. (Bartle 1987,2-3)

The program "A Technique for Listening" was written to accompany Bruce Benward's Ear Training-A Technique for Listening textbook and follow exactly the 14 exercises in the book. Included are 15 units dealing with harmonic dictation, 10 units dealing with harmonic error correction, and 16 units dealing with harmonic function. Hofstetter's discussion does not elaborate on the contents of these units, but the screen examples shown indicate that the student enters both Roman

numeral and position identifications. Progressions range from 4 to 8 chords and include all diatonic chords, seventh chords, and secondary dominants in all inversions. (Hofstetter 1988,202-203)

The last program containing harmonic dictation modules is "GUIDO" (Boody 1989, 65). The current version of this program is written for the IBM PC. The author, Fred Hofstetter, also wrote an earlier version of the program for use with

PLATO terminals. This earlier version of the program was used in a study of harmonic dictation (Hofstetter, 1978), the puipose of which was to analyze patterns of student learning. Subjects for the study consisted of 17 freshmen music majors at the University of Delaware. During their own time for at least two hours per week, students practiced harmonic dictation exercises consisting of examples from the Benward Workbook in Ear Training (1969). The first modules included only

the I and V chords. The viio 6 and IV chords were added next, in modules 2 and 4 respectively. The ii chord was introduced in module 9, the in module 12, the vi in module 14 and the iii chord in module 15. All subjects worked through the 15 modules in the same order. For each exercise, they were asked to provide the Roman numeral identifrcation of the chords and to notate the soprano and bass lines of the progression. The order of the tasks was fixed: the subjects had to

provide Roman numerals first and then the soprano and bass lines in that order. 15

The results of the experiment showed that some chords were easily mastered and not subject to confusion with other chords. Such chords were the I, I, V and vii®^. Other chords were subject to confusion even after they were mastered: the i^, IV, rv^, iv, and V^. Chords that were mastered with some difficulty but then not subject to confusion with others were the ^ and iv^ chords.Finally, certain chords

were never mastered: the i^, ii, ii^, ii®^, iii^, V^, V 5 , V 3 , and V^. From the wrong answers, Hofstetter identified seven classes of chord confusion:

1. Bass line confusions (e.g., ^ instead of iii^). 2. Confusions of inversion (e.g., i^ for i). 3. Confusions by chord function (e.g., ^ for V). 4. Confusions of chord quality (e.g., 1 for I). 5. Unperceived seventh (e.g., V for V^).

6 . Unperceived root (e.g., for vii®^). 7. Favorite response.

Finally, Hofstetter performed a Pearson Product Correlation for each unit based on the number of times each chord was asked and answered correctly. He found that subjects achieved higher scores on chords that were asked more frequently.

The studies cited above demonstrate that harmonic dictation is indeed a very complex task and that no one seems to know exactly how to proceed with instruction. Harriss (1974) concluded that harmonic dictation examples should not be randomly generated, since they are not stylistic. Alvarez's two studies (1980, 16

1981) showed that subjects who concentrate on whether particular notes are present in a chord, i.e., the scalar method of identification, score higher on the analysis of progressions than those who concentrate on identifying the root of each chord in the progression, i.e., the root method. Rahn and McKay (1988) confirm that the scalar method helps students. Alvarez (1981) also found that subjects do better on the analysis of harmonic functions if they leam to identify specifîc chords first before assigning general functions. Finally, Hofstetter (1978) discovered that students have difüculty identifying certain chords. Ife also discovered seven classes of chord confusions.

However, these studies also raise questions. A crucial question arises from Hofstetter's research. For his study, students had to provide the Roman numeral identification and then the soprano and the bass lines. The order of the tasks was fixed. But there are no studies to suggest that this is the optimum order of tasks.

Another important question concerns the order in which the chords are presented to students. In all of the experimental studies (and in Rahn and McKay’s guide-tone

method), the order of the presentation of the chords was predetermined. Usually the primary triads. I, IV and V, were presented first and the secondary chords added

later. However, no statistical evidence suggests that such orders chosen will help the students achieve higher scores.

In addition, we do not know whether the general function patterns of progressions

affect students’ scores. Harriss suggests that they may be a factor since he 17 recommends the progressions should not be randomly generated. Also, Alvarez's two studies suggest the importance of the function of the chords since higher scores result when students categorize the chords in the progression into three groups-tonic, dominant and pre-dominant. (These correspond to the usual tonic, subdominant and dominant functional categories.)

The present study attempts to provide answers to these questions. By means of two experiments, it investigates the relation of the order of four tasks—the identification of the general function and the quality of each chord in the progressions, and the notation of the bass and soprano lines~to the student's ability to provide an accurate harmonic analysis. In addition, it examines whether the progression's pattern of chordal function—tonic, subdominant and dominant—has an

effect on the analysis scores, and it investigates the relation of specific chord collection to the student's analysis scores. Chapter II contains a description of the materials and method used in conducting the first experiment. CHAPTER n

EXPERIMENT 1: MATERIALS AND METHOD

Experiment 1 was designed as an exploratory study of the manner in which subjects take harmonic dictation. It investigated the relation of the order of four tasks—the identification of chordal function and quality, and the notation of the bass and soprano lines—to the subject's ability to provide an accurate harmonic analysis.

It also investigated the relation of the specific chord collections to the subject's analysis scores. Experiment 1 also served to test the computer-assisted instructional program for design and programming problems and to determine the adequacy of data recorded. The results of this study were used to design the more tightly controlled Experiment 2.

Statistical Method

For Experiment 1, subjects were asked to complete at least six harmonic dictation exercises selected at random fi-om a bank of 24 progressions. For each progression, a different task order was chosen at random from the 24 possible orders. The progressions and orders were chosen in such a way that no subject would receive the same order or the same progression twice. After completing each task in the order, subjects were asked to provide a complete harmonic analysis of the 18 19 progression to determine if the previous task had aided them in providing a correct analysis. No feedback was given until subjects had completed all four tasks and all four analyses since providing feedback might have influenced the subjects' answers on subsequent tasks. Feedback shown at the conclusion of each exercise consisted of the subject's percentage score and the correct answers for the tasks and the analysis. The subjects' scores on the Roman and Arabic numeral identification tasks constituted the dependent variables for the analysis. For each score, one point was awarded for each correct answer provided.

I wrote a computer program to collect the data for the analysis. It is described later in this chapter.

Subjects

The subjects for the experiment were drawn from the students enrolled in

sophomore aural training (Music 424) at The Ohio State University in Autumn quarter 1987. All students were encouraged to participate. Each subject who completed the required six progressions was awarded a quiz grade of A. In addition,I devised a computer game (i.e., the Musical Sleuth game) as a further

incentive for the subjects. Completing a harmonic dictation exercise earned subjects the right to play and clues were awarded according to the success rate of their scores. 20

Of the 37 subjects who participated in the experiment, all but 1 were music majors. The non-music major was an English Education major. Twenty-two of the subjects were female and 15 were male. In the majority of cases, the subject's major instrument was either voice (11 subjects) or keyboard (10 subjects). In the

remaining cases, the subject’s major instrument was a brass (7), woodwind ( 6 ),

percussion ( 2 ) or string ( 1 ) instrument.

Computer Program

Subjects were instructed to complete six progressions. For each exercise, they received a different progression chosen at random from the bank of 24 progressions

found in Appendix A. All progressions are written in major keys with signatures

of no more than two flats or sharps, and each contains seven diatonic triads in various positions and spacings, set in four voice (SATB) texture. No seventh

chords are used. Each progression conforms to one of these patterns of tonic, subdominant and dominant functions:

Pattern 1: TTSSDDT Pattern!: TTSTSDT Pattern 3: TSTSDDT Pattern 4: TTDTSDT Pattern 5: TDTSDDT

Pattern 6 : SDTTSDT Pattern 7: TTTTDDT 21

Chords were classified as tonic, subdominant and dominant according to this scheme:

Tonic: I, vi, vi^, iii, non-cadential iii^ Subdominant: IV, TV^, ii, ii® Dominant: V, V®, v ii® ,c a d e n tia ll^ ,cadentialiii^

The progressions were presented by a computer program written specifically for this study. The program, written in Lightspeed Pascal^ was designed for use on a Macintosh Plus computer with a mouse but no keyboard.

The subject started the harmonic dictation program by double-clicking^ the harmonic dictation icon on the screen. After removing the title screen by clicking the "Continue" button, the subject saw the general directions displayed on the second screen. These required the completion of six harmonic dictation exercises, each of which entailed four tasks:

1 . identify the quality of each chord.

2 . identify the general function (tonic, subdominant or dominant) of each chord. 3. notate the bass line. 4. notate the soprano line.

^The Lightspeed P a sc a l^ Version 1, First edition compiler was marketed by Think Technologies, Inc of Lexington, Massachusetts. ^ See ARrendix B for deOnitions of Macintosh Plus terminology. 22

After each task, the subject was requested to provide a complete harmonic analysis, giving both the Roman numeral chord designations and the Arabic numeral position indicators. In all, each exercise required eight steps.

The next screen shown varied according to the order of the tasks. The program chose the order of the four tasks randomly from the 24 permutations possible, so that each progression was assigned a different task order. For the sake of this discussion, the following order of tasks will be presumed:

1 . identify the quality of each chord.

2 . identify the general function of each chord. 3. notate the bass line. 4. notate the soprano line.

Each screen displayed a button marked "Play" and a button marked "Done." Clicking the "Play" button caused the progression to be played once. The progression could be replayed any number of times and at any time. The progressions were played on the Macintosh Plus’ built-in Digital-Analog convertor using waveforms created for Blombach's MacGAMUT programs.

The "Done" button appeared only when answers were provided for every chord of the progression. Clicking the "Done" button ended the current task and caused the

next task or progression to be displayed. Clicking either the "Play" or the "Done" button caused the following information about the subject's performance to be written to disk: 23

1 . progression number.

2 . the number of times data were written to disk for this progression. 3. the task [Q(uality), F(unction), B(ass), S(oprano), or A(nalysis)] the subject was working on. 4. the time. 5. the date.

6 . whether the subject clicked the Play or the Done button 7. number of times the progression had been played to this point.

8 . the subject's answer thus far for the current task.

As shown in Figure 1, general directions were shown at the top of the screen for the identification of the quality of the chords. Below the directions were seven answer blanks (one for each chord in the progression), four boxes containing quality designations, and the "Play" button. The boxes containing the quality designations were marked: "d" for diminished, "m " for minor, "M" for major and "A" for augmented. 24

QURLiTV IDENTIFICRTION Prouide only the Quality of each chord of the progression by clicking the quality and then the position of the chord with that quality.

You may hear the progression again by clicking Play.

Click Done when you haue prouided a quality for each chord.

0: __ EHSCE]

I Way I

Figure 1 Experiment 1: Quality Identification Screen

At this point, the progression was played once. When the subject clicked one of the four quality boxes, the box was highlighted, i.e., displayed in reverse video. After selecting a quality, the subject clicked any of the blanks corresponding to the chords in the progressions, thereby placing the highlighted quality on the blank(s).

To edit the answer, the subject clicked another quality box and a blank already containing a quality designation. The quality designation on the blank was then replaced by the current choice. When all the blanks contained a quality designation, the "Done" button appeared. The subject could then continue to edit 25 click "Done" to end this task. When "Done" was clicked, the subject was asked to provide a complete analysis of the progression.

When the program was first conceived, I attempted to offer as much aid as I could without providing feedback until the final analysis was completed. Therefore, the subjects' answers on the previous tasks—the identification of the quality and function, and the notation of the soprano and bass lines—were shown at the top of the screen. The answers were only displayed; they could not be changed. Below the subjects' answers were seven blanks (one for each chord in the progression),

seven boxes with the Roman numeral designations and three boxes with the position indicators. The Roman numeral designations were displayed in upper and lower case to indicate the quality of the triad. The boxes indicating the positions of

the triads were marked: 3 for root position, 3 for first inversion and ^ for second

inversion.

Through some initial testing, I found that having the answers to the previous tasks on the screen confused subjects more than it aided them; since the previous answers

were often incorrect and the subject could not correct or erase them, they were distracting.

To alleviate the confusion, four options were possible: (1) show only the correct

answers to previous tasks on the analysis screen, ( 2 ) allow answers to be changed, (3) allow answers to be erased, but not changed, or (4) show no answers to tlie previous tasks. 26

Since no feedback was to be provided until all tasks were completed for a

progression, option 1 was ruled out—showing only correct answers for the previous tasks provided feedback. Options 2 and 3 were eliminated because allowing changes or erasures other than those that were part of the analysis task diverted the subject's attention from the analysis task. Thus option 4, showing no answers, provided the only viable solution.

The screen was revised for use in Experiment 1. On the new screen, as shown in Figure 2, the answers to the previous tasks were removed. The screen contained seven blanks (one for each chord in the progression), seven boxes with Roman numeral designations and three boxes containing the Arabic numeral indicators for the chord positions. The Roman numeral designations were displayed in upper and lower case, indicating the quality of the triad. The boxes for the positions of the triads were marked: g for root position, g for first inversion and ^ for second inversion. When the screen was first shown, the box for root position was already selected and highlighted; it was the default. 27

HRRMONIC OICTRTION On the blanks below, prouide a complete analysis of the progression played for you.

Be sure to specify both the ROMRN NUMERRL analysis and the POSITION of each chord.

0 :

III E~irT' VI VII® mm I M « y I

Figure 2

Experiment 1: Analysis Screen

The progression was played once. To provide the analysis, the subject first selected a Roman numeral and an Arabic numeral designation, then clicked all the appropriate blanks. The Roman numeral and position appeared in the blank(s) clicked. The subject could provide the analysis in any order desired. Answers could be edited by clicking new Roman and Arabic numeral designations and the corresponding blank. When an analysis for each chord of the progression was supplied, the "Done" button appeared. Clicking the "Done" button allowed the subject to proceed to the next task. 28

The screen that required the identifîcation of the general chord functions showed a list of chords to be considered tonic, subdominant and dominant (see Figure 3). Below the list of chords were seven blanks (one for each chord in the progression) and three boxes containing designations for the general functions—"T" for tonic, "S" for subdominant and "D" for dominant.

FUNCTION IDENTIFICATION Identify the function of eoch chord in the progression ployed by clicking a function and then clicking the place for the chord of that function.

Functions ore:

Tonic: I I* 1% iii m* in| vi vi® vij Subdominant: IZ IZ® 1Z| ii ii® ii§ Dominant: Z Z® Z% vii® vii®® vii*5 cadential 1$ iii®

0 : _ _ _ _ _ mam

( Play 1

Figures

Experiment 1: Function Identification Screen 29

The progression was played once. The subject clicked one of the three boxes containing function designations, and the box was highlighted. When one of the blanks corresponding to the chords in the progression was clicked, the highlighted function was transferred to the blank. To edit the answer, the subject clicked a function box and the blank already containing a quality designation. The function designation on the blank was then replaced by the one selected. Once all the blanks contained a function, the "Done" button appeared. The subject continued to

edit the answer or clicked "Done." When "Done" was clicked, the subject was

asked to provide a second harmonic analysis for the progression in the manner described above.

Next, the subject was asked to notate the bass line. The top of the screen showed a

staff with bass clef, key signature and time signature indicated. Below the staff was the key designation and seven blanks (one for each chord in the progression), six boxes containing accidentals-double sharp, sharp, natural, flat, double flat and an empty box—and four boxes containing duration values—eighth, quarter, dotted

quarter and half notes. The empty accidental box and quarter note duration were the defaults. When the empty box was selected, the accidentals in the key signature were assumed. 30

BBSS NOTATION

m

w, I. n tt X

[ Ploy

Figure 4

Experiment 1: Bass Line Screen

The progression was played once. To write a note on the staff, the subject first selected a box for an accidental and duration or used the default and then positioned the arrow (now changed into a notehead) on a line or space of the staff and clicked the mouse. A note, with the accidental and duration selected, was written at this position. The subject could enter notes in any order and could change any note by selecting a different accidental and duration, positioning the notehead on the staff and clicking the mouse. This caused the old note to be replaced by the new one. After all seven notes of the bass were notated, the "Done" button appeared. The 31 subject could continue to edit the answer or click "Done." When "Done" was clicked, the subject was asked to provide a third harmonic analysis for the progression.

Next, the subject was asked to notate the soprano line. As shown in Figure 5, the top of the screen showed a staff with treble clef, key signature and time signature indicated. Below the staff were seven blanks (one for each chord in the progression), six boxes containing accidentals-a double sharp, sharp, natural, flat, double flat and an empty box—and four boxes containing durations-eighth, quarter, dotted quarter and half note values. The empty accidental box and the quarter note duration were the defaults. When the empty box was selected, the accidentals in the key signature were assumed. 32

SOPRANO NOTATION

^ — — 1

— 1

I.I. i. # X

Figures Experiment 1: Soprano Line Screen

The progression was played once. To write a note, the subject first clicked the boxes corresponding to an accidental and duration or chose to use the default and then positioned the arrow (now changed into a notehead) on the line or space of the

staff and clicked the mouse. A note, with the accidental and duration selected, was

written at this position. The notes could be entered in any order. Any note could

be changed by selecting a different accidental and duration, positioning die notehead on the staff and clicking the mouse, thereby causing the note on the blank to be replaced by the note selected. After all seven notes of the bass were notated, the 33

"Done" button appeared. The subject either continued to edit the answer or clicked

"Done." If he clicked "Done," the subject was asked to provide a final harmonic analysis of the progression.

After the final analysis was completed, a screen with the subject’s score and the

correct answers for all tasks was displayed, as shown in Figure 6 .

HRRMONIC DICTATION The correct ansuiers for this progression are shouin below. Vour score is 100 %. ; È P me é

I I» E II* Y Y I M M M m M M M T T S S 0 0 T

( Play ] [ Continue ] EHit

Figure 6

Experiment 1: Correct Answer Display 34

The subject's score was equal to the total number of correct answers on the tasks—function, quality, Roman numeral and position identifications, and the notation of the soprano and bass lines-divided by the total number of points possible (i.e., 42).

Clicking "Play" caused the progression to be played once. Clicking "Exit" stopped the program and returned the subject to the Macintosh desktop. If the subject clicked "Continue," two options-to proceed to the next progression or to play the "Musical Sleuth" game-were given. If the subject chose to conünue with the next progression, the next harmonic dictation exercise was presented. If the subject chose to play the "Musical Sleuth" game, he proceeded as follows.

The Musical Sleuth game was designed as an incentive to complete and achieve high scores on the harmonic dictation exercises. The game dealt with music theory and history "mysteries" by presenting situations that required answers to the questions: who, what, when and where. Clues were provided to assist the subject in answering the questions. Correct answers earned points, and the fewer the clues required, the greater was the score. As the scores mounted, the subject was

"promoted" from the rank of "bobby" to "super sleuth." The game is described below.

As shown in Figure 7, the subject was first shown a scenario with four missing elements—who, what, when and where. 35

MUSICAL SLEUTH GAME The Situation In the ______(when) In the city o f______(where), a ce. composer, ______(who) was hosting a party for the first performance of his new baliet. During the piayiny of a courante by the harpsichordist, a woman came up to the composer and started to taik to him. "Jean," she said, "i want to congratulate you on the marueious fan of the first part of your ballet. I really ioued the way you combined a fugue with the introductory part. So what do you call this wonderful form?" The composer replied, "I am so glad you enjoyed it. I haue named the new form after my newly adopted country and the function the form performs in the ballet. Thus, it is called a ______(what)."

