A Synthesis of Schenkerian And Neo-Riemannian Theories: The First Movement Of Paul Hindemith’s Piano Sonata No. 1 As A Case Study
Yvonne Teo
Submitted in total fulfilment of the requirements for the degree of Master of Music
June 2017
Melbourne Conservatorium of Music Faculty of the VCA & MCM University of Melbourne Abstract This thesis explores the possibility of synthesising some aspects of Schenkerian and Neo-Riemannian theories and seeks to demonstrate the effectiveness of this approach in the analysis of a twentieth-century sonata. Although this study begins with a thorough understanding of Neo-Riemannian theory (NRT), the final hybrid method is not a strict application of NRT, employing its core principles rather than its specific method. Paul Hindemith’s Piano Sonata No. 1 is selected for this study as this work contains vestiges of tonic-dominant tonality (inviting Schenkerian analysis) but also employs a non-traditional post-tonal harmonic structure (inviting a NRT approach). The Schenkerian method has been long recognised as a useful tool to analyse primarily tonal repertoire whereas Neo- Riemannian theory is useful in analysing the heavily chromatic harmony of the nineteenth century. A hybrid analytical method encompassing aspects of the two approaches is designed to potentially strike a balance between a subjective and objective understanding of the music. A chart is designed with three systems: the Urlinie, pitch collections, and the Bassbrechung. Different sets of data are obtained to describe the transformation from one chord (or more loosely, “pitch collection”) to the next. In calculating these movements between the pitch collections, this NRT-inspired approach will substitute for a traditional harmonic analysis. The synthesis of the two theories will be illustrated through a line graph that charts the amount of intervallic movement between pitch collections against the Urlinie to observe the relationships between the two. Findings indicate that graphical representations deepen our understanding of the connections between one chord and the next through common tones, and furthermore, accommodate all types of chords and not just major and minor triads. Additional notes can then be added to the Urlinie as a result of the identification of significant movements in the graph. The synthesis of these two methods when combined with an analysis of performance recordings will allow a deeper understanding of Hindemith’s Piano Sonata to emerge. This suggests the importance of adopting this hybrid method in approaching Neo-Classical works and indicates how this approach might shape the performer’s interpretation. Therefore, this research can be seen to contribute to the formation of a bridge between music theory and performance.
i University of Melbourne Faculty of the VCA & MCM Melbourne Conservatorium of Music
This is to certify that:
(i) the thesis comprises only my original work towards the MMus;
(ii) due acknowledgement has been made in the text towards all other material used;
(iii) the thesis is fewer than 50,000 words in length, exclusive of tables, maps, bibliographies and appendices
Signature:
Name: Yvonne Teo
Date: 15 June 2017
ii Acknowledgements
Undertaking a Master of Music has been such a rewarding experience and it would not have been possible to do without the support and guidance from many people in both my academic and personal lives. First and foremost, I would like to extend my sincerest appreciation to my principal supervisor, Dr. Martin Greet. Words cannot express how grateful I am for Martin’s time, guidance, patience and enthusiasm throughout my candidature. His expert knowledge and scholarship has always been a source of inspiration, further igniting my passion in music analysis. Not only did he read countless drafts, but he consistently provided me with insightful and enlightening feedback and I am greatly indebted to him. One simply could not wish for a better or friendlier supervisor. I would also like to thank my secondary supervisor, Dr. Erin Helyard. Erin’s experience as a performer and passion as a scholar have played a crucial role in stimulating my interest in attempting to create a meaningful dialogue between analysis and performance. I am very grateful to have him on the supervisory team, to gain from his insights and from his advice during the writing process. During my candidature, I have been very privileged to be able to carry out this project with the assistance of the Research Training Program (RTP) Scholarship. A special thank you to the University of Melbourne and the Australian Commonwealth Government for providing me with the funding to undertake this study. Finally, I would like to thank my parents and friends for their unwavering support, their love and encouragement. Their names and contributions are too numerous to list here but I am very grateful to them all. Thank you in particular to Candice Basterfield, Rachel Blacow, Anita Leung and Imogen Telfer, who have shared this journey closely with me, offered their endless support, good-humour and love. However, special thanks to Megan Murray for offering many helpful suggestions and taking the time to proofread my work.