( Help ] [ Continue"^ [ Go To Progression""^ [ Euit ]

Figure? Musical Sleuth Situation Screen

By clicking Continue, the subject proceeded to the screen shown in Figure 8 . On this screen were four boxes marked who, what, when and where and four blank boxs for lists of answers. 36

MUSICAL SLEUTH GAME Number of clues you houe left: 16 ( Who ) J lllhen ) (

Ulhot I ] [ (Where

Help ] [ Check Hnsmer ) [ See Situation ] [ So To Progression ) ( Ëult ]

Figure 8 Musical Sleuth Clue Screen

If help was required, clues could be obtained by clicking the boxes marked who, what, when and where. The clue was shown under the box and under any other clues already shown. The number of clues that could be received was based on the subject's score on the harmonic progression exercise. The formula used to determine the number of clues earned was:

Number of Clues = score on progression/5 37

The maximum score possible on the harmonic dicatation exercise was 112 points.

To receive all 16 clues, the subject must have achieved a score of at least 75% on the harmonic dictation exercise.

The number of clues the subject could receive was shown at the top of the screen.

After a clue was given, the number was decremented. The subject chose the type of clues to be shown, but only four clues were available in each category. For example, if eight clues were earned, the subject might choose four clues for who, two for when, one for what, and one for where.

Clicking the blank boxes next the who, what, when or where boxes caused a list of possible answers for that category to be displayed. The answers to the "Who" question are shown in Figure 9. 38

WHO O Bach, J.s. O Handel, G.F. O Prokofiev, S. O Beethoven, L. O Haydn, FJ. 0 Puccini, G. O Berlioz, H. O Hindemith, P. O Ravei, M. O Bernstein, I. O Liszt, F. O Rossini, G. O Brahms, J. O Lully, J.B. O Scarlatti, 0. O Copland, B. O Luther, M. O Schubert, F. O Chopin, F. OMachout, G. O Strauss, H. O Bebussy. C. O Mahler, 6. O Stravinsky, 1. O OesPres, J. O Mendelssohn, F. O Sousa, J.P. O Bvorak, fl. O Mozart, W.R. O Tchaikovsky, P i. O Gershivin, G. O Mussorgsky, M. OUlagner, R.

( «K 1

Figure 9 Musical Sleuth Answer Screen

Clicking the circle next to the choice and the 'OK' box caused an answer to be selected. The answer was shown in the blank box next to the who, what, when or where box on the clue screen. Answers could be changed at any time by clicking the box containing the answer, the circle next to the new answer choice on the answer screen and "OK." The new answer would then be shown on the Clue Screen. 39

Clicking the "Check Answer" box caused the subject’s answers to be evaluated. A list of the categories that were correct and the number of points accumulated was shown. The subject earned zero points if the answer was incorrect. If the subject provided a correct game answer, he earned from one to five points based on the number of clues provided (e.g., one point if all four clues were needed to 5 points if none were needed). Thus, each subject could earn a maximum of 20 points on each situation. After the number of points and the categories answered correct were shown, the subject could choose whether to exit the game or to continue guessing at the answers.

When the game was exited, the total number of points accumulated on all tries on the game and the earned "Rank" were shown. The rank was calculated as follows.

01-24 points : Bobby 25-48 points : Detective 49-72 points : Captain 73-96 points : Inspector 97-120 points : Super Sleuth

Since each subject could be presented a maximum of 6 situations (i.e., one

following each of the 6 harmonic progressions in the exercise), the maximum

number of points was 1 2 0 .

At the bottom of the screen showing the subject's rank, there were two buttons: "Continue" or "Exit." Clicking "Exit" caused the program to stop and the subject

to be returned to the Macintosh desktop. When "Continue" was clicked, the subject was presented the next harmonic dictation exercise. 40

Procedure

Students enrolled in Music 424 during Autumn quarter 1987 were asked to complete six progressions using the computer-assisted instructional lesson described above. They were told only that there was a new computer assisted instructional lesson in harmonic dictation for them to try. In return for completing at least six progressions, subjects were given a quiz grade of A. Anyone not completing six progressions or not participating were given a quiz grade of E (i.e., failure). In class, the subjects received a Student Data Sheet and a copy of the directions, both of which are included in Appendix C.

When subjects arrived at the lab to complete the progressions, the monitor assigned unused disks in numerical order. Subjects wrote their names on the disk labels and, if necessary, completed the Student Data sheet at this time. They then continued with the exercises as explained in the Computer Program section of this chapter.

When the subjects finished the program, they clicked the "Exit" button. They then returned the disks and the completed Student Data sheets to the monitor. Subjects could end the session at any time, whether they completed six progressions or not. If progressions remained to be finished, the next resumed where the program left off. 41

The disks were then gathered and the data were analyzed by methods discussed in

Chapter 3. CHAPTER in

EXPERIMENT 1: STATISTICAL ANALYSIS

Experiment 1 was designed as an exploratory study of how students take harmonic

dictation. It investigated the relation of the order of four tasks-the identification of chordal function and quality, and the notation of the bass and soprano lines-to the student's ability to provide an accurate harmonic analysis. It also investigated the relation of the specific chord collections to the student's analysis scores. Thirty-

seven music students firom The Ohio State University used the computer program described above. The data were collected and analyzed as described below.

Results

To prepare the data for analysis, I combined the individual data files into one large file on the Macintosh. Since the amount of data collected precluded initial analysis

on the Macintosh, I uploaded the data to Youngstown State University's Amdahl mainframe. (Later, a subset of the data was entered on the Macintosh into a

product called Statview 512+% for further analysis.) The data consisted of various types of lines of information:

^ Statview 512+ is marketed by Brainpower, Inc. of Calabasas, California. 42 43

1 . time and date information for each answer.

2 . answers for the quality task. 3. answers for the function task. 4. answers for the bass task. 5. answers for the soprano task.

6 . answers for the analysis tasks.

Since students could enter or change answers to only the current task, information for the current task alone was recorded to save disk space. This recording method resulted in six different formats for the data. To use the mainframe's statistical software program. Statistical Analysis System (SAS), all lines of data in a file had to be formatted alike. So a program, written in the VM/CMS operating system's language called EXEC, separated the data into six files.

Next, a SAS program calculated the number of progressions each subject

completed. As Table 1 shows, 31 students completed at least 6 progressions. 44 Table 1

Number of Progressions Completed by Each Student

Student Nbr. progressions Student Nbr. Progressions

1 5 2 0 7

2 7 2 1 7

3 6 2 2 7

4 6 23 6

5 2 2 1 6

7 8 25 6

8 7 26 13

9 6 27 7

1 0 6 28 6

1 1 8 29 7

1 2 7 30 1 13 7 31 3 14 7 32 5 15 14 33 7

16 7 34 6

17 9 35 6

18 7 36 6 19 7 38 5

39 8

Student number 10 completed the required 6 progressions. However, her data were not included in the analysis since one of her progressions provided faulty data. Of

the remaining subjects, 1 0 completed precisely 6 exercises and the remaining 26

completed either more or less than the 6 required progressions. Since each subject

was required to complete only 6 progressions, data for anyone completing fewer

than 6 progressions were eliminated. For subjects completing more than the 45

required 6 progressions, data from only the first 6 completed progressions were included in the analysis.

To determine which progressions were the first 6 completed, a SAS program read the data in each file, assigned sequence numbers for each progression, and determined the task order that had been used for each exCTcise. The program printed the student number, progression number, progression sequence number, the number of times the last analysis was tried, and the order of the tasks. Considering only those that had four tasks in the order of tasks and one or more tries on the last

analysis, I then chose the first6 completed progressions for each student and wrote a series of SAS " if statements to choose only these progressions in all remaining analyses.

I wrote another SAS program to score the subjects' answers on each task. Since each correct answer was assigned one point, the scores on the quality, function, bass and soprano tasks ranged from zero to seven points. For the analysis tasks, a separate grade was given for each chord’s Roman numeral designation and its position indicator so that a total score ranged from zero to fourteen points. These scores did not account for the differences among the students, progressions and orders. To account for these effects, I calculated the mean score for the last analysis according to each progression, each order and each student and added two new columns to the data, using the following formulas:

( 1 ) progression score = score -us-uo

(2 ) order score = score -up-us 46 where up is the mean for the progression, us is the mean for the student, and uo is the mean for the order.

In its current format, the data could be used to answer the following questions:

1. Of the 24 possible task orders, was there any order that resulted in higher scores on the final analysis? If so, which? 2. Was there any task for which the position in the order does not matter? 3. Were the analysis scores higher on some progressions than others? If so, for which?

The first step in answering question 1 was to count the number of times each order was presented. These frequencies are shown in Table 2. 47

Table 2

Frequency of Task Order Presentations

Order Count

QFSB 18

QSBF 1 1 QFBS 16

FQSB 1 0

SFQB 6 BFSQ 4

EBSQ 6

BQSF 1 2 FBQS 5 BFQS 7 QBFS 9 SQFB 7

BSQF 8

BQFS 6

FSQB 6 FQBS 5 SQBF 7 FSBQ 4 SFBQ 9

QSFB 1 0 SBFQ 4 QBSF 7 BSFQ 3

SBQF 0

Due to an error in the random generator function, one order (SBQF) never appeared.

Since order was one of the major factors being tested, one order not appearing presented a problem that could be resolved only by further experiment. 48

To determine which orders contributed to higher and lower scores, I ranked them from highest to lowest according to mean scores on Roman numeral and position identifications, as shown in Table 3.

Table 3

Ranking for Orders by Mean Scores on Roman Numeral and Position Identifications

Older Rank for Roman Num Rank for Pos

BFSQ 1 2

FBQS 2 1 SFQB 3 3

BFQS 4 6

QFBS 5 1 0

SFBQ 6 9 FQBS 7 18

FQSB 8 1 1 QSFB 9 17

FSBQ 1 0 13

BQFS 1 1 7

QFSB 1 2 14

QBFS 13 8

SBFQ 14 2 0 QSBF 15 15 SQBF 16 5

SQFB 17 1 2

QBSF 18 2 1 FSQB 19 16

BQSF 2 0 19

BSFQ 2 1 4 FBSQ 2 2 23

BSQF 23 2 2 49

The rankings indicate that subjects achieved the highest scores while using orders BFSQ, FBQS and SFQB, and the lowest scores while using orders BSQF and FBSQ. Looking at the orders associated with high scores shows that high scores result if the function task is one of the first two tasks and the quality task is one of the last two tasks. Looking at the orders associated with of low scores shows a similar result, but only for the quality task. In the orders used when subjects scored lowest, quality is the third task in one order (BSQF) and the fourth task in the other order (FBSQ). However, the conclusion that high scores are achieved when the function task is one of the last two tasks is not confirmed, for in the order FBSQ, the function task is the fîrst task, but this order results in low scores.

No conclusions can be drawn concerning the bass and soprano tasks, since subjects achieved high scores when these tasks occurred first and last in the order.

Curiously enough, using the order FBSQ resulted in high scores while using the order FBQS resulted in low scores. The only difference in these two orders is that

the sequence of the last two tasks, soprano and quality, is interchanged. This result

suggests that subjects get more information 6 om the soprano task than the quality task.

Although these comparisons are interesting, no one order emerges as the one always leading to high scores. To search for underlying patterns linking high scores to the order of the tasks, I plotted the mean score and the mean plus and minus two times the standard error (i.e., u +/- 2SE) for the Roman numeral answer 50 and for the position answer according to their sequence in the order. The resulting plots are shown in Figures 10-17.

Flat plots—ones in which there is no curve created by the means—indicate that the sequence of the task in the order does not contribute to a higher score. If the plot has a curve to it, the sequence of the task does contribute to a higher score.

Furthermore, if the line from plus two to minus two times the standard error for one sequence position has no points in common with another line on the same plot, the sequence of the task makes a great difference. In this case, we can assume that higher scores will result when the task is presented in the sequence position corresponding to the higher mean.

It is important to note that these plots do not indicate whether the tasks are helpful to the subject. Eliminating a task with a flat curve may have a detrimental effect

on the overall score. The plots only indicate that the sequence of the task within

the order does not matter; the subject will score the same or nearly the same number of points whether that task is fîrst, second, third or fourth in the order.

The quality task was the only one for which the sequence did not affect the analysis score. As Figure 10 shows, the plot for the quality task has almost no curve. 51

OMeanR OMeanR+2e AMeanR 2 'e

-4.2.

-4.4. & I I -4.8

-5.2

-5.4 0 .5 1 1.5 2 2.5 3.53 4 4.5 Sequence

Figure 10:

Mean and Mean +/- 2SE for Roman Numeral Score on the Quality Task

However, as Figures 11,12, and 13 show, the positions of the function, bass and soprano tasks did affect the analysis score. The plot of the means for the function task. Figure 11, indicates that the highest score resulted when the function task was second in the order. 52

AMeanR-2*e -3.8

-4.2 S) -4.4 -4.6 -4.8

-5.2 -5.4 0 1 1.52 2.5 3 3.5.5 4 4.5 Sequence

Figure 11: Mean and Mean +/- 2SE for Roman Numeral Scores on the Function Task

Note that the lines plotted when the function task is second and fourtli in the order

have no points in common. This shows that the difference in these means is significant. The inference is that higher scores will be achieved if the function task is second in the order.

Figure 12, the plot of the means for the bass task, indicates that the best position for the bass task was the third position in the order. However, there are no statistically significant differences in the positions of the bass task. 53

OMeanR AMeanR-2*e

-4.2.

-4.4. g I -4.6. 1 -4.8.

-5.2

-5.4 2 2.5 3.5 4.5 Sequence

Figure 12:

Mean and Mean +/- 2SE for Roman Numeral Scores on the Bass Task

Figure 13-the plot of the means for the soprano task—indicates that the best position in the sequence for the soprano task was the fourth (last) position in the

Older. 54

OMeanR

-4.2

-4.4

« -4.6 I -4.8

-5.2

-5.4 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 Sequence

Figure 13; Mean and Mean +/- 2SE for Roman Numeral Scores on the Soprano Task

Plots of the means for the identification of the chord inversions. Figures 14, 15, 16 andl7, show results similar to those shown in the plots for the means for the Roman numeral identification: the position of the quality task makes no difference, while the position of the other tasks results in higher scores when the function task was second, the bass was third and the soprano task was last in the sequence. 55

OMeanP -4.7. -4.8 -4.9

I

-5.5 -5.6 -5.7 -5.8 0 5 1 2 31.52.5 3.5 4 4.5 Sequence

Figure 14;

Mean and Mean +/- 2SE for Position Scores on the Quality Task 56

OMeanP □ MeanP+2e AMeanP-2e

-4.8

I» -5.Z. I -5.4 -5.6

-5.8

2 2.5 3.5 4.5 Sequence

Figure 15:

Mean and Mean +/- 2SE for Position Scores on the Function Task 57

OMeanP -4.8

:«D -5.2 -5.6

-5.8

0 .5 1 1.5 2 2.5 3 3.5 4 4.5 Sequence

Figure 16;

Mean and Mean +/- 2SE for Position Scores on the Bass Task 58

OMeanP □ MeanP+2e AMeanP-2e -4.6

-4.8.

& I -5.2 g -5.4

-5.6.

-5.8 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 Sequence

Figure 17:

Mean and Mean +/- 2SE for Position Scores on the Soprano Task

From the results shown in the above plots, the best order for the tasks appears to be function, bass and then soprano. The quality task may appear anywhere in the order.

The second question—Are there any tasks for which the position in the order does not matter?—can be answered using the results shown above. Since (1) the results indicate that the sequence position of the quality task has no effect on higher

scores, and since ( 2 ) it is the task order that is of primary interest, the quality task may be eliminated in further experiments. This does not mean that it is not 59 beneficial for the student to concentrate on chord qualities; it only means that the order in which this task is considered does not matter.

To answer the third question—Were the analysis scores higher on some progressions than others?—I plotted the mean and the mean plus and minus two times the standard deviation for each progression, as shown in Figure 18.

OmeanR □ MeanR + 2SD AMeanR - 2SD □ □ n ...... ^1 u J n [ 1 t 1 ' P n ...... 1I Q ^ r □ 1 a Ï1 [ n A > 1»o < >°<) O() < r ! i > <> /L 2 ^ O ...... i L...... A ^ A A ^A^ A A àk A ..^ .. L A L A

8 10 12 14 16 18 20 22 24 26 Progression

Figure 18:

Means and Mean +/- 2SD for Each Progression

As Figure 18 shows, subjects do score higher on some progressions than on others since the means for some progressions are lower than the means for other progressions. However, none of the differences proves to be significant since all of 60 the lines from the mean plus two to the mean minus two times the standard deviation have some points in common.

Several factors may have contributed to the higher scores associated with some progressions. Among these factors are (1) the general function pattern of the progression, (2) the spacing of the chords and (3) the specific chord collection used in the progression. To determine which of these factors contributed to the achievement of higher scores, I ranked each progression's mean score for the Roman numeral answers and marked their quartiles (75%, 50%, 25%), as shown in Table 4. 61 Table 4

Progressions Ranked by Means

Rank Progression Mean TSD Pattern

“ 1 3 -4.000 4 2 11 -4.093 5 3 4 -4.115 3 4 22 -4.200 4 5 6 -4.279 4 6 1 -4.339 1 7 13 -4.361 2 -25% 8 18 -4.396 3 9 17 -4.433 3 10 2 -4.452 1 11 5 -4.475 4 12 15 -4.494 2 13 10 -4.542 5 14 7 -4.618 4 15 9 -4.640 1 16 20 -4.647 7 17 14 -4.667 2 18 21 -4.693 6 19 2A -4.708 5 -50% 20 3 -5.004 2 21 16 -5.039 3 -75% 22 8 -5.227 1 23 12 -5.479 6 2A 19 -5.495 6

Legend: TSD pattern : pattern of general chord function (i.e., tonic, subdominant and dominant functions)

The last column, TSD Pattern (i.e., tonic, subdominant and dominant pattern), was added to determine whether the pattern of general chord function within the 62 progression contributed to a higher score on the analysis. The numbers in the column correspond to these seven patterns:

Pattern 1: TTSSDDT Pattern 2: TTSTSDT Pattern 3: TSTSDDT Pattern 4: TTDTSDT Pattern 5: TDTSDDT Pattern 6: SDTTSDT Pattern 7: TTTTDDT

Of these patterns, number 6 (SDTTSDT) appears to be the most difficult. Perhaps this is because it does not start with a tonic function chord. The results conHrm this hypothesis: Subjects scored lowest and second lowest on progressions following pattern 6 (progressions 19 and 12). The only other progression using this pattern (progression 21) ranked seventh from the lowest. Likewise, subjects scored high on progressions following pattern 4 (TTDTSDT)-progressions 10,5, 6, 22 and 23, ranked 1, 4, 5, 11 and 14 respectively. The means for the progressions following the other five patterns were neither all high nor all low. So, it appears the function pattern did have some effect on the score.

To determine if chord spacing in the progressions had an effect on the analysis score, I examined the spacing each progression exhibited and indicated the spacing type in Table 5. Progressions were considered to be in "open" spacing if the distance between the soprano and tenor voices was greater than an octave for all chords, in "closed" spacing if the distance was an octave or less for all chords. If 63

some chords within the progression were in open and others in closed spacing, the progression was indicated as "mixed."

Table 5

Progressions Ranked by Means with Spacing Marked

Rank Progression Spacing

1 23 closed 2 11 closed 3 4 closed 4 22 closed 5 6 closed 6 1 closed 7 13 closed 25% 8 18 closed 9 17 closed 10 2 mbced 11 5 open 12 15 closed 13 10 cltsW 14 7 closed 15 9 closed 16 20 closed 17 14 closed 18 21 closed 19 24 closed ■50% 20 3 closed 21 16 open ■75% 22 8 closed 23 12 closed 24 19 closed 64

Since only two progressions, numbers 16 and 5, were in open spacing and only one progression, number 2, in mixed spacing, no conclusions could be drawn about the effect of chord spacing on the analysis score.

The third factor that might have contributed to differences in analysis scores was the specific collection of chords in the progressions. To determine if the collection was a factor, I wrote a Pascal program to score the analysis of each chord in each progression. The answer was considered correct if both the Roman numeral identification and the position designation were identified correctly. Table 6 shows the number of times each chord was answered correctly (R) and incorrectly (W).

Chords answered more often incorrectly than correctly are printed in bold typeface. Table 6

Nutnb^ of Correct and Incorrect Chord Identifications by Progression

Progression 1 Progression 5 I VÎ IV li V I I4 1. vi VVI IV 1 w 0 41 40 43 19 2 0 W 0 34 27 30 20 12 0 R 72 31 32 29 53 70 72 R 44 10 17. 14 24 32 44

Progression 2 Progression 6

I 16 IV Ü6 Y V 1 1 16 V vi Ü6 V 1 W 5 33 35 44 57 16 1 W 0 6 16 14 18 5 0 R 59 31 29 20 7 48 6 R 20 14 4 6 2 15 20

Progression 3 Progressif 7

I 16 IV Ü6 V 1 1 iii V 1 ii V 1 W 0 13 10 10 16 2 1 W 0 45 38 24 39 6 0 R 24 11 14 14 8 22 23 R 60 15 22 36 21 54 60

Progression 4 Progression 8

I iii IV ii VÜ06 V 1 V I IV I M ...... I W 0 20 9 19 20 1 0

W 4 14 1 2 25 16 4 5 R 20 II 19 20 R 28 15 20 7 16 28 27 8} Table 6 (continued): Progression 13 Progression 9 I iii IV I IV V I I vi Ü6 ii iii6 V I W 0 12 6 4 8 4 4 w 2 7 12 10 20 6 2 R 12 0 6 8 4 8 8 R 18 13 8 10 0 14 18 Progression 14 Progressif 10 I vi . IV I IV VÜ06 T W 0 20 10 17 22 32 0 IV V IV vi .54 1 - D 32 12 22 15 10 0 32 W 1 9 9 7 8 0 0 R 15 7 7 9 8 16 16 Progression 15

I vi6 Ü 6 I IY6 V I w 2 32 44 9 33 4 2 R 46 16 4 39 15 44 46 1 1 V6 I iiti 4 V W 1 11 3 32 16 6 1 Progression 16 R 35 25 33 4 20 30 35 I Ü6 I ii VÜ06 V I Progression 12 W 0 16 5 14 16 4 0 R 16 0 11 2 0 12 16 IV V I vi ii6 V I 14 10 7 10 16 3 0 W Progression 17 R 2 6 9 6 0 13 16 vi TV I IV V V I W 12 10 12 11 15 4 0 R 8 10 8 9 5 16 20 & Table 6 (continued): Progression 22 Progression 18 _ÜL 1 viîoH _L _ü jdial W 20 16 17 10 20 19 1 u ____ ------3 ------V 1 12 LL J4_ R 0 4 3 10 0 1 19 W 4 16 2 8 2 1 0 R 20 8 22 16 22 23 24 Progression 23

Progression 19 1 iii V vi IV V Ü 0 6 I W 0 22 24 16 19 30 3 ii viio6 I U i LM V_ IR 32 10 8 16 13 2 29 W 0 8 1 19 24 17 0 R 24 16 23 5 0 7 24 Progression 24

Progression 20 1 vliofe I ii viio6 V I W 0 16 2 8 16 5 1 R 16 0 14 8 0 11 15 ï 16 iiiH li^ I4 V I W 0 4 13 19 1 2 0 R 24 20 11 5 23 22 24

Progression 21

IV V I .....li . ü .... I W 25 27 16 27 9 22 4 R 3 1 12 1 19 6 24 68

The information in Table 6 is important, yet it is difficult to see how the subjects responded to a particular chord because of the layout of the table. I wrote a Pascal program to summarize the data and to make it easier to see the responses to a particular chord and inversion. It read all the student answers on the analysis task, graded the answers and printed the total number of times the subjects provided correct and incorrect answers for each chord. These frequencies are shown in Table 7. €9 T ab le?

Number of Correct and Incorrect Identifications by Chord

Chord % Incorrect % Correct Nbr Times Present in Progressions

I 13.6% 86.4% 59

37.2% 62.8% 6 V 37.3% 62.7% 29

6 V 44.6% 55.4% 1

1 6 48.8% 51.2% 6

IV 56.8% 43.2% 18

vi 6 6 . 1 % 33.9% 1 0

ii 67.6% 32.4% 1 0 IV6 70.4% 29.6% 1

iu 6 T 71.1% 28.9% 1 ■vi 6 76.1% 23.9% 2 iii 81.4% 18.6% 5 ü6 84.0% 16.0% 9 viio 6 90.6% 9.3% 1 0 iü6 D 1 0 0 .0 % 0 .0 % 1

Legend: ^ = the chord has a dominant function; ^ = the chord has a tonic function

As the information in Table 7 indicates, the identifications of the primary chords,

I, I^, 14 , V and V^, were more often answered correctly than incorrectly. Those for the subdominant chord were almost evenly divided between correct and incorrect answers. However, responses for the secondary chords (ii, ii^, fii, iii^T iii^D, vi. 70

vi^ and vii® 6 ) were more often incorrect than correct, with scores ranging from

66.1% to 100% incorrect. The iii^ chord having a dominant function was never identified conectly.

To deteimine which misidentifications were being confused with the chords played,

I wrote a Pascal program to print a matrix. Table 8 , of responses for each chord. Tables

Chord Confusions: Experiment 1

(Correct answers across; Student answers down)

I 16 I6/4D ii Ü6 iii iii6T iii6D IV 1V6 V V6 vi vi6 VÜ06

I 2276 33 18 33 55 7 2 2 80 2 81 0 51 21 19 I® 70 151 11 4 26 42 4 0 68 0 53 1 27 6 1 16/4 20 6 194 21 24 4 6 12 25 6 66 0 16 0 18 ii 44 29 2 110 21 10 0 0 18 1 30 0 24 7 11 ii6 14 1 0 15 76 10 0 2 35 0 13 1 13 1 7 ii6/4 0 0 0 0 2 0 0 0 5 0 9 0 0 1 0 iii 18 7 1 0 7 30 0 0 13 0 11 7 9 1 2 iij6 3 0 0 0 0 1 11 0 2 0 7 0 1 3 0 iil6/4 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 IV 69 1 26 54 112 20 0 2 331 14 72 0 32 7 25 IV6 14 5 1 3 24 1 1 0 18 16 17 0 31 5 2 Iv6/4 5 0 1 6 2 1 0 0 6 0 2 0 2 4 4 V 54 1 47 27 38 0 11 5 73 1 838 4 23 1 S2 V6 6 5 1 5 6 6 0 0 20 0 49 31 8 1 16 v6/4 4 17 2 8 11 11 0 0 13 0 20 3 9 0 42 vi 26 20 4 23 29 4 2 0 38 6 30 0 140 0 21 vi6 7 1 1 4 7 1 0 0 5 0 2 0 4 22 0 vi^4 0 0 0 2 9 4 0 0 3 4 3 0 0 0 0 vii® 5 0 0 11 6 5 0 2 8 4 22 4 10 2 19 viio6 0 18 0 14 18 3 1 0 4 0 9 5 13 0 28 viio6/4 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 72

From Table 8 , it can be seen that some chords were identified as one or two particular incorrect chords more times than they were identified as the correct chord. Examples are these misidentifications are these; ii® as IV, iii as I®, iii®D as I^, vi® as I, and vii°® as V and v f. Also, the iii®^ was misidentified as V as often as it was identified correctly.

Table 9 shows the most frequent confusions for each chord. 73

Table 9

Frequent Chord Confusions: Experiment 1

For Chords answered more often incorrectly than correctly:

Chord Student answer % of time

ii IV 15.9 ii6 IV 23.6* iii l6 26.7* üi6T V 28.9+ üi6D ( 46.4* üi6D V 24.2 IV6 IV 25.9 vi I 12.3 vi6 I 33.7* viio6 V 27.6* vii06 v5 14.9*

For Chords answered more often conectly than incorrectly:

Chord Student answer % of time

I l6 2.7% I IV 2.7% l6 I 112% V 152% IV I 10.4% IV V 9.5% V I 6.0% V6 iii 12.5%

Legend: * This confusion occurs more often than the correct answer. + This confusion occurs the same number of times as the cwrect answer. 74

For chords answered more often incorrectly than correctly, the most common confusion was with a chord in the same general function category—tonic, subdominant or dominant. More often than not, the iii^ chord was identified as a dominant functioning chord regardless of its actual usage.

In addition to having the same function, the iii 6 and the dominant functioning V or

I4 also share the same bass note. This was not the only instance of this source of double confusion. Other examples were the confusions of the IV for ii^, I^ for iii,

I for vi^, V for V 4 , and the V 4 for vii° 6 . Also, the above pairs of chords share two notes in common.

Another type of confusion students made was one of position. Examples of this type of confusion is the identification of a IV^ as IV, I as I® and I^ as I.

Discussion

Experiment 1 investigated the relation of the order of four tasks and of specific chord collections to the student's analysis score. The following conclusions can be drawn from the statistical analyses of the data;

1. The sequence of the quality task in the order did not affect the score on the analysis task. For the remaining 3 tasks, the order FBS—function, bass and then soprano task-resulted in the best score on the analysis.

2. The underlying pattern of chordal function seemed to affect the score on the analysis task. 75 3. Some specific chords were easier for students to identify. For example, primary triads were easier than secondary triads.

The results shown in Figures 10-17 indicate that the sequence of the quality task did not affect the analysis scores. Perhaps, the reason for this is that subjects already listen for the quality when providing an analysis. Therefore, having the identiRcation of the quality as a separate task provides no additional information because the sequence of the task does not matter.

That higher analysis scores are achieved when the order FBS is used likewise seems explainable. Subjects, when trying to identify the function of the chords in the progression, likely concentrate on the Roman numeral and position designations for the chords and then fit the chord analysis into one of the function categories. Thus, the subjects may have already provided an analysis of the progression mentally. So it makes sense that higher scores result when the function task is first; the students have, in a sense, already provided the analysis twice.

If subjects cannot identify the chord after completing the function task, the requirement of providing a correct bass line next helps the subjects by forcing them to attend to a note of the chord. At this point, subjects can make a better guess at

the chord identification. In addition, if subjects provide a correct bass line and

know the chords, they can derive the position of each of the chords, thereby adding to their score. 76

If subjects still can not identify the chords, providing a correct soprano line after the bass gives them two notes of the chord, thereby reducing the number of possibilities. If they already know the chord, providing the soprano will add little information.

The pattern of general chord functions in the progression does seem to have an effect on the analysis scores. As the results in Table 4 show, the only pattern associated with consistently low scores was the pattern that did not begin on a tonic chord. In this pattern, the first chord, a subdominant, was not followed directly by a tonic triad. This pattern may result in more diffîcult progressions because the key is not established as quickly as in progressions following the other patterns. This conclusion is verified by the fact that using pattern 4 (TTDTSDT) resulted in easier progressions. This pattern clearly establishes the key early through the use of an authentic cadence progression (TTDT). Pattern number 3 (TSTSDDT) also produces easy progressions. This pattern also establishes the tonic at the beginning, although a bit less definitely, through the use of a plagal cadence progression. It seems that to achieve high analysis scores, subjects need to have the key established as soon as possible.

Anyone who has taught aural training has noticed that subjects find some chords more difficult than others. The results in the current experiment, in particular the

results shown in Tables 7 and 8 , confirm this observation. It is interesting that the results in Table 7 indicate that secondary triads are identified incorrectly more often than primary triads. This problem may be due to the fact that teachers 77 typically begin teaching harmonic dictation with only the primary triads, saving the secondary triads until later. (If this conclusion is tme, teachers should consider introducing secondary chords earlier in the training.) Another explanation may be that the primary triads are simply easier to identify. So, when subjects are in doubt, they assume that tonic, subdominant or dominant functions require primary chord designations.

From the frequent chord confusions, as shown in Table 9, one can draw some conclusions about what the subjects will answer when they are in doubt. Subjects tend to confuse the chord played with one that

1 . has the same function category.

2 . has two notes in common with the chord played. 3. has the same bass note. 4. has the same Roman numeral designation but a different position.

Otherwise, when subjects guess, they choose a primary triad.

Table 9 also provides examples of subjects confusing secondary triads with chords in the same function category. For example, the ii chord was identified as a IV (both are subdominant in function), the vi chord as a I (both are tonic in function) and the vii ° 6 as a V (both are dominant in function.)

An example of the second type of confusion was the identification of the chord as a iii chord. The two chords have two notes in common—the fifth and seventh scale degrees. More over, the remaining note in the chord-the second scale 78 degree—is only a step away from the remaining note of the iii chord—the third scale degree. The difference in the two chords is not pronounced; therefore, subjects may confuse them.

Several examples of the subjects guessing a chord with the same bass are shown in

Table 9. When the ii^ chord is played, subjects identified the chord as a IV. Both chords have the fourth scale degree in the bass. Likewise the subjects answered when iii was played, ^ or V when iii^ was played, I when vi^ was played, and

when vii ° 6 was played.

When identifying the primary triads incorrectly, subjects often got the Roman numeral designation right, but placed the chord in an incorrect position. Examples of this confusion are these identifications: for I, I for I^» and IV^ for IV.

Beyond these confusions, subjects tended to identify doubtful chords as primary triads. Examples of this are the misidentification of I as TV, IV as I, IV as V, and V as I. It is significant to note that primary chords were more often confused with each other then with other diatonic chords. Confusing I, IV and V chords may result from the subject losing the sense of tonic. To avoid this, the subject needs to have the option of reestablishing the tonic while completing a harmonic dictation exercise.

The chords that were confused with one or two other chords more often than they were identified correctly, as indicated in Table 9, were those that followed 3 of the 79 aforementioned confusion characteristics. These chords were always primary triads of the same function category as the correct triad, and they had whose bass notes that were the same as the bass note of the correct triad. It can be concluded that, if more than one confusion category is present, chords are more likely to be answered incorrectly than correctly.

Because of a problem with the random generation of the orders and the progressions in the execution of Experiment 1, the conclusions discussed above, although seemingly valid, lacked statistical proof; they needed to be verified through a second experiment. So, a second experiment was undertaken; it is discussed in Chapters 4 and 5. CHAPTER IV

EXPERIMENT 2: MATERIALS AND METHOD

Experiment 2 was designed to determine which order of three tasks—identifying the

general function of each chord, notating the soprano and notating the bass lines—best facilitates the analysis of harmonic dictation exercises and whether the pattern of general chord functions—tonic, subdominant and dominant—in progressions affects the analysis scores. Six different patterns of general chord function were used:

Pattern 1: TTSSDDT Pattern 2: TTSTSDT Pattern 3: TSTSDDT Pattern 4: TTDTSDT Pattern 5: TDTSDDT

Pattern 6 : SDTTSDT

Based on the analysis of Experiment 1, the results expected from Experiment 2 are presented in the following hypotheses:

1. Analysis scores will be affected significantly by the order of the tasks. Highest scores will be attained by students using the order FBS.

2. Analysis scores will be significantly affected by the pattern of general chord functions in the progression. Highest scores will be attained by students working on progressions that emphasize the tonic early (e.g.. Pattern 4-TTDTSDT). 80 81

3. The performance of the individual subjects will be different from each other.

4. Students from the two different schools (i.e., The Ohio State University and Youngstown State University) will attain similar analysis scores.

5. There will be one order of the tasks that results in higher analysis scores regardless of the pattern of chordal functions.

Statistical Design

The design for Experiment 2 was a Partially Balanced Incomplete Block (PBIB)

6 x6 Latin Square associated scheme^ as shown in Table 10. The two variables

were the order of tasks and the pattern of general chord functions.

^ According to Ott, "The Latin Square design can be used to compare ( treatment means in the presence of two extraneous sources of variability, which are blocked off into ( rows and t columns. The t treatments are then randomly assigned to the rows and columns so that each treatment appears in every row and every column of the design." (Ott 1977,248-249) A block is an "extraneous source of variability." (Ott 1977,247) In a balanced design, for each pair of independent variables, one independent variable ^rpears the same number of times as a second independent variable. (Ott 1977,486) 82 Table 10

6 X6 Latin Square Design for E 3 q)eriment 2

Treatment Codings

Patterns 1 2 3 4 . 5 6 O idere A 1 1 2 3 4 5 6 B l 7 8 9 10 11 12 C l 13 14 15 16 17 18 Di 19 20 21 22 23 24 E l 25 26 27 28 29 30 F 1 31 32 33 34 35 36

Student Pattem(s) Qider(s) Progressions

1 1 all 1 7 13 19 25 31 2 2 aU 2 8 14 20 26 32 3 3 an 3 9 15 21 27 33 4 4 an 4 10 16 22 28 34 5 5 an 5 11 17 23 29 35 6 6 an 6 12 18 24 30 • 36

7 a ll A 1 2 3 4 5 6 8 a ll B 7 8 9 10 11 12 9 a ll C 13 14 15 16 17 18 10 a ll D 19 20 21 22 23 24 11 a ll E 25 26 27 28 29 30 12 a ll F 21 32 33 34 35 36

The students' scores on the progressions constituted the dependent variable. The total score for each exercise was the total of the scores on each of the tasks with 83 each item—the notation of the soprano and bass lines, and the identification of the function, quality, Roman numeral and position of each chord—valued at one point.

I wrote a computer program to collect the data for the analysis. Its features are described later in this chapter.

Subjects

The subject pool for Experiment 2 consisted of the students, music and non-music majors, enrolled in sophomore Aural Training (Music 425 and 426) at The Ohio State University and the students either currently or recently enrolled in sophomore theory (Music 630-632) at Youngstown State University. As an incentive to complete the experiment, subjects participating in the study were given a quiz grade of A if they were enrolled in a theory class that quarter. The Musical Sleuth Game, used as an incentive in Experiment 1, was discontinued; it proved to be a less effective incentive than the quiz grade.^ Forty-foiu’ students participated in the study. One Ohio State student was eliminated because he misunderstood the directions and failed to provide an analysis for the progressions. Data from the remaining 43 students were used in the analyses of the results.

All 43 subjects were music majors. One subject's major was unknown. Seventeen of the subjects were female and 26 male. In the majority of cases, the

^ Only 50% of the students (i.e., 16 students) participating in Experiment 1 tried the Musical Sleuth game, accumulating a total of 170 points. Of the 16 students who tried the game, 9 tried only 1 situation. 84 subject's major instrument was a woodwind (11) or keyboard (11) instrument. In the remaining cases, the subject's major instrument was voice (9), a brass (7) or a string (4) instrument. One subject did not indicate her instrument.

Computer Program

The computer program used in Experiment 2 was written in Pascal, using the Lightspeed Pascal compiler, for the Macintosh Plus computer with a mouse but no keyboard. The program was based on the one used in Experiment 1, but it had these major modifications:

1. For each progression, the student completed only three tasks—the identification of the function of each chord, and the notation of soprano and bass lines—instead of four. The identification of the chord qualiQr was eliminated as a separate task.

2. Students provided a complete harmonic analysis only after finishing the last task instead of after completing each task.

3. Students could see their answers to previous tasks while working on the later tasks and the analysis. Furthermore, the students could alter or complete the answers to the previous tasks while working on the later tasks and the analysis.

4. Students were no longer required to provide an answer for every chord before continuing with the next task.

Experiment 1 showed that the sequence of the quality task did not affect the score on the harmonic dictation exercises. Therefore, for Experiment 2, the identification of the quality of each chord was not included as a separate task, but was integrated

into the analysis task. By eliminating the separate quality task, the number of 85 tasks was reduced from 4 to 3 and the number of the permutations reduced from 24

to 6 . Every subject could now complete a harmonic dictation exercise using all of the order permutations.