iii Table of Contents
Abstract i Acknowledgments iii List of Figures vii List of Examples viii List of Tables ix List of Analytical Charts xi List of Analytical Tables xiii
CHAPTER ONE: Background 1
1.1 Introduction 1 1.2 Paul Hindemith 3 1.3 Existing Studies 6
CHAPTER TWO: Schenker, NRT and Extended Tonality 9
2.1 Schenkerian Method 9 2.1.1 Strengths and Limitations 10 2.2 Neo-Riemannian Theory 12 2.3 Integration of NRT and Schenkerian Methods 14 2.4 Expansion of NRT and Schenkerian Methods 18
CHAPTER THREE: Analysis and Performance 22
3.1 Approaches to Analysis and Performance 22 3.2 Schenker and Performance 24 3.3 A Schenkerian/Formenlehre Approach? 25 3.4 A “Performative” Approach 27 3.5 Moving Past Formal Analyses 30 3.6 Performance Recordings of Hindemith’s Piano Sonata No. 1 33
CHAPTER FOUR: Analytical Method 35
4.1 The Craft of Musical Composition 35 4.2 Rhythmic Reduction and Segmentation 36 4.3 Voice-Leading and Intervallic Movement 39 4.4 Visual Representations 41 4.4.1 Schenkerian and NRT chart 41 4.4.2 Intervallic Movement Graphs 43 4.4.3 Relationships between the Urlinie and the Data Points 43 4.4.4 Mean, Median and Mode 44
iv CHAPTER FIVE: Application of the Analytical Method Part I: Preliminary Schenkerian Analysis 46
5.1 Application 5.1.1 Whole Sonata 47 5.1.2 1st movement 47 5.1.3 2nd movement 50 5.1.4 3rd movement 50 5.1.5 4th movement 51 5.1.6 5th movement 52 5.2 Discussion 53 5.3 Strengths and Limitations 62
CHAPTER SIX: Application of the Analytical Method Part II: Segmentation (First Movement) 64
6.1 Application 65 6.2 Discussion 75
CHAPTER SEVEN: Application of the Analytical Method Part III: NRT-Inspired Voice-Leading Data - Completing the Schenkerian Chart 99
7.1 Bars 1 to 10 103 7.1.1 Discussion (Bars 1 to 10) 107 7.2 Bars 11 to 22 113 7.2.1 Discussion (Bars 11 to 21) 117 7.2.2 Additions to the Urlinie (Bars 11 to 21) 121 7.3 Bars 22 to 26 123 7.3.1 Discussion (Bars 22 to 26) 127 7.3.2 Additions to the Urlinie (Bars 22 to 26) 128 7.4 Bars 26 to 32 130 7.4.1 Discussion (Bars 26 to 32) 134 7.4.2 Additions to the Urlinie (Bars 26 to 32) 139 7.5 Bars 33 to 37 143 7.5.1 Discussion (Bars 33 to 37) 147 7.6 Bars 37 to 51 152 7.6.1 Discussion (Bars 37 to 51) 156
v CHAPTER EIGHT: Application of the Analytical Method Part IV: Beyond Schenker and Further Observations 159
8.1 Data Collection 160 8.1.1 Statistics and Frequency of Voice-Leading Movement - Minim Subdivision 160 8.1.2 Statistics and Frequency of Voice-Leading Movement - Crotchet Subdivision 163 8.2 Discussion 175 8.2.1 Data Obtained from Minim Subdivision 175 8.2.1.1 Voice Leading Movement 175 8.2.1.2 Intervallic Movement between Each Chord and its Basic Interval Pattern (BiP) 175 8.2.2 Data Obtained from Crotchet Subdivision 181 8.2.2.1 Voice Leading Movement 181 8.2.2.2 Intervallic Movement between Each Chord and its Basic Interval Pattern (BiP) 182
CHAPTER NINE: Towards A New Model of Analysis for Neo-Classical Music 192
BIBLIOGRAPHY 198
APPENDIX 211
Appendix A1.1 Hindemith, Piano Sonata No. 1, bars 1 to 24. 211 Appendix A1.2 Hindemith, Piano Sonata No. 1, bars 25 to 51. 212