In Experiment 1, the student was asked to provide a complete harmonic analysis of the progressions after each task in an attempt to determine whether the task had contributed to the attainment of higher analysis scores. During the process of analyzing the data from Experiment 1,1 learned it was not necessary to have the student provide an analysis after each task. The information needed to discover the effect of each task could instead be derived from the final analysis alone by plotting the final analysis score when each task occupied each sequence position. Thus, in

Experiment 2, the student was asked to provide an analysis only after all tasks were completed. Having the students provide only one analysis also served to reduce the amount of time required of each subject to complete the project.

Initially, the computer program used in Experiment 1 was designed to show the subjects their answers to previous tasks on the analysis screen. Since they could not change or erase wrong answers, displaying the answers proved to be distracting.

Thus, the answers were subsequently removed from the screen. In Experiment 2, the answers for the previous tasks were present on the analysis screen and the students were allowed to change the answers for previous tasks. This change seemed fitting because this procedure is nearer to that followed in a normal classroom situation. 86

Finally, in Experiment!, the "Done" button appeared on the screen only after the subject had provided an answer for every chord. This procedure was changed in

Experiment 2 since students do not always provide an answer for every chord in the classroom situation. Students were thus allowed to proceed to the next task or even quit the exercise without providing complete answers.

In Experiment 2, students proceeded through the computer program as follows. The subject started the harmonic dictation program by double-clicking the "MATE" (Music Aural Training Exercises) icon on the screen. After removing the title screen by clicking the "Continue" button, the subject saw the general directions displayed on the second screen and proceeded to complete six harmonic dictation exercises. Each exercise involved a different progression. All progressions were written in major keys with key signatures of no more than two flats or sharps. Progressions contained seven diatonic triads set in foiu* voice (SATB) texture, and these triads appeared in various positions—root position, Erst or second

inversion—and spacings—closed or open. There were no seventh chords. Each progression conformed to one of these patterns of general chord functions:

Pattern 1: TTSSDDT Pattern 2: TTSTSDT Pattern 3: TSTSDDT Pattern 4: TTDTSDT Pattem 5: TDTSDDT

Pattern 6 : SDTTSDT

The chords classified as tonic, subdominant and dominant were: 87 Tonic: I, vi, vi^, ill, non-cadential iii^ Subdominant: IV, IV^, ii, ii^ Dominant: V,V^, viio,vii°^,cadential , cadentialiii^

Twelve new progressions were added to the 24 progressions used in Experiment 1,

so that now there were 6 progressions following each of the 6 patterns of general chord functions. The progressions are found in Appendix D,

The set of progressions the student received depended on the student number (i.e., the number that was the name of the student's disk), as shown in Table 10. For

example, if this number ranged from 1 to 6 , the student heard six progressions, all of which followed the same pattem of general chord functions. If the number ranged from 7 to 12, the student heard six progressions, each following a different function pattem. The sets of six progressions were fixed in the program; students

with the same student number received the same six progressions in the same order. Students with different student numbers received a different set of progressions using a different order of tasks.

Each harmonic dictation exercise entailed three tasks presented in any order:

identify the general function (tonic, subdominant or dominant) of each chord, notate the bass line, notate the soprano line.

After completing all three tasks, the subject was required to provide a complete harmonic analysis, indicating the quality, the Roman numeral chord designation, 88 and the Arabic numeral position indicator for each chord. In all, each exercise required four steps.

The order of the tasks for the subject also depended on the assigned disk number, as

shown in Table 10. If the number ranged from 1 to 6 , a different order of the tasks was used for each progression. If the number ranged from 7 to 12, all progressions were presented using the same order of the tasks. For the sake of illustration here, this order of tasks will be presumed:

1 . identify the general function of each chord.

2 . notate the bass line. 3. notate the soprano line.

After showing the general directions, the program presented a series of screens giving detailed instructions for using the program. At the end of the instructions, the student was given the option to continue or exit the program. Clicking "Exit" ended the program and returned the student to the Macintosh desktop. Clicking

"Continue" allowed the student to continue with the harmonic dictation exercises.

The answer screen is shown in Figure 19. 89

Sop: g W

„ s . : S

Function: Analysis: D:

OT OS Qi GlllQü Qd CM o l o ; CD Oil Oiu OUI OUll Om OB

[ P l o y 1 [ Done )

Figure 19

Experiment 2: Answer Screen

Several elements were always present on the screen. The words "Sop," "Bass," "Function" and "Analysis" at the left side of the screen marked the position of the blanks for the subject’s answers. Buttons marked "Play" and "Done" always appeared at the bottom of the screen. Clicking the "Play" button caused the progression to be played once, but replays could be summoned any number of times and at any time. The progressions were played on the Macintosh Plus's built-in Digital/Analog Convertor using waveforms created for Blombach’s MacGAMUT programs. Clicking the "Done" button ended the current task and caused the next one to be displayed. Clicking either the "Play" or the "Done" 90 button caused the following infonnation about the subject's performance to be written to disk:

1 . student number

2 . progression number 3. Older number 4. the order of the tasks 5. the number of times this progression's data were written to disk

6 . the task [Q(uality), F(unction), B(ass), S(oprano), or A(analysis)] the student was working on 7. the time

8 . the date 9. whether the subject clicked the Play or the Done button

1 0 . number of times the progression had been played to this point

1 1 . the subject's answer for each task

1 2 . the subject's grade on each task

Since the function task was the first task in this illustration, the screen showed, next to the word "Function," seven blanks (one corresponding to each chord in the progression). In the lower left comer of the screen (under the word "Analysis") were radio buttons, one corresponding to each of the three functions, tonic (T), subdominant (S) and dominant (D).

The subject heard the progression played once. When the subject clicked one of the radio buttons for function, the circle next to the function was highlighted. After selecting a function, the subject clicked any of the blanks corresponding to the chords in the progressions, and the function selected was placed on the blank(s). To edit the answer, the subject clicked another radio button and a blank already containing a function designation. This caused the function designation on the 91 blank to be replaced by the current choice. Such editing could continue at any time, or the subject could click "Done" to end this task.

Clicking "Done" produced the answer blanks for the next task. In this illustration, the next task was to notate the bass line. Therefore, beside the word "Bass" appeared a staff showing a bass clef, key signature and time signature. The progression was played once. To write a bass note, the subject positioned the arrow (now changed into a notehead) on a line or space of the staff and clicked the mouse. This caused a note of correct duration to be written at that position. The subject could change any note by repositioning the notehead on the staff and

clicking the mouse. While working on the bass line, the subject could edit any of

the answers for the previous function task. At any time, the subject could proceed to the next task by clicking "Done."

The next task was the notation of the soprano line. Therefore, near the word

"Sop," a staff with treble clef, key signature and time signature appeared. The progression was played once. To write a soprano note, the subject positioned the arrow (now changed into a notehead) on the line or space of the staff and clicked the

mouse. This caused a note of correct duration to be written at that position. The

subject could change any note by repositioning the notehead on the staff and clicking the mouse. The subject could continue to edit the soprano line or either of the previous tasks, or could click "Done." By clicking "Done," the subject proceeded to the analysis of the progression. 92

The last task was indicating a complete harmonic analysis for the progression. The screen displayed seven blanks (one for each chord in the progression) next to the word "Analysis." At the bottom of the screen, next to the radio buttons for the functions, were seven radio buttons with Roman numeral designations, four radio buttons containing the four qualities, and three radio buttons containing the Arabic numeral indicators for the chord positions. The Roman numeral designations were displayed in upper case only so as not to indicate the quality of the chord. The quality radio buttons were marked "d" for diminished, "m" for minor, "M" for major and "A" for augmented. The radio buttons for the positions of the triads were marked: | for root position, g for first inversion, and^ for second inversion.

The progression was played once. To provide the analysis, the subject first selected a Roman numeral, a quality and an Arabic numeral designation, then clicked all the appropriate blanks. This procedure produced a Roman numeral, in upper or lower case, and an appropriate "+" or symbol to indicate the quality of the chord and position. The subject could provide the analysis in any order desired. Editing was accomplished by clicking new Roman and Arabic numeral designations, quality choice, and the corresponding blank. While working on the analysis, the subject could edit any answer for the fimction, bass and soprano tasks.

When answers were deemed correct, the subject clicked the "Done" button and ended

After the subject clicked "Done," a screen showing the subject's score and the correct answers for all tasks was displayed, as shown in Figure 20. 93

HARMONIC DICTATION CORRECT ANSWER Your score on this progression is 100 %.

lii À m à m r ; Vi I Iff ii I§ vli'G I m M M m M d M TTSSDDT

[ Ploy ] ( Continue ] [ Euit ]

Figure 20 Experiment 2: Correct Answer Display

One point was given for each correct answer on the six tasks-notating the soprano and bass notes, and identifying the function, quality, Roman numeral and position designations for each chord. The score was equal to the subject's score divided by the total number of points possible (i.e., 42).

Clicking "Play" caused the progression to be played once. Clicking "Exit" stopped the program and returned the subject to the Macintosh desktop. If the subject clicked "Continue," a screen was displayed showing the number of progressions 94 that were completed and the number that remained to be done. Clicking

"Continue" on this screen allowed the subject to continue to the next progression.

When all six progressions were finished, a separate screen displayed a message stating that the subject had completed the required six progressions. Clicking the

"Exit" button, the only button on this screen, ended the program and returned the subject to the Macintosh desktop. The subject could not restart the program using this disk.

Procedure

In Winter and Spring quarters 1989, students at The Ohio State University and Youngstown State University were asked to complete the experiment following the instructions described above. In return for completing at least six progressions, the students enrolled in Aural Training class that quarter were given a quiz grade of A.

When subjects arrived at the lab to complete the progressions, the monitor

assigned unused disks in numerical order. Students wrote their names on the disk labels and, if necessary, completed the Student Data sheet (see Appendix E). They

were given a copy of the directions and asked to continue with the exercises as explained in the Computer Program section of this chapter. 95

When the students finished the program, they clicked the "Exit" button. They then returned the disks and the completed Student Data sheets to the monitor and completed the Student Survey sheets, shown in Appendix E.^

The disks were gathered and the data were analyzed by methods discussed in Chapter

5.

^ Results of the Student Survey are shown in Appendix F. CHAPTER V

EXPERIMENT 2: STATISTICAL ANALYSIS

The data collected firom Experiment 2 were analyzed to determine whether the order of tasks, the pattem, the interaction of pattem and order, the individual student or the school of the student affected the analysis scores on the harmonic dictation exercises. In addition, information was sought as to whether some progressions and chords are easier than others for students to identify. Experimenting with various scoring procedures also provided answers to questions about some of the grading methods used for harmonic dictation exercises.

Results

In order to use the Statistical Analysis System (SAS) for the analysis, I combined the individual data files into one large file on the Macintosh and uploaded the data to Youngstown State University's Amdahl mainframe. Each line of data consisted of the following information:

1 . student number.

2 . number of progressions started. 3. progression number. 4. order number. 5. order (as characters B, S, F, and A). 96 97

6 . number of times data were written to disk. 7. number of times the example was played.

8 . time and date information. 9. current task.

1 0 . when data were recorded: I = initial P= when ask for progression to be played D = when done with task wswers for the quality task.

1 1 . answers and score for the function task.

1 2 . answers and score for the soprano task. 13. answers and score for the bass task. 14. answers and score for qualiQr identification. 15. answers and score for Roman numeral identification. 16. answers and score for position designation.

The scores on each task were equivalent to the number of correct answers given. A score of 7 points could be attained for each task.

A Pascal program was written to add the following information to each line of data: the university of the student (OSU or YSU); the progression's pattem of general chord functions (e.g., 1 for TTSSDDT); and a total score. The total score was equivalent to the sum of the scores on the function (fgrade), bass (bgrade) and soprano (sgrade) tasks, and the quality (qgrade), position (pgrade) and Roman numeral (rgrade) identification as:

total = rgrade + pgrade + qgrade + fgrade + sgrade + bgrade

The total score could range from 0 to 42 points. 98

Data in the current format were analyzed using an analysis of variance. The expected results are stated in the following hypotheses:

1. Analysis scores will be affected significantly by the order of the tasks. Highest scores will be attained by students using the order FBS.

2. Analysis scores will be significantly affected by the pattem of general chord functions in the progression. Highest scores will be attained by students working on progressions that emphasize the tonic early (e.g., Pattem 4 -TTDTSDT).

3. The performance of the individual subjects will be different from each other.

4. Students from the two different schools (i.e.. The Ohio State University and Youngstown State University) will attain similar analysis scores.

5. There will be one order of the tasks that results in higher analysis scores regardless of the pattem of chordal functions.

The results of the analysis of variance (ANOVA) using the total score as the dependent variable are shown in Table 11. 99

Table 11

General Linear Models Procedure for Total Score

Source df SS F pr > F

Model 8 8 19062.590 5.33 0 . 0 0 0 1 Error 175 7108.557 Corrected Total 263 26171.148

Source df Type m SS F pr > F

Order 5 176.892 0.87 0.5018 Pattem 5 551.500 2.72 0.0217

School 0 0 . 0 0 0

Student 42 10439.844 6 . 1 2 0 . 0 0 0 1 Order/Pattern 25 2225.831 2.19 0.0017

Pattern/School 5 205.713 1 . 0 1 0.4116

Order/School 5 204.129 1 . 0 1 0.4163

Legend: df = degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability

The results indicate no significant effect of order ( F(5,175) = 0.87, p > .50), thus they contradict Hypothesis 1. However, the results do indicate significant

differences of pattem, of individual students and of the interaction of order and pattem. 100

The significant effect of function patterns ( F(5.175) = 2.72, p < .03) supports

Hypothesis 2. Post hoc application of the Tukey HSD (studentized range) test^ indicates that signiHcantly (p < .05) higher scores were attained on progressions following pattem 4 (TTDTSDT). Also, significantly (p < .05) lower scores were

achieved on progressions following pattem 6 (SDTTSDT).

Also significant is the interaction of order and pattem ( g(5.175) = 2.19, p < .01), and this contradicts Hypothesis 5. To see the interactions, the mean scores for each pattem (the y-axis) were plotted by order (the x-axis), as shown in Figure 21. Many interactions are evident firom the number of crossed lines.

^ An Analysis of Variance (ANOVA) tells the investigator only that a specific factor has a significantly effect on the results o f the experiment The Tiikey test indicates which of the fiactw's treatments is producing the effect by constructing simultaneous confidence intervals for all pairs o f treatment differences. The confidence intervals are tested using a set confidence level, i.e., alpha. (Ott 1977,389-392) OoaHem I □N ttfm 2 3 101 37.5.

325.

/\

275.

I

22.5.

175

12.5

or4»r order t^FSS; order 2’8SF; order 6«eFS

Figure 21 Interaction Between Order and Pattem Using Total Score 102

Figure 21 also shows that using Order 2 (FBS) results in the highest scores for all patterns except one, pattem 5 (TDTSDDT). In the case of pattem 5, using order 1

(FSB) or order 6 (BFS) produced higher scores than using order 2. Post hoc application of the Tukey HSD test, set at .05 alpha, conOrms that subjects using order 2 (FBS) attained significantly (p < .05) higher scores than subjects using all other orders except order 1 (FSB).

The significant effect of the individual student ( £(42.175) = 6.12, p < .001) supports Hypothesis 3. To determine what attributes of the student made this variable so significant, the subjects were recategorized according to their gender and their major instmment. ANOVAs were Üien ron using these recategorizations, and the results are shown in Tables 12-14 (students by gender) and 15 (students by instmment class). 103

Table 12

General Linear Models Procedure for Total Score

Students Classified by Gender

Source (f SS F pr > F

Model 48 9886.240 2.72 0 . 0 0 0 1 Enor 215 16284.908 Corrected Total 263 26171.148

Source (f Type m s s F pr > F

Order 5 1851.183 4.89 0.0003

Pattem 5 1942.295 5.13 0 . 0 0 0 2

School 1 13.596 0.18 0.6722

Gender 2 1263.494 8.34 0.0003 OrderyPattem 25 2241.469 1.18 0.2565 Pattern/School 5 607.829 1.60 0.1599 Order/School 5 213.556 0.56 0.7276

Legend: d f= degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability

As Table 12 shows, the effect of the gender of the student is statistically significant ( F(2.215) = 8.34, p < ,001). Post hoc application of the Tukey HSD test indicates that male students scored significantly higher (p < .05) than female students on the harmonic dictation exercises. 104

To determine if males score higher than females at both schools, ANOVAs were run on students from each school recategorized by gender. The results of these

ANOVAs are shown in Tables 13 and 14.

Table 13

General Linear Models Procedure for Total Score YSU Students Classified by Gender

Source df SS F pr > F

Model 1 1 2864.499 3.22 0.0007 Enor 132 10680.055 Corrected Total 143 13544.889

Source df Typein SS F pr > F

Order 5 1149.714 2.84 0.0180 Pattem 5 1288.059 3.18 0.0095 Gender 1 109.054 1.35 0.2478

Legend: d f= degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability

As the results in Table 13 show, the gender of the students at YSU was not significant (p > .24). Post-hoc testing using the Tukey HSD procedure, however. 105 indicated that male student scored significantly higher (p < .05) than female students at YSU.

The results shown in Table 14, however, indicate that OSU students of different gender scored significantly different scores (p < .0001). Post-hoc testing using the

Tukey HSD procedure indicated that male students scored significantly higher (p <

.05) than female students at OSU.

Table 14

General Linear Models Procedure for Total Score OSU Students Classified by Gender

Source (f SS F pr > F

Model 37 7012.120 2.79 0 . 0 0 0 1 Error 82 5578.670 Corrected Total 119 12590.791

Source Type m SS F pr > F

Order 5 948.630 2.79 0.0224 Pattem 5 964.393 2.84 0.0206

Gender 2 1655.329 12.17 0 . 0 0 0 1 Order/Pattern 25 1791.913 1.05 0.4134

Legend: df = degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability 106

The results shown in Table 15 indicate that there is no significant difference between subjects having different major instruments Q£(5,212) = 1,91, p > .05).

Table 15

General Linear Models Procedure for Total Score Students Classified by Instrument

Source (f SS F p r> F

Model 51 9380.838 2.32 0 . 0 0 0 1

Error 2 1 2 16790.310 Corrected Total 263 26171.148

Source df Typein SS F pr > F

Older 5 1697.276 4.29 0 . 0 0 1 0

Pattem 5 2137.758 5.40 0 . 0 0 0 1

School 1 147.258 1 . 8 6 0.1741 Instrument 5 758.092 1.91 0.0932 Qider/Pattem 25 2229.891 1.13 0.3152 Pattern/School 5 953.703 2.41 0.0377 Order/School 5 228.396 0.58 0.7178

Legend: df = degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability 107

Both Tables 12 and 15 indicate no significant difference between students from the two different schools (p < .05); thus they support Hypothesis 3. In addition, both

tables indicate that the effect of order is significant (p < . 0 0 1 ), but that the interaction of order and pattem is not significant (p > .25), contrary to the results shown in Table 11.

The grading procedure used above did not account for the relative importance of the Roman numeral identifications and the function, bass and soprano tasks. So the grading procedure was changed to reflect this importance by weighting the subject's answers on these tasks. The weighted total was calculated as;

weighted total =

(rgrade x 2 ) + pgrade + qgrade + (fgrade x 2 ) + (bgrade x 2 ) + (sgrade x 2 )

The results of the analysis of variance (ANOVA) using the weighted total score as the dependent variable are shown in Table 16. 108

Table 16

General Linear Models Procedure for Weighted Total

Source (f SS F pr > F

Model 8 8 57088.958 5.64 0 . 0 0 0 1 Enor 175 20134.371 Corrected Total 263 77223.329

Source F

Order 5 562.439 0.98 0.4329 Pattern 5 1637.815 2.85 0.0169

School 0 0 . 0 0 0

Student 42 30853.080 6.38 0 . 0 0 0 1 Order/Pattern 25 6817.659 2.37 0.0006 Pattern/School 5 437.302 0.76 0.5797 Order/School 5 527.128 0.92 0.4717

Legend: d f= degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability

The results of this ANOVA are similar to those using the total as the dependent variable: there is no signifrcant effect of order (F(5,175) = 0.98, p > .40). However, the results do indicate significant effects of pattern ( E(5,175) = 2.85, p < .05), student ( F(42,175) = 6.38, p < .001), and of the interaction of order and pattern ( F(5,175) = 2.37, p < .001). 109

Post hoc application of the Tukey HSD test was completed for order, pattern, school and the interaction of order and pattern. The results of the Tukey tests are similar to those using the Total score as the dependent variable: Scores for progressions following pattern 4 (TTDTSDT) were significantly higher (p < .05) than scores for progressions following other patterns, while scores for progressions

following pattern 6 (SDTTSDT) were significantly lower than those for progressions following other patterns. The graph for the interaction between order

and pattern is shown in Figure 22. It also shows that subjects attained the highest

scores on all patterns except pattern 5 when using order 2 (PBS). The Tukey test

for the effect of order indicates also that subjects using order 2 attained significantly higher scores than subjects using other orders. 110

I I

3 4 ord*r ordtr 1=fS8; ordtr 2«fBS; order 3»SFB; order 4=SCF; order 5*BSF; order 6=GfS

Figure 22 Interaction Between Order and Pattern Using Weighted Total I l l

ANOVAs run on data recategorizing students by gender and instrument, where

Weighted Total was the dependent variable, also show results similar to those above. The gender of the student was a significant (F(2,215) = 8.24, p < .001) factor with male students attaining significantly (p < .05) higher scores than female students. The major instrument of the student, however, was not statistically significant (F(5,212) = 2.11, p > .05). In addition, the school the students attend was not significant (p > .24).

For a third ANOVA, the total score, now designated as Totall,’ was equivalent to the score on the function, bass and soprano tasks, as before, plus a new combined analysis score (ascore). A chord was now counted as correct if the Roman numeral designation, position identification gn^ quality identification were correct. Totall was calculated as:

totall = ascore + fgrade + sgrade + pgrade

Totall ranged from 0 to 28 points. The results of the analysis of variance (ANOVA) using Totall as the dependent variable are shown in Table 17. 112

Table 17

General Linear Models Procedure for Totall

Source d SS F pr > F

Model 8 8 11452.918 6.35 0 . 0 0 0 1 Enor 175 3584.946 Corrected Total 263 15037.864

Source d Type m SS F pr > F

Older 5 120.545 1.18 0.3224 Pattern 5 300.758 2.94 0.0143

School 0 0 . 0 0 0

Student 42 6096.816 7.09 0 . 0 0 0 1

Order/Pattem 25 1323.609 2.58 0 . 0 0 0 2 Pattern/School 5 50.450 0.49 0.7815 Order/School 5 72.249 0.71 0.6201

Legend: df = degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability

Again, similar results were attained: There was no significant effect of order ( F(5,175) = 1.18, p > .30). There were significant effects of pattern (F(5,175) = 2.94, p < .05), student ( £(42,175) = 7.09, p < .001), and of the interaction of order and pattern ( £(5,175) = 2.58, p < .001). 113

Post hoc application of the Tukey HSD test (p < .05) again indicated that higher scores were attained on progressions following pattern 4 (TTDTSDT), while lower

scores were attained on progressions following pattern 6 (SDTTSDT). The graph for the interaction between order and pattern is shown in Figure 23. The graph shows that subjects using order 2 (PBS) attained the highest scores on all patterns

except pattern 5 and pattern 6 . However, a Tukey test for the effect of order

indicated that subjects using order 2 attained significantly higher scores those using all other orders. Ooattem 1 □Mttem2 A M ttem S 114 27.5

22.5.

/&1

17.5.

12.5.

75.

-r 1 2 1 4 order order 1 SB; order 2=fBS; order 3*SfB; order 4>S8F; order 5*BSf ; order 6"GfS

Figure 23 Interaction Between Order and Pattern Using Totall 115

ANOVAs using the recategorizations of student by gender and instrument and

Totall as the dependent variable also show results similar to those above. The gender of the student is a significant (F(2,215) = 6.99, p < .01) factor with male students attaining significantly (p < .05) higher scores than female students. Also, the major instrument of the student significantly affected the results (F(5,212) =

2.54, p < .05). However, the school the students attend was not significant (p > .19).

At this point, I tried a new method for grading the subjects' answers on the soprano and bass tasks because the previous method of grading appeared to be too harsh. In the previous method, subjects received credit only if every note was correct. No credit was given if the student started on an incorrect note but correctly notated each interval (i.e., the distance between adjacent notes) of the line. In the new scoring method, credit was awarded for getting the contour of the line correct even though each note of the line was incorrect. A correct starting note for the line was worth one point. For the remainder of the line, each correct interval was worth one point. The new score for the bass line was designated as *bscore' (rather than bgrade) and the new score for the soprano line as 'sscore.' The three total scores tested above were recalculated using the new scores on the soprano and bass tasks as follows: 116 New Total = rgrade + pgrade + qgrade + fgrade + bscoie + sscore

New Weighted Total = rgrade*2 + pgrade + qgrade + fgrade*2 + bscore*2

sscore * 2

New Totall = ascore+ fgrade +bscore + sscore

The results of the analyses of variance using New Total, New Weighted Total and New Totall as the dependent variable are shown in Tables 18,19 and 20.

Table 18

General Linear Models Procedure for New Total

Source (f SS F pr > F

Model 8 8 16786.631 6.03 0 . 0 0 0 1 Error 175 5532.460 Corrected Total 263 22319.090

Source F

Order 5 97.713 0.62 0.6861 Pattern 5 412.124 2.61 0.0266

School 0 0 . 0 0 0

Student 42 9861.070 7.43 0 . 0 0 0 1

OrdCT/Pattem 25 1811.918 2.29 0 . 0 0 1 0 Pattern/School 5 133.033 0.84 0.5219 Order/School 5 166.137 1.05 0.3894

Legend: d f= degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability 117

Table 19

General Linear Models Procedure for New Weighted Total

Source df SS F pr > F

Model 8 8 49319.301 6.67 0 . 0 0 0 1 Error 175 14694.392 Corrected Total 263 64013.693

Source df Type m s s F pr > F

Order 5 240.081 0.57 0.7215

Pattern 5 1136.491 2.71 0 . 0 2 2 0

School 0 0 . 0 0 0

Student 42 29237.117 8.29 0 . 0 0 0 1 Order/Pattem 25 5240.561 2.50 0.0003 Pattern/School 5 223.926 0.53 0.7508

Order/School 5 419.479 1 . 0 0 0.4198

Legend: d f= degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability 118

Table 20

General Linear Models Procedure for New Totall

Source df SS F pr > F

Model 8 8 9697.104 8.23 0 . 0 0 0 1 Error 175 2343.225 Corrected Total 263 12040.330

Source Typein SS F pr > F

Order 5 39.816 0.59 0.7040 Pattern 5 185.711 2.77 0.0194

School 0 0 . 0 0 0

Student 42 5843.667 10.39 0 . 0 0 0 1

Order/Pattem 25 930.286 2.78 0 . 0 0 0 1 Pattern/School 5 11.690 0.17 0.9718 Order/School 5 53.497 0.80 0.5517

Legend: d f= degrees of freedom; SS = Sum of Squares F = ratio of variances; pr = probability

In each case, the results were similar to those achieved in the first three ANOVAs:

The order of the tasks by itself was not significantly different (p > .70), but there were significant differences between the individual function patterns (p < .05),

individual students (p < . 0 0 1 ) and the interaction of order and pattern (p < . 0 0 1 ). 119

Post hoc application of the Tukey HSD test for each variable confirms the findings above: Subjects attained higher scores (p < .05) when their progressions followed pattern 4 (TTDTSDT), while subjects attained lower scores when the progressions

followed pattern 6 (SDTTSDT). The graphs for the interaction between order and pattern for the three totals are shown in Figures 24,25 and 26. The graphs show that subjects using order 2 (FBS) attained the highest scores on all patterns except

pattern 5 and pattern 6 . However, in each case, Tukey tests for the effect of order

indicate that subjects using order 2 attained significantly higher scores than subjects using all other orders. Ooattem 1 AwHern 3 120 37.5.

32.5

27.5

I

22.5

17.5.

12.5. 0 2 3 4 5 6 7 order order W S8; order 2>FBS; order S>SFB; order 4>S8F; order 5>8SF;arder6s8FS

Figure 24 Interaction Between Order and Pattern Using New Total 121

4 5.

I

25.

3 4 order

order I »FS8; order 2»fBS; order 3«SfB;order4»S8F; order 5-BSF; order 6-BFS

Figure 25 Interaction Between Order and Pattern Using New Weighted Total 122

I V

order order l*fS8; order 2=FBS; order 3=SFB; order 4=S8F; order 5=BSF; order 6=8FS

Figure 26 Interaction Between Order and Pattern Using New Totall 123

ANOVAs using the recategorizations of student by gender and New Total, New Weighted Total, and New Totall as the dependent variable show a significant effect of gender (p < .01). In each case, male students attained significantly (p < .05) higher scores than female students. ANOVAs using the recategorization of subjects by major instrument and the New Total and New Weighted Total as dependent variables show no significant differences (p > .05). However, the

ANOVA using New Totall as the dependent variable indicates that students with different major instruments are statistically different (F(5,212) = 2.71, p < .05). In this case, students playing keyboard instruments attained higher scores than all other students, but scores statistically higher (p < .05) than only woodwind, voice and brass majors. In addition, the school the students attend is not significant (p >

.05) in all cases except when New Total is the dependent variable and the students are categorized by instrument (p < .05).

Since the progressions' pattern of general chord function was always significant, I then wished to determine if any factors built into the progressions had an effect on the results. Two of these factors were the spacing of the chords and the collection of the chords in the progression.

To determine if chord spacing had an effect on the results, I ranked the progressions according to mean Total’ score, as shown in Table 21, and indicated the spacing of each progression. Chords were considered to be in "open" spacing if the distance between the soprano and tenor voices was greater than an octave, while chords were in "closed" spacing if the distance was an octave or less. A progression was 124 considered to exhibit open spacing if all chords in the progression were open and to exhibit closed spacing if all chords were closed. If some chords were in open and others in closed spacing, the progression was labeled as having "mixed" spacing. 125

Table 21

Progressions Ranked by Total Mean Score

Rank Progression Mean Spacing

1 6 36.000 Qosed 2 2 32.500 Mixed 3 7 32.375 Qosed 4 30 32.000 Mixed 5 3 31.571 Qosed 6 31 31.000 Mixed 7 23 30.428 Closed 75% 8 5 29.500 Open 9 14 29.000 Qosed 10 IS 28.667 Qosed 11 1 28.375 Qosed 12 4 27.857 Qosed 13 11 27.625 Qosed 14 33 27.250 Open 15 13 26.714 Qosed 16 24 26.000 Qosed 17 10 25.875 Qosed 18 22 25.714 Qosed 19 IS 25.714 Qosed 20 34 25.625 Qosed 21 17 25.428 Qosed 22 25 25.285 Open 50% 23 16 23.857 Open 24 20 23.750 Open 25 19 23.625 Qosed 26 32 23.000 Open 27 9 22.571 Qosed 28 12 21.875 Qosed 29 26 21.375 Open 30 21 21.000 Qosed 31 29 21.000 Open 25% 32 8 18.625 Qosed 33 27 18.571 Open 34 35 15.750 C ^n 35 36 13.857 Nfixed 36 28 13.167 Open 126

Mean scores could range from 0 to 42. As seen in Table 21, the actual scores ranged from 36.000 (85.7%) to 13.167 (31.35%). Quartiles are indicated by the lines marking 25%, 50% and 75% of the range of student scores.

Progressions in open spacing proved to be more difficult for the students. Of the

11 progressions in open spacing, 8 (72.7%) of them fall at or below the 50% mark in the range. It could be argued that the pattern of the progression had more to do with the rank of the progression than the spacing of the chords. However, for each pattern, except pattern 4, there were two progressions in open spacing. Pattern 4 had only one progression (number 5) in open spacing, and it had the highest mean of all the progressions in open spacing.

Since only three progressions were in mixed spacing, no conclusions could be drawn concerning the effect of mixed spacing.

To determine if the specific chords contained in the progressions were a factor in the significant effect of the chordal pattern, I wrote a Pascal program to score the analysis of each chord in every progression. The answer was considered correct if the Roman numeral identification, the position designation and the quality of the chord were identified correctly. If any part of the answer was incorrect, the answer was considered incorrect. The number of times the subjects responded correctly, incorrectly or gave no answers for each chord is shown in Table 22. 127

Table 22

Number of Correct and Incorrect Identifications by Chord

ChcHd Correct Inconect No Answer Nbr Times Present in Progressions

I 69.7% 2 2 .0 % 8.3% 79 V 53.3% 38.7% 8 .0 % 43 P 51.1% 40.2% 8.7% 13

44.8% 44.8% 10.3% 8

28.6% 57.1% 14.3% 1 vi 32.6% 58.2% 9.2% 19 V6 37.5% 58.3% 4.2% 3 IV6 26.7% 60.0% 13.3% 2

IV 26.8% 63.2% 1 0 .0 % 29 iii 26.4% 6 6 .0 % 7.5% 7 ii 21.9% 6 6 .6 % 11.5% 13 — 14.3% 71.4% ^ - 14.3% 1

iii® 14.3% 71.4% 14.3% 1 viio 6 13.9% 73.0% 13.0% 16 ii6 8 .6 % 83.6% 7.8% 16 vi 6 0 0 . % 1 0 0 .0 % 0 .0 % 1

Legend: T = chord functions as tonic; D = chord functions as dominant

As the information in Table 22 indicates, the identifications of I, l 6 , and V were more often correct than incorrect. The subjects' answers for the | functioning as dominant was evenly divided between correct and incorrect answers. For the 128 remaining chords (V^, vi, V^, IV^, TV, iii, ii, I^.iii®, as tonic, viio 6 , and vi^), subjects provided inconect answers more often than correct answers.

This information leads to several questions:

1. Could the number of difficult chords in the progressions have an effect on the score for that progression?

2. What chords do students answer when they identify the chord incorrectly?

To determine an answer to question 1, difficult chords were defined as those answered more often incorrectly than correctly, i.e., the vi, V^, IV^, IV, iii, ii,

iii®, as tonic, vii°®, and vi® chords. Table 23 was then constructed showing the number of difficult chords and the pattern of chordal function for the progressions ranked by mean Total score. 129

Table 23

Ranked Progressions with Number of Difficult Chords Indicated

Rank Progression Nbr Difficult Pattern Chords 1 6 2 4 2 2 2 1 3 7 2 4 4 30 2 3 5 3 2 2 6 31 4 4 7 23 4 4 75% 8 5 2 4 9 14 4 2 10 18 2 3 11 1 3 1 12 4 2 3 13 11 2 5 14 33 4 5 15 13 3 2 16 24 3 5 17 10 2 5 18 22 3 3 19 15 3 2 20 34 3 5 21 17 3 3 22 25 4 1 50% 23 16 3 3 24 20 4 6 25 19 4 6 26 32 1 5 27 9 4 1 28 12 3 2 29 26 3 3 30 21 4 . 3 31 29 3 3 25% 32 8 4 1 33 27 5 2 34 35 3 6 35 36 3 6 36 28 4 2 130

The results in Table 23 indicate that students attain higher scores on progressions which contain fewer difficult chords and lower scores on progressions which contain more difficult chords. 71.4% of the progressions in the top quartile contain 1 or 2 difficult chords and 80% in the second quartile contain 2 or 3

difficult chords. However, 8 8 .8 % of the progressions in third quartile and 100% in the bottom quartile contain 3-5 difficult chords, with 60% of the bottom quartile progressions containing 4 or 5 difficult chords.

From the data in Table 23, it appears that the difficulty of the progressions may have more to do with the number of difficult chords in the progressions than just the difficulty of the pattern of general chord function. To determine if this is an accurate assumption from the data, the patterns were ranked by mean, and the total number of difficult chords present in progressions of each pattern was tallied, as shown in Table 24.

Table 24

Mean and Total Number of Difficult Chords by Pattern

Pattern Mean Nbr Difficult Chords

4 30.956 2+2+2+S+4+4 =17 3 26.550 2+3+34-2+3+2 = 15 5 25.956 2+2+3+Ï+4+3 =15 1 24.826 3+2+4-f4+4+3 = 20 2 24.275 2+3+4+3+5+4 =21 6 20.086 3+4+44-4+3+3 =21 131

As the information in Table 24 shows, progressions with a high number of

difficult chords (i.e., 2 0 or 2 1 ) had low mean scores whereas progressions with

fewer difficult chords (i.e., 15 and 17) had high mean scores. Pattern 6 , which had

the significantly lowest mean score, and pattern 2 , the next lowest mean score, contained more difficult chords than the rest. However, pattern 4, which had the

signifcantly highest mean score, did not contain the least number of difficult chords. Progressions following Patterns 3 and 5 had the least number of difficult chords (15) but lower mean scores. This variance may be due to the placement of

the difficult chords within the progressions. In the pattern 4 progressions, the

number of difficult chords is split almost evenly between the first 4 chords ( 8 or 47%) and the last 3 chords (9 or 53%). However, in both pattern 3 and 5

progressions, there are more difficult chords in the first 4 chords (13 or 8 6 .6 %, 12 or 80%) than in the last 3 chords (2 or 13.4%, 3 or 20%).