vi List of Figures Figure 2.1 “Traditional” and “Total” Views of Voice Leadings from Chord X to Chord Y. Figure 4.1 Calculating the Intervals Between Two Sets of Pitch Collections. Figure 4.2 An Example of a Modified Schenkerian and NRT Chart. Figure 6.1 Identifying the Melodic Features in Bars 1 to 4. Figure 6.2 3-note Step Progression (SP) in Bar 4. Figure 6.3 Observing the Cadence in Bar 2. Figure 6.4 Further Observations in Bars 3 and 4. Figure 6.5 Horizontal Connections in Bars 5 and 6. Figure 6.6 Uncovering the Larger Connections in Bars 2 to 10. Figure 6.7 Step Progressions and Rhythmic Reduction in Bars 5 to 9. Figure 6.8 Identifying the Melodic Ideas in Bars 11 to 16. Figure 6.9 Step Progressions and Rhythmic Reduction in Bars 11 to 16. Figure 6.10 Identifying the Two Phrases in Bars 17 to 22. Figure 6.11 Step Progressions and Rhythmic Reduction in Bars 17 to 22. Figure 6.12 Step Progressions in Bars 23 to 26. Figure 6.13 Step Progressions and Rhythmic Reduction in Bars 23 to 26. Figure 6.14 Step Progressions in Bars 27 to 32. Figure 6.15 Step Progressions and Rhythmic Reduction in Bars 27 to 32. Figure 6.16 Identifying the Phrases in Bars 33 to 36. Figure 6.17 Step Progressions and Rhythmic Reduction in Bars 33 to 36. Figure 6.18 Identifying the Melodic Ideas in Bars 37 to 51. Figure 6.19 Step Progressions in Bars 37 to 39. Figure 6.20 Step Progressions in Bars 40 to 42. Figure 6.21 Step Progressions in Bars 43 to 46. Figure 6.22 Step Progressions in Bars 47 to 51. Figure 6.23 Step Progressions and Rhythmic Reduction in Bars 37 to 51. Figure 7.1 C major Chord and its Neighbouring Transformations on the Tonnetz. Figure 9.1 Representation of Major and Minor Triads on the Tonnetz. Figure 9.2 Tonnetz using Integers. Figure 9.3 An Alternate Tonnetz. Figure 9.4 Illustration of Pitch Collections form a Minim Subdivision in Bars 1 to 5. Figure 9.5 Illustration of Pitch Collections form a Crotchet Subdivision in Bars 1 and 2.
vii List of Examples Example 4.1 An Excerpt from Hindemith’s Melodic Analysis of de Machaut’s “Il m’est avis”. Example 7.1 Lower Neighbour Note B in Bars 3 and 4. Example 7.2 Phrasing and Shaping in Bars 13 and 14. Example 7.3 Prolongation of Fs in Bars 14 to 18. Example 7.4 Descending Arpeggiated Figures in Bars 19 and 20. Example 7.5 A Lower Neighbouring Movement in Bars 13 to 16. Example 7.6 Addition of D to the Bars 16 to 19. Example 7.7 The Inner Voice in Bars 15 and 16. Example 7.8 Melodic Fragment “x” and its Extensions in Bars 23 to 26. Example 7.9 Prolongation of B to Bf in Bars 23 to 26. Example 7.10 First Appearance of the First Statement of the Second Idea. Example 7.11 Second Appearance of the First Statement of the Second Idea. Example 7.12 Bars 29 to 32 (With the Intervallic Movement for Bars 31 and 32). Example 7.13 Identifying the Melodic Ideas in Bars 31 and 32. Example 7.14 Chromatic Movements in Bars 27 to 29. Example 7.15 Prolongation of Fs/Gf in Bars 29 to 31. Example 7.16 Addition of D to Bar 27. Example 7.17 Bars 29 to 31. Example 7.18 Addition of C to Bar 31. Example 7.19 Identifying the Significant Intervallic Movement in Bars 27 to 29. Example 7.20 Identifying the Key Chords in Bars 33 to 37. Example 7.21 Data Points to B in Bars 33 to 37. Example 7.22 Data Points in Bars 37 to 39. Example 8.1 Intervallic Movement Between Each Chord at a Minim Level in Bars 1 to 4. Example 8.2 Intervallic Movement of 3 in Bars 7 to 8. Example 8.3 Intervallic Movement of 3 in Bars 17 to 19. Example 8.4 Intervallic Movement of 3 in Bars 33 to 37. Example 8.5 Intervallic Movement of 3 in Bars 44 to 48. Example 8.6 First Appearance of the Arpeggiated Figure (Bar 40). Example 8.7 Second and Third Appearances of the Arpeggiated Figure (Bars 44 and 48). Example 8.8 Intervallic Movement of 4 and its Corresponding BiPs in Bars 19 and 20.
viii Example 8.9 Intervallic Movement of 7 in Bars 33 to 37. Example 8.10 Intervallic Movement in Bars 37 to 39. Example 8.11 BiP in Bars 31 and 32. Example 8.12 BiP in Bars 27 and 28. Example 8.13 Segmentation of Bars 33 to 36. Example 8.14 BiP and Intervallic Movement in Bars 37 to 39.