The information in Tables 23 and 24 indicates that some progressions are more difficult than others, even if they follow the same pattern of chordal function. This can be seen graphically in Figure 27. 132

Omean Omean+2SD Amean-2SD 70

6 .....□ □ 5 I-l □ nO , ] I % ° [ ' I 4 ...... 11 n n o □ "tt.....o O □ □ P o . o n ...... Q >Q I 3 cr 6^ [o oO^ ° < >o0^o< J O 0( ) □ 2 ...... b A b 1 A Ai i--....----...... ^j1.....A... O A A AA A A AA *^ A iAA^A A A % ....A...... A

10 15 20 25 30 35 40 prog

Figure 27

Mean and Mean +/- 2 Standard Deviations by Progression

To determine which chords the subjects were confusing with the chords played, question number 2 above, I wrote a Pascal program to print a matrix. Table 25, of the student answers for each chord. Table 25

Chord Confusions: Experiment 2

(Correct answers across; Student answers down)

I I® #T I^/4D ii ii® iii iii®D IV IV® V V® V®/4 vi vi® viio®

I 403 14 0 4 4 8 1 0 17 1 5 I 1 15 2 0 I® 32 47 2 2 2 4 7 0 19 0 5 1 0 9 0 1 17 2 1 26 4 2 0 0 13 1 15 0 0 8 0 2 n 2 0 0 0 I 0 0 0 0 0 0 0 0 0 0 1 # 1 0 0 1 1 1 2 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 m I 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 in® 1 1 0 0 0 2 1 0 0 0 1 0 0 1 1 0 fflW 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 IV 2 1 1 3 4 2Q 3 0 56 1 7 0 0 4 0 4 IV® 4 1 0 1 3 5 0 0 4 4 4 0 0 4 0 1 iv w 2 0 0 0 2 2 0 0 6 0 3 0 1 2 0 4 V 10 2 1 8 5 9 1 0 16 0 172 2 0 6 0 15 V® 6 1 0 1 3 5 0 1 4 0 16 9 0 4 1 15 V®/4 8 3 1 1 5 3 5 2 2 1 15 0 2 2 0 13 VI 0 0 0 0 1 1 0 0 2 0 0 0 0 4 0 0 VI® 0 0 0 0 2 0 1 0 2 0 0 0 0 0 I 2 VI®^4 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 vn 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 vn® 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 V I # 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ 0 > » CT>' I s O '“ OO0\^N-OOS»Ot0>— W K>0(0^00>0\ Î

OOOOSIOOOOOO m O O U ^ O m UIO m »*

ooooooooooooooooooooo

OO h-00«000000^- 000*^^000 I

OO>-*b00\0>OON)O>^»->O O KaN-ttih-OO*-*

00'-‘00ifc-00000u>h- W tooao-uooo

OOO*— >-*00000baN-0 •— »OK>-UOOO

OOOOOOOOOOOOO -*000000 D

—*oots>oa^ooooo-i^o M w o m —) —« o o

OOOO^h^OOOOOOO O OO m^OOO

Oi>- -^MtOtaaOOtOOx—Oi-* UJ O»^ OtOOtOtO

OwOOOOOOOOOOOO w o -* w o —* o

c OOOOOOOOOOOOO o ooo—>ooo

0 -*0sj(00»000i O O V)

OOOOOOOOOOOOOI-* l—OOOOOO

-*»00 — OO — I—OOOO o — o o o — o o m 135

00»-0000t

% OOOOOOOOOO OOOO

— oowMoomoo OOOO co

% 00000000 — 0 OOOO

% OOOOOOOCSOO OOOO

OO — OOO — 0 — 00 \o (S

'h 00000000-0 OOOO es

00000000-0 0-00 —

s OOOOOOOOOO OOOO —

00000-00-0 OOOO Tf

OC400000 — OO 00-0 0 \

— OOO — OO — — o OOOO

I OOOOOOOOOO OOOO \o

OOOOOOOOOO OOOO

OOOOOOOOOO OOOO 00

î 00000000-0 — OO— M s

I i à \ g 136

For the chords played, the following confusions are prominent:

Table 26

Frequent Chord Confusions: Experiment 2

Chad Student answer % of time

no response 8.3 5.5 3.0

I 15.2 no response 8.7 I 6 /4 T 16 28.6* I 6 /4 T IV 14.3+ I 6 /4 T V 14.3+ I 6 /4 T V6/4 14.3+ I 6 /4 T no response 14.3+ I 6 /4 D V 13.8 I6 / 4 D no response 10.3 ii no response 11.5 11 vi6 6.3 ii \ 6/4 5.2 11 V 5.2 ii6 IV 25.9* ii6 no response 7.8 ii6 V 7.8 ii& I 6.7 iii I« 13.2 iii 9.4 111 no response 7.5 111 11 7.5 iii^ V 6/4 _,28.6*

Legend: * This confusion occurs more often than the correct answer. + This confusion occurs as often as the cmrect answer. 137

Table 26 (continued)

Chord Student answer % of time

IV no response 10.0 IV 9.0 IV I 8.1 IV V 7.7 IV 16/4 6.2 i v 6 no response 13.3 V no response 8.0 V y 6 5.0 V y6/4 4.6 V IÊZ4 4.6 V 6 ii 8.3 V 6 iii 8.3 V 6 V 8.3 V 6 viiS. 8.3 y6/4 I 14.3 y6/4 ly 6/4 14.3 y6/4 ii 14.3 '^/4 vii°® 14.3 y ê ü no response 14.3 V i I 10.6 vi no response 9.2 vi6 I 28.6* v i6 m® 14.3* v i6 V® 14.3* vi® VI® 14.3* vi® iii 14.3* vi6 iii6 14.3* viio6 no response 13.0 vii°® V 13.0 vii°® V® 13.0 vii°® y 6/4 11.3 Y ljO S ii 8.7

Legen± * This confusion occurs more often than the correct answer. + This confusion occurs as often as the correct answer. 138

Four of the chords (i.e., those marked with a * in Table 26) were misidentified as particular chords more often than they were identified correctly: The was identified as a I® 28.6% of the time and only identified coirecdy 14.3% of the time. The vi^ was never identified correctly; it was identified as 1 28.6% of the time and as ni^, V^, VI^, iii, and iii^ 14.3% of the time. The iii^D was identified as V ^

28.6% of the time. And the ii^ was answered as IV three times as often as it was answered correctly (25.9% of the time).

Certain chord confusions are also evident from the prominent confusions shown in Table 26. Chords were confused with

1 . a primary triad. (19 times)

2 . a different chord having the same function as the correct chord. (16 times) 3. no response. (12 times) 4. a chord with the same bass note. (11 times) 5. a chord whose bass note is a step away from the correct bass note. (10 times)

6 . the same chord but in a different position. (7 times) 7. the correct chord but of incorrect quality. (1 time)

Examples of each of these confusions are shown in Table 27. 139

Table 27

Chords Listed by Types of Confusions

Chad Student answer % of time Confusion Types for chord IV 1.7 Pri Ü6 I 6.7 Pri ii V 5.2 Pri IV I 8.1 Pri VÊZ1 I 14.3 Pri I 6/4T v6/4 14.3 Pri, Func VI I 10.6 Pri. Func ii y6/4 5.2 Pri, Bass I 6 /4I V 14.3 Pri. Bass I 6/4D V 13.8 Pri, Func, Bass ü6 IV 25.9 Pri, Func, Bass viü I 28.6 Pri. Func. Bass I 6/4T IV 14.3 Pri, Bassl ü6 V 7.8 Pri, Bassl IV 16 9.0 Pri, Bassl IV V 7.7 Pri, Bassl IV 16/4 6.2 Pri, Bassl v6/4 IV 6/4 14.3 Pri, Bassl viÊ. v i 14.3 Pri. Bassl iü6D y6/4 28,6 Func V^ iii 8.3 Func vi6 14.3 Func vi6 iii 14.3 Func vi6 iii6 14.3 Func VÜ06 V 13.0 Func VÜ2& v i 13.0 Func iii I^ 13.2 Func, Bass V 16/4 4.6 Func, Bass V6 VIIO 8.3 Func, Bass v iis i V iM 11.3 Func. Bass V^/4 ii 14.3 Bass VÊZi viifii 14.3 Bass ii vi® 6.3 Bassl iii V<6/4 9.4 Bassl III II 1 3 ...... Bassl 140

Table 27 (continued)

Chad Student answer % of time Confusion Types for chord I 16 5.5 Pos I # 8.3 Pos l6 I 15.2 Pos I 6/4T 16 28.6 Pos V V6 5.0 Pos V V^4 4.6 Pos V6 V 8.3 Pos I no response 8.3 No response no response 15.2 No response I 6/4T no response 14.3 No response I 6/4D no response 10.3 No response ii no response 11.5 No response no response 7.8 No response iii • no response 7.5 No response IV no response 10.0 No response IV6 no response 13.3 No response V no response 8.0 No response vi no response 9.2 No response viiSl no resDonse 13.0 Noiesoonse vi^ VI6 14.3 Oual

Legend: Pos = incorrect positim id, correct chord id Pri = incorrect chord id that is a primary chord Func = same function, different chord id Bass = bass note same in both chords Bassl = bass note of correct and incorrect chmds 1 step apart Qual = correct chord, incorrect quality T = chmd functions as tonic; D = chord functions as dominant 141

Discussion

Experiment 2 was designed to determine which order of three tasks—identirication of the general function of each chord, notation of the soprano and notation of the bass lines—would best facilitate the analysis of harmonic dictation exercises and whether the pattern of general chord function-tonic, subdominant and dominant—affected the analysis scores. The design for the study was a Partially

Balanced Incomplete Block (PBIB) 6 x6 Latin Square associated scheme. The two variables were the order of the tasks and the pattern of general chord function used in the progressions. The subjects' scores on the progressions constituted the dependent variable. The results of Experiment 2 are:

1. The order of the tasks did not have a significant effect on the score. However, the orders FBS, FSB and BPS produced higher mean scores than the other orders.

2. The underlying pattern of general chord function had a significant effect on the analysis score.

3. The interaction of order and pattern had a significant effect on the analysis score.

4. The effect of the individual student had a significant effect on the score with male students scoring higher than female students. However, students from the two different universities were not significantly different in their performance on harmonic dictation tasks. Also, the student's major instrument had no statistically significant effect on the results.

5. Using different scoring methods did not change the results.

6 . Progressions in open spacing were more difficult than progressions in closed spacing. 142

7. Some specific chords were easier to identify than others. When students could not identify a chord, they tended not to respond or answered according to specific confusion patterns.

The ANOVAs indicate that there is no significant effect of order. However, the strong interaction of pattern and order may be overshadowing the direct influence of the order since, in several cases, Tukey HSD tests for order do indicate that using the order FBS results in significantly higher scores on the exercises than using other orders. Figiures 21-26 graphing the interaction of order and pattern confirm that the orders FBS, FSB and BFS produce higher scores on the exercises than the other orders.

In the orders FBS and FSB, the function task appears first. In the third order, BFS, function is second. Therefore, it appears that having the subjects concentrate first on the analysis of the chords produces better results than having them begin by notating the soprano and bass lines. If the function task is not the first task, having the subjects first provide the bass line appears to lead to the best results. Perhaps concentrating on the bass line provides information about the position of the chord. If the chord is in root position, as 190 chords were in the 36 progressions presented, notating the bass provides the root of the chord and thus a clue to the correct analysis.

The pattern of the general chord functions in the progression has a significant effect on the subjects' scores. Progressions following pattern 4 (TTDTSDT) produce

significantly higher results than other patterns while progressions using pattern 6 143

(SDTTSDT) produce significantly lower results. These findings lead us to conclude that the key needs to be established early in the progression or before the progression is played to produce higher scores. Perhaps the teacher or the computer program should establish the key by playing a cadence or a scale. This conclusion is supported by the fact that subjects identifying progressions following pattern 4 (TTDTSDT) attained high scores. Pattern 4 clearly emphasizes the key at the beginning of the progression (TTDT) through the use of dominant and tonic

chords. However, in pattern 6 (SDTTSDT), a tonic functioning chord is not sounded until the third chord of the progression. It may be that, when students are

presented progressions using pattern 6 , they hear the first chord, a subdominant, as a tonic. They then confuse the tonality and analyze the chords incorrectly. If students are losing the tonic, they should be allowed to reestablish their tonic by having the cadence or scale used to establish the tonic played again. It is very

important, therefore, to establish the key as early as possible in the progression if the subjects are to be able to identify the chords easily.

The significant effect of pattern may also be due to the number and placement of the chords that are difiicult for the student to identify, i.e., those chords answered

more often incorrectly than correctly. Progressions following the "easier" pattern 4 had 17 difficult chords which were spread almost evenly between the first 4 chords

(47%) and the last 3 chords (53%) of the progression. The "harder" progressions

following pattern 6 had 2 1 difficult chords and in every progression the first chord

and the fifth chord (the first chord of the cadence formula) was a difficult chord.

The conclusion may thus be made that progressions on which the students attain 144 higher scores are ones that have few difficult chords or which spread them evenly and avoid them at the beginning or at the cadence.

The interaction of the order and the pattern is very significant as well. Students achieve higher scores on some progressions if certain orders are used. Perhaps factors of the progression that lead to making correct decisions about individual chords may be made more apparent because of a particular order. Using the order FBS results in the highest scores for progressions following all patterns except pattern S. For pattern 5 progressions, using the orders FSB and BFS result in higher scores than using the order FBS. This may be because of the chords

contained in pattern 5 progressions. As Table 28 shows, pattern 5 progressions

have the least number of chords in root position (69%).

Table 28

Frequency of Positions of Chords by Pattern

Pattern Root Pos 1st Inversion 2nd Inversion

4 34 80.9% 8 19.0% 0 0 .0 % 3 30 71.4% 9 21.4% 3 7.1% 5 29 69.0% 9 21.4% 4 9.5%

1 31 73.8% 9 21.4% 2 4.8%

2 31 73.8% 1 0 23.8% 1 2.4%

6 35 83.3% 7 16.6% 0 0 .0 % 145

Therefore, the conclusion can be drawn that students attain higher scores using the order FBS if the progressions contain a large number of root position chords. As the number of first and second inversion chords increases (e.g. 30.9% in pattern 5 progressions), other orders, such as FSB and BFS, help the students attain higher scores.

There was a significant difference in the performance among the students participating in the study. However, there was bascially no difference between students from the two universities involved (i.e.. The Ohio State University and Youngstown State University). Both of these results were expected. Theory teachers would probably agree that students at various universities do not differ significantly in their abilities, yet some students demonstrate more ability in music dictation than others. The results here support both of these conclusions.

The gender of the student did have a significant effect on the scores. Moreover, it was shown that male students at both universities achieved higher scores than female students. This result might be thought to be related to the fact the males hear the bass line of the progression more accurately and therefore identify the chords correctly, as shown in Table 29. 146

Table 29

Mean Scores for Each Task by Student Gender and School

YSU Students:

Task Male Female

Bass 3.917 3.042 Soprano 4.323 3.104 Quality 5.010 4.812 Function 5.042 4.417 Roman Numeral 4.187 3.646 Position 4.573 4.208

OSU Students:

Task Male Female

Bass 4.883 2.815 Soprano 4.950 3.648 Quality 5.167 3.111 Function 5.417 4.444 Roman Numeral 4.400 2.389 Position 4.650 2.852

However, the results in Table 29 also indicate that male students attained higher scores than female students on every task, indicating that male students are better than female students at dictation tasks in general. These results may be due to the uneven distribution of students participating; there were 26 male students but only 17 female students. Further research with larger and equal numbers of female and male students needs to be undertaken to verify this result 147

None of the results stated above change dramatically when the grading method is changed. The six different scoring methods that were used resulted in different totals. For some, the scores were weighted differently; for others, new ways of scoring the analysis, soprano and bass tasks were used. But, no matter which scoring system was used, the results of the ANOVAs remained basically unchanged. This is an important observation; teachers use various grading methods since they are uncertain as to which method will most fairly credit the student for what he has heard. The findings here indicate that a range of grading methods will yield similar measures of attainment.

Experiment 2 also indicates that subjects have more difficulty identifying some chords than others. The conclusion could then be drawn that some specific chords were more difficult for subjects to identify than other chords. Noteworthy

examples were the vi6 chord, which subjects never identified coirecdy, and the ii 6 , ^ and iii^ chords, which subjects misidentified as certain chords more times than they provided the correct analysis. By studying these confusions and those indicated in Table 26, several chord confusion patterns emerge. Subjects tended to confuse the chord played with

1 . a primary triad.

2 . a different chord having the same function as the correct chord. 3. no response. 4. a chord with the same bass note. 5. a chord whose bass note is a step away from the correct bass note.

6 . the same chord but in a different position. 7. the correct chord but of incorrect quality. 148

When the subjects could not identify the chord, they tended to identify it as a primary triad. Subjects may have learned primary triads first and so tend to identify uncertain chords as those stressed early in training. Or it may be that the students hear the general function of the chord and provide the Roman numeral most commonly identified with the category.

Confusions by function and position seem most plausible. In confusing the function of the chord, the subjects may hear the general function but not the particular chord. In confusing the position of the chord, they may hear the chord but not the bass note.

It is interesting that the third most frequent type of confusion is one of no response; instead of providing an incorrect response, students offer none at all. This may indicate that students are simply baffled or that they are afraid to misidentify the chord. Perhaps teachers should encourage students to risk making mistakes and to guess at the answer. It is only through students' guesses that more can be learned about the process of learning harmonic dictation.

Confusions with chords that have identical bass notes may also involve confusions of chord function since two of the examples of confusion by function (e.g., V for

^ ,l6 for iii, and IV for ii®) were also examples of confusion by bass note. In these cases, it is difficult to know which of these confusions the subject is encountering. 149

Confusions of the correct chord with one whose bass note is one step away from the correct bass may have resulted from problems in the notation of the bass line. The subject may have notated the bass a step higher than it was played and analyzed the chords to match the incorrectly notated bass line. Using the order FBS and concentrating on the function of the chord first may eliminate this

The last type of confusion was one of chord quality; students provided the correct

Roman numeral and position identifrcation, but an incorrect quality identification.

Further calculations indicate that, when answers are provided, students correctly identify major quality 86.3% of the time, but minor quality only 44.1% of the time, and diminished quality only 21% of the time. And this does not include the instances where no answer was provided at all. From this data it may be concluded that students, even at the sophomore level, need more drill on quality identification.

Chords in open spacing were more difficult to identify than chords in closed spacing. In the training at both schools, chords in closed position were taught before chords in open position were introduced. Therefore, students had more

practice with chords in closed position than chords in open position. Perhaps this explains the difficulty.

In the next chapter, the results of Experiments 1 and 2 will be compared. The

implications of the experiments on teaching methods and the needs for further experimentation will be discussed. CHAPTER VI

CONCLUSIONS

The present study investigated orders of four tasks to discern which order would best facilitate the analysis of harmonic dictation exercises. The tasks involved the identification of the general function and the quality of each chord in the progressions, and the notation of the bass and soprano lines. In addition, the study, by means of two experiments, assessed whether the pattern of general chord function in the progressions had an effect on the analysis scores. The following conclusions can be drawn from the results of both experiments:

1. The order of the quality task does not significantly affect the students' scores. Nevertheless, it is important that students attend to chord quality.

2. No order of the tasks tested in the experiments was significantly better than the others, but it does appear that having students concentrate on the function task first and not on the melodic soprano and bass lines leads to high scores on the analysis task.

3. For progressions with a preponderance of root position chords, using the order FBS results in high analysis scores. However, other orders (e.g., FSB and BFS) result in high scores if there are more inverted chords.

4. Students tend to attain high scores on progressions that firmly establish the key during the first few chords.

150 151

5. Students tend to attain high scores on progressions that have few difficult chords (i.e., ones that are answered more often incorrectly than correctly), or that have the difficult chords spread evenly throughout die progression.

6 . Students from the two schools attained similar levels of scores, with male students attaining higher scores on harmonic dictation tasks than female students.

These conclusions are important to both teachers and students of harmonic dictation since they provide verified directions for the teaching and learning of harmonic dictation.

The results of the experiments indicate that the order of the tasks did not significantly affect the students' scores on the exercises. However, certain facts were discovered.

First, as the results of Experiment 1 shown in the plots of mean and standard error for each task by sequence position indicated, the order of the quality task did not affect the analysis scores. Yet, it was important that students concentrate on the quality of the chords played. In Experiment 2, students most often correctly identified the quality of only major chords; they correctly identified the quality of minor chords only 44.1% of the time and diminished chords only 21% of the time. This result is important to teachers since they often assume that students, by their sophomore year, can reliably distinguish chord qualities. However, the evidence shows that this assumption is false. The students' inability to identify chord qualities may be the result of placement in the progression or of chord spacing or inversion. More studies should be conducted to discover what factors make the identification of quality difficult for students. In the 152 meantime, teachers should continue to stress quality identification as part of harmonic dictation training.

For the tasks of function, bass and soprano, the order FBS most often resulted in higher scores. This finding is important for teachers, since they now know better results win be attained by initially concentrating on the chordal sonorities themselves

(the vertical aspect) rather than on the lines in the progression (the horizontal aspect). This conclusion is confirmed by the fact that even when the order FBS did not result in the highest score, the orders FSB and BFS did. In all of these orders, the function task was presented as either the first or second task, forcing students to concentrate on the chordal sonorities early in the procedure.

The effect of task order, however, is influenced by the progressions' patterns of chord function. One pattern or one order will not always produce optimum results. Instead, it is the combination of patterns and orders that is important. The results of this study indicate that students will attain higher scores using the task order FBS on progressions that contain many root position chords. However, for progressions with more chords in inversion, other orders, such as FSB and BFS, produce higher scores than the order FBS. This finding is important for teachers because it cautions them to be flexible when teaching harmonic dictation; they must be willing to modify their approach because of differences in the harmonic dictation exercises.

The significant effect of the pattern of chord functions indicates that a perception of the general function pattern of the progression enhances the ability of the student to 153 provide correct analyses. Evidence also suggests that students achieve higher scores on patterns for which the tonal center is firmly established at the beginning of the progression. It may be that students will benefit even more by the establishment of the tonic through the playing of a scale, tonic triad or short cadential progression

before the progression is presented. It also may be important for students to have the

option of reestablishing the key during the harmonic dictation exercise since the chord confusion charts indicate that students confuse the primary triads with each other. The confusions of primary chords may be due to the fact that the students lose their sense

of tonic. Allowing students the option of reestablishing the tonic during the exercise may eliminate these confusions.

The significant effect of pattern may also relate to the difficulty level of the

progressions themselves and not just to the pattern of chord functions. Evidence from the two experiments suggests that the number and placement of difficult chords in the

progression may influence the scores. Progressions constituting the patterns with low mean scores contain more difficult chords and concentrate them at the beginning (i.e.,

in the first 4 chords). Progressions constituting patterns with high mean scores have few difficult chords and these are spread evenly rather than clustered. These findings are

important for teachers because teachers can make harmonic dictation exercises easier for

students by controlling the number of difficult chords and by spreading these chords

throughout the progression. Findings such as these may lead to a more effective ordering of harmonic dictation exercises in the course of study. 154

The results also suggest that students from similar schools are not significantly different in their attainment. This knowledge should ease the teachers' task, since it is another indicator that methods used and proven successful at one university should prove successful at others.

Evidence clearly shows that the effect of the individual student was significant. Therefore, not every method used to present harmonic dictation will work equally well for every student Teachers must remain alert and flexible in their methods.

Evidence also indicates that male students were more adept at harmonic dictation exercises than female students. Furthermore, the male students performed better on all tasks involved in harmonic dictation. The reason for this result could not be obtained from the data collected in these experiments; perhaps it was an effect of the particular group of students that participated. There were more males than females and it was known to the investigator that at least 3 of the male students were exceptionally adept at harmonic dictation. The scores of those 3 male students may have skewed the results. However, it is an interesting finding that should be investigated further.

To these conclusions we may add several others drawn from the previous chapter.

1. Changes in the scoring methods did not alter the basic findings.

2. Progressions in open spacing were more difficult than those in closed spacing.

3. When students were confused by the chords played, their misidentifications followed specific confusion patterns. 155

In Experiment 2, the students' scores were calculated by six different methods:

1 . fgrade + bgrade + sgrade + rgrade + pgrade + qgrade. 2. (fgradeX2) + (bgradeX2) + (sgradeX2) + (rgradeX2) + pgrade + qgrade. 3. fgrade + bgrade + sgrade + qgrade + ascore. 4. fgrade + bscore + sscore + rgrade + pgrade + qgrade. 5. (fgradeX2) + (bscoreX2) + (sscoreX2) + (rgradeX2) + pgrade + qgrade.

6 . fgrade + bscore + sscore + qgrade + ascore.

For the above equations, fgrade, bgrade, sgrade, rgrade, pgrade and qgrade were equal to the number of correct answers on the function, bass, soprano, Roman numeral, position and quality tasks respectively. Ascore (the analysis score) was equal to the number of chords for which the student provided a correct Roman numeral designation, position indicator and quality designation. Bscore and sscore (bass and soprano scores) were calculated by counting a correct starting note as one point and each correct interval thereafter as one point. Regardless of the method of scoring that was used, the results of the analyses of the data were the same. Because teachers of harmonic dictation use many scoring methods, the findings indicated here are informative. Teachers can see that a range of scoring methods seems to produce similar measures of student performance.

The finding that progressions in open spacing appear to be more difficult than those in closed spacing is important to consider because it indicates that teachers should give special attention to open spaced progressions. Chords in open spacing may also need

to be introduced earlier in training so that students will htwe more practice on them. 156

It appears that chords in different spacings do not sound the same to students. This conclusion agrees with the findings of Gibson (1988), even though Gibson used non- traditional chords, not triads, in his experiment. He used 22 examples each of which contained a pair of two chords: The two chords in the first pair (chords A and Al) contained notes of the same pitch class, but in different octaves. The soprano note of A became the bass note of A l, and the bass note of A became the soprano note of Al. The notes in the inner voices, which varied in number from 1 to 7, were also exchanged. The two chords in the second pair (chords A and B) also contained notes of the same pitch class in the outer voices, but contained different inner notes. The soprano note of chord A became the bass note of chord B, and the bass note of chord A became the soprano note of chord B. The notes in the inner voices, which varied in number from 1 to 7, were exchanged and altered by means of changing the accidental.

For example, a Bb as the alto of chord A became a B-natural as the tenor of chord B. Gibson found that there was only limited evidence of the perception of similarity in the chords presented-not enough that the idea of octave equivalence should be taken as an assumption in aural perception. His conclusion lends weight to the conclusion arrived at in the present study: chords in different spacings do not always sound the same to theory students.

The present study also indicates that certain chords are easier to identify than other chords, and that patterns of confusions between chords are evident. As detailed in the Chapters 3 and 5, these confusion patterns, listed by number of occurrences, include confusing the chord played with: 157

1 . a primary triad.

2 . a different chord having the same funcdon as the correct chord. 3. a chord with the same bass note. 4. a chord so uncertain that students chose not to respond. 5. a chord whose bass note is a step away from the correct bass note.

6 . the same chord but in a different position. 7. the correct chord but of incorrect quality.

The confusions of chord position, function and bass note seen in this study are similar to those reported by Hofstetter (1978). Discovering such chord confusions is important to the teaching of harmonic dictation because this knowledge can enable teachers to provide more help to the student. The awareness of certain chord confusions can also help them to provide more effective orderings of chord presentations.

Although the results cited above help teachers and students alike, much research still remains to be conducted. It is important to note that the two experiments presented here did not test every possible pattern-only these six:

Pattern 1: TTSSDDT Pattern 2: TTSTSDT Pattern 3: TSTSDDT Pattern 4: TTDTSDT Pattern 5: TDTSDDT

Pattern 6 : SDTTSDT

Certain important combinations are missing. For example, none start with a dominant or subdominant chord followed directly by a tonic. Also missing are patterns that end with a cadence other than an authentic or deceptive cadence. Students must also leam to identify half and plagal cadences. Further experiments are needed to compare more patterns. 158

Also, it would be interesting to investigate whether differences in scores would result from different methods of establishing the key. A study might test which of 3

methods aids the student: ( 1 ) playing a scale before the progression, ( 2 ) playing a cadence before the progression or (3) starting the progression with a key-defining cadence. The results of the present study suggest the third method helps the students; however, the first two methods were not tried.

Since the interaction of the function pattern and task order proved to be statistically significant, further experiments are needed to discover which combinations are optimal for training and to determine if the interaction is affected by the positions of the chords.

My findings also indicated that students' gender had a significant effect on analysis scores, but their major instrument did not Both of these results seem surprising.

Teachers would probably expect gender to be insignificant but the student's major instrument to be important. The results obtained should not be taken as final results, however, since the gender and the major instrument of the student were not statistically controlled in the experiments. The results may simply be an effect of the group of students tested. To verify these results, further tests need to be conducted on larger populations—tests that control the factors of the gender and major instrument of the subjects. 159

The results of this research indicate that students may not hear chords in open and closed spacing as the same chord. However, there was no statistical control over the spacing of the chords. Thus, further research needs to be conducted to test the validity of this notion. And, research is needed to discover which chords are confused and why certain confusions occur.

In addition to the research needs suggested above, more attention must be given to psychological theories of learning that might apply to harmonic dictation. One promising learning theory is that of "chunking." Chunking may be described as the process of "recoding . . . information to form chunks" which "consist of individual items that have been learned and stored as a group in [long-term memory]" (Reed 1982,

70). Examples of chunking are encountered in everyday life. One such example is the way in which people group telelphone numbers into three groups, e.g., the area code, 3 and 4 digits. Similarly, people break their social security number into 3 chunks, consisting of 3, 2 and 4 digits. In music, chunking may be taking place when

listeners group the notes of a melody into phrases and motives. In harmonic dictation, students may be grouping chords into chunks by, for example, grouping the chords at

the cadence into a set pattern to which they can assign a name (e.g., plagal or deceptive cadence).

There has been much writing and research in the area of chunking (Miller, 1956;

Mandler, 1967; Johnson, 1968; Johnson, 1970; Restle, 1970; Johnson 1972; Glazner and R a^l, 1974; Simon, 1974; Crowder, 1976; Reed , 1982). But little research has

been conducted using chunking in conjunction with musical exercises. Dowling 160

(1973) considered the application of chunking to melodies. Leidahl and Jackendoff

(1987) use the principles of chunking in their theory text for the analysis of music. In harmonic dictation, chunking theory could be applied by ordering the exercises in such a way that students are first presented short harmonic progressions. Longer progressions might then be built up by combining the chunks that had already been mastered. Before chunking can be used in harmonic dictation, researchers need to ascertain the size of a chunk and what chords constitute a chunk. Researchers need also to determine if chunks are affected by the chords that precede or follow them.

Summary

The results of this study have many implications for the teaching of harmonic dictation. It appears that students should usually first attend to the chords in the progression before concentrating on the lines of the progression. It also appears that

progressions are more difficult if ( 1 ) the toitic is not emphasized at the beginning, ( 2 ) the chords are in open spacing, and (3) the difficult chords are not spread out over the length of the progression. Furthermore, it seems that progressions following various general function patterns may require different approaches to their analysis. Finally, the method of scoring used for harmonic dictation seems to have little effect on the measure of students’ attainment.

Further research is still required in the area of harmonic dictation, especially for comparing more chord function patterns and for measuring the interaction of the task order and function pattern. The effect of open and closed chord spacings and of 161 students' gender and major instrament need clarification. Further research also needs to be conducted on the efficacy of using psychological learning theories, such as chunking, in the learning of harmonic dictation. The results of my research suggest that such an endeavor could lead to further advances in aural training pedagogy. APPENDIX A

PROGRESSIONS USED IN EXPERIMENT 1

162 163

Progression 1: (Pattern 1: TTSSDDT; close spacing)

—t

Progression 2: (Pattern 1: TTSSDDT; mixed spacing)

J—1 i t 1 — t - J J il I —y

D J - J. % %

Progression 3: (Pattern 2: TTSTSDT; close spacing)

Ql 164

Progression 4: (Pattern 3: TSTSDDT; close spacing)

2 ------1------l-H = W z j = i = t

V j T f T i i i - - r \ ------

D X j L I II" xi| -X X

Progression 5: (Pattern 4: TTDTSDT; open spacing)

à a f I I n

f F:

Progression 6 : (Pattern 4: TTDTSDT; close spacing)

l u S

f n niz; S f # B % VI II' 165

Progression 7: (Pattern 4: TTDTSDT; close spacing)

Progression 8 : (Pattern 1: TTSSDDT; close spacing)

^ - r - s ----- J----- j - = ^ = h i i t r T -T) T ^ r p i 1 —p---- —T—F—^----- 1------— 1---- — L = M l = p M F' X m iV. u X X-

Progression 9: (Pattern 1: TTSSDDT; close spacing)

i - f - - V f 1— r

1 J U -Ty-ya— -f - ^ i ' r f ' M ^ 6 ' X ,,<» ,, X J- 166

Progression 10; (Pattern 5: TDTSDDT; close spacing)

■' I -f-— <- n n T î f s. T VI IL T

Progression 11: (Pattern 5: TDTSDDT; close spacing)

>

- y D ' ;) '/ 1 = i = h = M -M — ©!------r = * = 4 = N 1 1 ---- # IT L - f ------f ------1 — f — i=±=4 ==l==b= L = M

6 * I x f ï J-

Progression 12: (Pattern 6 : SDTTSDT; close spacing)

= W = q . a — )— 1 - — t»------#) 4 ( f=\ . À J l TT J ç l-3 f f ï ^ i f - = — 4 8^ JI X X VI \\'^ % X 167

Progression 13: (Pattern 2: TTSTSDT; close spacing)

|] a J j :|F ^ = = h 4 T—r - r - i i T - C) ,— — ^ ------f — " 4-- . 1 C X ill • ir X % ^

Progression 14: (Pattern 2: TTSTSDT; close spacing)

— —]— J = * = N = H r t - x W r - a — > / - ...... 1 JV ------l=M =H ô" :L K I - ii. X

Progression 15: (Pattern 2: TTSTSDT; close spacing)

* W:

f \ J. ë X TZ' 168

Progression 16: (Pattern 3: TSTSDDT; open spacing)

— 1— u ------J: - - J = ^ > - 4 - 4 1 f T - _ r - y - -M- J f - J - L M 1 { A = M — 1 - - 0(o X II T II VII

Progression 17: (Pattern 3: TSTSDDT; close spacing)

------1 )— j = M = i = t = > = i r = H si_ ." q .. / _

- i — H 1 - i 1 J ^ W - 5 ■ ------f— -y — I f L = | J

6 * '- VI 3 : T t 2 X J-

Progression 18: (Pattern 3: TSTSDDT; close spacing)

■y J- - 1 - 1 1 - f p i i U r y f — ■="¥"5------y — ------j - - - 1 "I f f = M = - c X II IS I X 169

Progression 19: (Pattern 6: SDTTSDT; close spacing)

f = f . f f 1 I 'I

M

c: T3L X X-

Progression 20: (Pattern 7: TTTTDDT; close spacing) —.----1--- u -7 . c/ -y ^ —^^—g 1 ^ — r— r—=f=f=- - h - : i i ^ i a :=C ■ y F- L=L=^ c, %r L /I*»

Progression 21: (Pattern 6 : SDTTSDT; close spacing)

J 1 1=4 = 4 = W = H - 4 — . :f|—j r H tri i - -%-L --i%- - rr — ,r— F ■' ■ r. M = ^ D I z % J. VI U VU®^ X 170

Progression 22: (Pattern 4: TTDTSDT; close spacing)

n n 1 i •ot pt p

Progression 23: (Pattern 4: TTDTSDT; close spacing)

fÀ—V------^ ----- —^—4—

, li i l / _ , V-p—“^1—/—p—c\. iT a— — —f—f— />•> ' Lf—

Progression 24: (Pattern 5: TDTSDDT; close spacing)

“7 F = M = i 1 1 1- 1 'n

TYTT> -v>- :=C —f ------±=±=±=±t===4===t=^ P ' % 3 - il X APPENDIX B

MACINTOSH TERMINOLOGY

171 172

Macintosh Terminology

application: a program used on the Macintosh computer. arrow: a pointer shaped like an arrow that appears on the Macintosh screen. boldface: text that is printed darker than normal. button: a rectangular box with rounded comers used to carry out some type of

action.

click: to depress and quickly release the button on the mouse. desktop: the screen that appears when the Macintosh is started. It was a menu

bar and a gray area which contains icons for the various application programs active.

disk: a 3.5 inch square magnetic medium that stores programs and data which can be read by the Macintosh. 173 double-click: to press and quickly release the button on the mouse twice in succession. drag: the process of moving items by moving the mouse while depressing the mouse button.

Enter key: the return key on the keyboard. It is used to end a command and send it to the Macintosh.

highlight: to make certain text prominent to the viewer. This may be

accomplished by displaying the text in boldface, italics, reverse video or underlined.

icon: a pictoral representation of an object.

mouse: a device used to move a pointer on the screen. The mouse is a rectangular box having one large button on the top of it and a long cord connecting it to the Macintosh.

mouse button: a large square control on top of the mouse which can be depressed.

radio button: an area of the screen used to make a selection. Radio buttons

appear as round circles with accompanying text to the right of the circle. 174

reverse video; displaying text as white letters on a black background. select: to designate an item on the screen by placing the arrow on the item and clicking. APPENDIX c FORMS USED IN EXPERIMENT 1

175 176

Student Questionnaire

Name: ______Oast) (first) (middle)

Major (e.g., Music Education, Music Performance)

Applied Music Area: Brass Woodwind Strings Percussion Voice Keyboard

Years of Study in that area: _____

If you have a secondary applied area, please indicate which area:

Years of study in that area:.

Have you had any theory or dictation training outside of OSU? _ If yes, please indicate the length of time.

Theory Dictation High School______College ______

Have you ever been tutored in theory/dictation? _____ If yes, please indicate the length of time. _____

Dictation course now enrolled in: ______

Have you ever taken this course before? ____ If yes, what quarter?_____

Last quarter's dictation grade: _____ 177 Harmonie Dictation Student Directions

1. Go to the Lab monitor and ask for your disk by number.

If this is your Arst time doing the exercises and you do not have a disk number, just ask the monitor for a disk for the Harmonic Dictation exercises.

Then write your name (in ink) on the disk and note the number on the disk. The next time you come, you should ask for your disk by number. If you forget the number, tell the monitor your name and he/she will get the disk for you.

If you have not completed a Student Data sheet, please do so and give it to the lab monitor.

If you need a direction sheet, ask the lab monitor for one.

The monitor will give you the disk; in return, you must give the monitor your ID card.

2. Go to a computer and turn it on.

3. Insert the Harmonic Dictation disk into the drive. The machine should now start working and you should see a little 'Happy Macintosh.' This means everything is working fine.

4. When you get a screen with one disk icon (picture) on it, double click the icon.

5. Then a screen should appear with an icon named Harmonic Dictation. Double click this icon.

You will now see the first screen of the Harmonic Dictation exercise. From here on, it should be self-explanatory. There are directions for you. Please read them the first time you go through an exercise.

You are to do 6 progressions. Each progression is seven chords long, in major keys from 2 sharps to 2 flats, and uses only diatonic triads. For each progressions you will be asked to identify the quality and function of each chord, and notate the soprano and bass voices. After each task you will be asked to provide a complete harmonic analysis. It takes about 10-15 minutes to 178 do one progression. So you will need two 1-hour sessions to complete 6 progressions.

NOTE: Each disk is set up to allow you to do only 6 progressions. If you want to do more than 6 progressions, get a new disk from the monitor after you complete the 6 allowed on the disk.

After you have finished each progression, you may continue to the next progression or play a musical 'whodunit' game called 'Musical Sleuth'. (Directions are on the disk.) Try not to spend more than 5 minutes at a time on die game.

6 . When you are finished for the day, click the box marked Exit in the Harmonic Dictation program. This will end the session and you will see the screen with the Harmonic Dictation icon on it.

7. Move the Mouse's arrow to the word 'Special' on the top line of the screen. Click on this word and while holding the button down, drag the arrow to the phrase 'Shut Down'. Then release the button. The machine should turn off and the disk should come out

8 . Then take the disk back to the monitor and get your ID back.

If you have problems: 1. Try to exit and restart the program. 2. If that doesn't work, check with the lab monitor. 3. If he/she can't help, call x. 2-9821 (weekdays from 8-5) or (216) 742- 3568 (weekdays 8-5) or (216) 534-5502 evenings or weekends.

Good luck and thanks for your participation! 179 Harmonic Dictation Lab Monitor Directions

1. When a student comes in to use the Harmonic Dictation exercises, he/she will ask for his/her disk by number. Get the disk for the student.

If it is the student's first time using the program, he/she will not have a disk number. In this case, find an unused disk (one without a student name on it) and give it to the student. Have the student write his/her name on the disk (in ink). This way, if he/she doesn't remember the disk number, you can find the disk by searching for the one with his/her name on it.

2. When you give the disk to the student, get the student's ID card. You will return the ID card when the disk is returned to you.

3. If the student has not completed a Student Data sheet, have the student complete one and file it with the disks.

4. If the student needs a direction sheet, please give him./her one.

5. Each disk is set up to allow the student to do 6 progressions. If the student wishes to do more progressions, another disk must be used. If the student asks for a new disk, give it to him.her and have him/her write his/her name on it, as before.

If there is a problem:

1 . have the student exit and restart the program. 2. call James at x. 2-9821 weekdays from 8-5. 3. call Barb at (216) 742-3568 weekdays from 8-5 or (216) 534-5502 evenings or weekends. 180 Teacher Directions

The Hannonic Dictation program is part of my (Barbara Muiphy's) dissertation. I want to thank you for your help and appreciate anything you can do to get the students to participate by doing the exercises.

The students will be asked to:

1. fill out a student data sheet. I would appreciate it if you would have every student complete this sheet in class. If a student is not there when you have the class complete the sheet, please ask the student to fill out the sheet when you give him the direction sheets. There will be some down in the lab too, for those real stragglers.

2. complete 6 harmonic dictation exercises. For each exercise (i.e., 1 progression), the student will be asked to identify the quality and function of each chord and notate the soprano and bass voices. After each of these tasks, the student is asked to provide a complete harmonic analysis.

For each progression, the tasks will be in a different order. Also, the students will get a different progression each time.

The progressions are all in major keys from 2 sharps to 2 flats, are 7 chords long, and use only diatonic triads. Each progression (all tasks) should take about 10-15 minutes to complete. Therefore, the students will need at least two 50-minute sessions to complete the 6 progressions.

After the students have completed each progression, they may choose to sign off, go to the next progression, or play a little musical 'whodunit' game called Musical Sleuth. They should spend no more than 5 minutes on the game in any session.

If a student wants to do more than 6 progressions, he/she will need to get a new disk. This is explained on the direction sheet.

As 1 said above. I'd really appreciate anything you could do to encourage the students to complete the exercise. APPENDIX D

PROGRESSIONS USED IN EXPERIMENT 2

181 182

Progression 1: (Pattern 1: TTSSDDT; close spacing, 3 difficult chords)

t I J rt i VI TL

Progression 2: (Pattern 1: TTSSDDT; mixed spacing; 2 difficult chords) i_l ii t TM t I I i 1 =3: Î D X U ii** % % __

Progression 3: (Pattern 2: TTSTSDT; close spacing; 2 difficult chords) 183

Progression 4: (Pattern 3: TSTSDDT; close spacing; 2 difficult chords)

--/Pjt ■ J-----i—(-1 70 ^

i ' > Tv'T- ...... T 1J ^ f------—1_— n M =t= i. H =I X H i r T lj

Progression 5: (Pattern 4: TTDTSDT; open spacing; 2 difficult chords)

-I

r r f I I -f-— i I _4L) I m f i VI Ts: %

Progression 6 : (Pattern 4: TTDTSDT; close spacing; 2 difficult chords)

■1 - 1 1■ 1 1 1------1------tt

, ^ ') i (Y \ l a ------7 - ^ —i 3------T^— J >■■ 4 - f , -1 1 1 1 6 ^ : X 2 VI 1|V 1 X 184

Progression 7: (Pattern 4: TTDTSDT; close spacing; 2 difficult chords)

x y

Progression 8 : (Pattern 1: TTSSDDT; close spacing; 4 difficult chords)

) s ------J — j - = ‘= H t r T := F FM ------f------=— - f ------— p------1— t . L F M = l " 1 1 ' - = t = H F : X II' H II v ir^ X X-

Progression 9: (Pattern 1: TTSSDDT; close pacing; 4 difficult chords)

4 * a I I r T f L SI ■J i ■ î - f

II II III 185

Progression 10: (Pattern 5: TDTSDDT; close spacing; 2 difficult chords)

n

i 2 . VI ï £ T

Progression 11: (Pattern 5: TDTSDDT; close spacing; 2 difficult chords)

A w i = ± ■V . — i F n n [i j r - r i 6

Progression 12: (Pattern 6 : SDTTSDT; close spacing; 3 difficult chords)

i M

I ' f Ü 2- X v\ \i*® s: X 186

Progression 13: (Pattern 2: TTSTSDT; close spacing; 3 difficult chords)

41 f

j i n 1 — ^ ------i ( — i _

C I III H X K X _1 _

Progression 14: (Pattern 2: TTSTSDT; close spacing; 4 difficult chords)

-f:------^ h FT FT VT Î 5 f. - 1 _L t T J . VI % ISL VH*k X.

Progression 15: (Pattern 2: TTSTSDT; close spacing; 3 difficult chords)

.. X

.1 a J i 1.11/: P (r- IE'* X J - 187

Progression 16: (Pattern 3: TSTSDDT; open spacing; 3 difficult chords) —1—u> / w - -f-t- r "-r- -1 ' J — /—f— 1 ^—f--- 4 n - \=^

Progression 17: (Pattern 3: TSTSDDT; close spacing; 3 difficult chords)

- f 9 ------) ------J —1

, U h . I 3 f ------:T— — r ' ^ ^ 1 1 1 1

Progression 18: (Pattern 3: TSTSDDT; close spacing; 2 difficult chords)

f--\X J--- \- = k = h = M l k I TT T - % - a — -— -T— -- 7--- ^ ------1— "1 r - ( M = i = X H 188

Progression 19: (Pattern 6: SDTTSDT; close spacing; 4 difficult chords)

f v t I 'I

ou II VIC X ill TJC X X

Progression 20: (Pattern 6 : SDTTSDT; open spacing; 4 difficult chords)

-VI /- 1 . . J 1 35: n r n n À m i

II X- ill 3£

Progression 21: (Pattern 6 : SDTTSDT; close spacing; 4 difficult chords)

- 4 —

4 ^ H - = 4 = : 1 J. J. t î i - k - = 3 F ' T - - ' ' > ------1------

D H z II VII®*’ X 189

Progression 22; (Pattern 4: TTDTSDT; close spacing; 3 difficult chords) J i % m $ X X il yn

Progression 23: (Pattern 4: TTDTSDT; close spacing; 4 difficult chords)

= 4 = 4 = i = M = i H = ! W I f f

, i i , ! i -----^ ------Æ.----- b 4 = t =

Progression 24: (Pattern 5: TDTSDDT; close spacing; 3 difficult chords)

4^-.-^- ' l-'t -—5--^—r=M=i- n 1 •' ■■

n IT X — f.------1-J b ^---t— y = = ^ L=M P" ] 4 3. II -21 X- 190

Progression 25; (Pattern 1: TTSSDDT; open spacing; 4 difficult chords)

t il , „ j - d i : | I I I g = F = f r - r t — r f J__ L I I i

? f f oL-

Progression 26: (Pattern 1: TTSSDDT; open spacing; 3 difficult chords)

---- 1— -----^ f ---- : i5» * / . — ^ ^— 1------y---- 1 F - i—-t—-f- -t—- f r ..... - h - 1 I 1 1 -----—— .. J .... . I i — r— .. r-|—1- — 1 — #— - cr i._.. 1 - 1 ------^=4— p - -t—4— ^ Y 1 c- X 3T I YuCk

Progression 27: (Pattern 2: TTSTSDT; open spacing; 5 difficult chords)

j _ U ' -I J - i ±

TT f t T \ I ' i J 1 1 Ê

3 ÏL X. VI 6 “- 1 1 1 E - z 191

Progression 28: (Pattern 2: TTSTSDT; open spacing; 4 difficult chords)

j _ J i I J___

T = T I I n J J 4- i f = T !’ • vi X X ‘’ IÎ- ^

Progression 29: (Pattern 3: TSTSDDT; open spacing; 3 difficult chords)

A ry------T------^------7~~

p

:= t -H- 1 1 1 1 c; i l X

Progression 30: (Pattern 3: TSTSDDT; mixed spacing; 2 difficult chords)

^ j J . ' i l

t~r t i n 1

i m f X‘’ 3Î X X X 192

Progression 31: (Pattern 4: TTDTSDT; mixed spacing; 4 difficult chords)

É a II r n m ? Vi X i t '' X ,|b % VI

Progression 32: (Pattern 5: TDTSDDT; open spacing; 1 difficult chord)

f n !

? jfc ^ T % X

Progression 33: (Pattern 5: TDTSDDT; open spacing; 4 difficult chords)

i_J i I .J Î i i i i - i- ; J. I(VI — iCfc # -r /I X IE X ^11' 193

Progression 34; (Pattern 5: TDTSDDT; close spacing; 3 difficult chords)

Vll,

Progression 35; (Pattern 6 ; SDTTSDT; open spacing; 3 difficult chords)

i à f = r r r r T I I

o'- 3 '/’I % "ne %

Progression 36; (Pattern 6 ; SDTTSDT; mixed spacing; 3 difficult chords)

•s, \ I é r=r I I n n J: 3 = ) - 4""I Ts :s. APPENDIX E

FORMS USED IN EXPERIMENT 2

194 195

Student Questionnaire (1989)

Name: ______(last) (first) (middle) Address: ______City: State:______Zip:______University: ______

Major (e.g.. Music Education, Music Performance)

Applied Music Area: Brass Woodwind Strings Percussion Voice Keyboard Total years of Study in that area:,

If you have a secondary applied area, please indicate which area:

Total years of study in that area:.

Have you had any theory or dictation training outside of YSU? _ If yes, please indicate the length of time.

Hieoiy Dictation High School ______College ______

Have you ever been tutored in theory/dictation?. If yes, please indicate the length of time..

Dictation course now enrolled in: ______Have you ever taken this course before?. If yes, what quarter?_____

Last quarter's dictation grade: _____ 196 Harmonie Dictation Student Directions

1. Get your disk. If this is your first time doing the exercises, ask the monitor for a disk for the Harmonic Dictation exercises. Then write your name on the disk (in ink) and note the number on the disk. The next time you come, you should ask for your disk by number. If you forget the number, tell the monitor your name and he/she will get the disk for you.

If you have not completed a Student Questionnaire (1989) sheet, please do so and give it to the lab monitor.

The monitor will give you the disk; in return, you must give the monitor your ID card.

2. Go to a computer and turn it on.

3. Insert the Harmonic Dictation disk into the drive. The machine should now start working and you should see a little 'Happy Macintosh.' This means everything is working fine.

4. When you get a screen with an icon (picture) marked MATE on it, double click this icon.

You will see the title screen for the Harmonic Dictation exercise. From here on, it should be self-explanatory. There are directions for you. Please read them carefully the first time you go through an exercise.

You are to do 6 progressions. Each progression is seven chords long, in major keys from 2 sharps to 2 flats, and uses only diatonic triads. For each progression you will be asked to identify the general function of each chord and notate the soprano and bass voices. You will then be asked to provide a complete harmonic analysis. You will be asked to do one task (function, bass, soprano, analysis) at a time. Click Done when you want to go on to the next task.

It takes about 10 minutes to do one progression. So you will need

approximately one 1-hour session to complete all 6 progressions. (Some students

have needed 1 1 / 2 to 2 hours to complete the six progressions.)

NOTE: Each disk is set up to allow you to do only 6 progressions. If you want to do

more than 6 progressions, get a new disk firom the monitor after you complete

the6 allowed on the disk.

5. When you are finished, click any box marked Exit. This will end the session and you will see the screen with the MATE icon on it. 197

6 . Move the Mouse's arrow to the word 'Special' on the top line of the screen. Click on this word and while holding the button down, drag the arrow to the phrase 'Shut Down'. Then release the button. The disk will come out. Take the disk out and turn off the machine.

7. Take the disk back to the monitor and retrieve your ID. Then fill out a Harmonic Dictation Survey form to let me know what you thought about the exercises.

If you have problems:

1. Try to exit and restart the program. 2. Check with the lab monitor. 3. Call X. 2-9821 (weekdays firom 8-5) or (216) 534-5502 evenings and weekends.

Good luck and thanks for your participation! 198 Harmonie Dictation Survey

Name: Disk Number: University:

Circle vour choice of answer:

Were the directions clear? yes no

Was it easy/hard to hear the bass voice? easy medium hard

Was it easy/hard to hear the soprano voice? easy medium haid

Were the progressions too easy/hard? easy medium hard

Was the feedback on your answer (i.e., showing the correct answer) sufficient? yes no

If not, what other information would you want to know about your perfonnance?

Did you think the program was helpful? yes no

Would you use such a program for practice in harmonic dictation if it were available? yes no

If not, why?

Did you have any problems while working on the program? yes no 199 If yes, please list them below:

Any other comments or suggestions: 200 Harmonie Dictation Lab Monitor Directions

1. When a student comes in to use the Harmonic Dictation exercises, he/she will ask for a disk. Get the next disk (in numerical order) for the student from the boxes marked 'Harmonic dictation, 1989 B. Murphy.' Have the student write his/her name on the disk (in ink). This way, if the student comes in again and can't remember the disk number, you can find the disk by searching for the one with his/her name on it.

2. When you give the disk to the student, get a student ID card. You will return the ID card when he/she returns the disk to you.

3. If the student has not completed a Student Questionnaire (1989), have him/her complete one and Ale this sheet with the disks.

4. If the student needs a direction sheet, please give him/her one.

5. Each disk is set up to allow the student to do 6 progressions. If the student wishes to do more progressions, he/she must get another disk. If he/she asks for a new disk, give it to him/her and have him/her write his/her name on it, as before.

6 . After the student is done with the six progressions and gives the disk back to you, have him/her complete a Harmonic Dictation Survey form. File the completed form with the disks.

If there is a problem:

1 . have the student exit and restart the program. 2. call James at x. 2-9821 weekdays from 8-5. 3. call Barb (216) 534-5502 evenings and weekends. APPENDIX F RESULTS OF STUDENT SURVEY USED IN EXPERIMENT 2

201 202 Harmonie Dictation Survey R esu lts

Total responses: 35 students

Questions ______Rgsppnsgs Were the directions clear? yes 33 no 1 no answer 1

Was it easy/hard to hear the bass voice? eaqr 11 medium 9 hard 15

Was it easy/hard to hear the soprano voice? easy 18 medium 8 hard 9

Were the progressions too easy/hard? eaqr 7 medium 21 hard 7

Was the feedback sufficient? yes 18 no 17

Did you think the program was helpful? yes 31 no 3 no answer 1

Would you use such a program for practice if available? yes 23 no 12

Did you have any problems while working on the program? yes 5 no 30 LIST OF REFERENCES

Alvarez, Manuel. "A Comparison of Scalar and Root Harmonic Aural Perception Techniques," Journal of Research in Music Education 28/4 (1980), 229- 235.

. "Effects of Sequencing, Classifying, and Coding on Identifying Harmonic Functions," Journal of Research in Music Education 29/2 (1981), 135- 141.

Battle, Barton K. Computer Software in Music and Music Education: a guide. Metuchen, NJ: The Scarecrow Press, 1987.

Benward, Bruce. Workbook in Ear Training. Second edition. Dubuque: Wm. C. Brown Company Publishers, 1969.

Blombach, Ann K. and Regina T. Pairish. "Acquiring Aural Interval Identification Skills: Random Vs. Ordered Grouping," Journal of Music Theorv Pedagogy 2/1 (1988), 113-131.

Boody, Charles, ed. Association forTechnologv in Music Instruction Courseware Directorv 89-90. Published by the Association for Technology in Music Instruction, 1989.

Boomsliter, Paul and Warren Creel. "The Long Pattern Hypothysis and Harmony and Hearing," Journal of Music Theorv 5/2 (1961), 2-31.

Carlsen, James C. "Programmed Learning in Melodic Dictation," Journal of Research in Music Education 12/2 (1964), 139-148.

. Melodic Perception. New York: McGraw Hill Book Co., 1965.

Crowder, Robert G. Principles of Learning and Memorv. Hillsdale, NJ: Lawrence Erlbaum Associates, 1976.

Deutsch, Diana. "Interactive effects in memory for harmonic intervals," Perception & Psvchophvsics 24/1 (1978), 7-10. 203 204

Deutsch, Diana and Philip Roll. "Error Patterns in Delayed Pitch Comparison as a Function of Relational Context," Journal of Experimental Psychology 103/5 (1974), 1027-1034.

Dowling, W.J. "Rhythmic groups and subjective chunks in memory for melodies," Perception & Psychophysics 14/1 (1973), 37-40.

Gibson, Don B Jr. "The Aural Perception of Similarity in Non-Traditional Chords Related by Octave Equivalence," Journal of Research in Music Education 36/1 (1988), 5-17.

Glazner, Murray and Michal Razel. "The Size of the Unit in Short-term Storage," Journal of Verbal Learning and Verbal Behavior 13 (1974), 114-131.

Harriss, Ernest. "Study of a Behaviorally Oriented Training Program for Aural Skills," Journal of Research in Music Education 22/3 (1974), 215-225.

Henderson, Ian H. "Music Education," Review of Educational Research 37/2 (1967), 200-204.

Hofstetter, Fred T. "Computer-Based Recognition of Perceptual Patterns in Harmonic Dictation Exercises," Journal of Research in Music Education 26/2(1978), 111-119.

. Computer Literacy for Musicians. Englewood Cliffs, NJ: Prentice-Hall, 1988.

Jeffries, Thomas B. "The Effect of Order of Presentation and Knowledge of the Results on the Aural Recognition of Melodic Intervals," Journal of Research in Music Education 15/3 (1967), 179-190.

Killam, Rosemary N., Paul V. Lorton Jr, and Earl D. Schubert. "Interval Recognition: Identification of Harmonic and Melodic Intervals," Journal of Music Theory 19/2 (1975), 212-234.

Lerdahl, Fred and Ray Jackendoff. A Generative Theorv of Tonal Music. Cambridge, Mass.: The MIT Press, 1987.

Mandler, George. "Organization and Memory." In K.W. Spence and J.T. Spence, eds. The Psychology of Learning and Motivation. Vol 1. New York: Academic Press, 1967,327-372. 205 Miller, George. "The Magical Number Seven, Plus or Minus Two: Some Limits on our Capacity for Processing Information," The Psychological Review 63/2(1956), 81-97.

Ott, Lyman. An Introduction to Statistical Methods and Data Analysis. North Scituate, MA: Duxbiuy Press, 1977.

Penner, M.J. "The effect of marker variability on the discrimination of temporal iritervals," Perception & Psvchophvsics 19/5 (1976), 466-469.

Peters, G. David and John M. Eddins. "Applications of Computers to Music Pedagogy, Analysis and Research: A Selected Bibliography, " Journal of Computer-Based Instruction 5/1-2 (1978), 41-44

Prevel, Martin and Fred Sallis. "Real time generation of harmonic dictation progressions in the contect of microcomputer-based ear training," Journal of Computer-Based Instruction 13/1 (1986), 6-8.

Rahn, Jay and James R. McKay. "The Guide-Tone Method: An Approach to Harmonic Dictation," Journal of Music Theorv Pedagogy 2/1 (1988), 101- 111.

Randel, Don M., ed. The New Harvard Dictionary of Music. Cambridge, MA: The Belknap Press of Harvard University Press, 1986.

Reed, Stephen K. Cognition: Theorv and Applications. Monterey, CA: Brooks/Cole Publishing Company, 1982.

Reitenour, Steve. "Music, Higher Education, and Technology: Annotated Bibliography", Eric Document ED 263 850.

Restle, Frank. "Theory of Serial Pattern Learning: Structural Trees," Psychological Review 77/6 (1970), 481-495.

Siegel, Jane A. and William Siegel. "Absolute identification of notes and intervals by musicians," Perception & Psvchophvsics 21/2 (1977), 143-152.

Simon, Herbert A. "How Big Is a Chunk?" Science 183 (1974), 482-488.

Stwolinski, Gail de, James Faulconer and A.B. Schwarzkopf. "A Comparison of Two Approaches to Learning to Detect Harmonic Alterations," Journal of Research in Music Education 36/2(1988), 83-94. 206 Zatoire, Robert J. and Andrea R. Halpem. "Identification, discrimination, and selective adaptation of simultaneous musical intervals," Perception & Psvchophvsics 26/5 (1979), 384-395.