List of Tables Table 4.1 Characteristics of the VL Movement from 0 to 6. Table 4.2 An Example of Data Categorisation. Table 6.1 An Alternate View of the SP. Table 7.1 Examples of NRT Transformations. Table 7.2 Total Amount of Intervallic Movement Between Each Chord. Table 7.3 A Neighbouring Movement and its Corresponding Data Points in Bars 1 to 5. Table 7.4 Data Obtained from a Minim Subdivision in Bars 5 and 6. Table 7.5 Data Obtained from a Crotchet Subdivision in Bars 5 and 6. Table 7.6 Data Obtained from a Crotchet Subdivision in Bar 7. Table 7.7 Overall Description of the Data Points in Bars 5 to 10. Table 7.8 Observing the Melodic Movement and its Corresponding Data from a Minim Subdivision in Bars 11 and 12. Table 7.9 Data Obtained from a Crotchet Subdivision in Bars 16 to 21. Table 7.10 Data Obtained from a Minim Subdivision in Bars 23 to 26. Table 7.11 Data Obtained from a Crotchet Subdivision for the Key Notes in Bars 23 to 26. Table 7.12 Data Obtained from a Crotchet Subdivision in Bars 23 to 26. Table 7.13 Data Points on Key Note @ in Bars 27 to 33. Table 7.14 Key Note and 3-prg and its Data Points in Bars 27 to 29. Table 7.15 Data Points on Fs and Gf in Bar 29. Table 7.16 Additions to the Urlinie for Bars 26 to 32. Table 7.17 Data Points and its Movements in Bars 33 to 36. Table 7.18 Key Note and Unfoldings Identified in Bars 33 to 36. Table 7.19 Identifying the Individual Movements in the Unfoldings. Table 7.20 Key Notes and its Data Points at a Minim Subdivision for Bars 37 to 51.
ix Table 7.21 Key Notes and its Data Points at a Crotchet Subdivision for Bars 37 to 51. Table 7.22 Unfoldings in Bars 41 to 51. Table 8.1 Most to Least Common VL Movements from a Minim Subdivision (Bars 1 to 21). Table 8.2 Most to Least Preferred BiP Intervallic Movement from a Minim Subdivision. Table 8.3 Characteristics of BiP [012]. Table 8.4 A Comparison of the Intervallic Movement Between Bars 23 to 25 and Bars 27 to 29. Table 8.5 Most to Least Common VL Movements from a Crotchet Subdivision (Bars 1 to 21). Table 8.6 Most to Least Common VL Movements from a Minim Subdivision (Bars 1 to 21). Table 8.7 Most to Least Common VL Movements from a Crotchet Subdivision (Bars 22 to 51). Table 8.8 Characteristics of BiP [0112] and [0022]. Table 8.9 Phrase Subdivision of the 2nd Idea and its Corresponding Intervallic Movement and BiPs. Table 8.10 Statistical Overview of Bars 22 to 51 in its Respective Phrase Divisions. Table 8.11 VL Movement, BiP, and Intervallic Movement in Bars 38 and 39. Table 8.12 BiP and Observations on the Overall Movement in Bars 33 to 36. Table 8.13 Intervallic Movement and its Number of Occurrences from a Crotchet Subdivision in the First Idea (Bars 1 to 21). Table 8.14 Intervallic Movement and its Number of Occurrences from a Crotchet Subdivision in the First Idea (Bars 22 to 51). Table 8.15 Intervallic Movement and its Number of Occurrences from a Crotchet Subdivision in the First Movement. Table 9.1 Pitch Class and Tonal Names.
x List of Analytical Charts Analytical Chart 5.1 Ursatz of All Movements of Piano Sonata No. 1. Analytical Chart 5.2 A Detailed Ursatz of the First Movement. Analytical Chart 5.3 Foreground, Middleground, Background Sketches of Bars 1 to 22 of the First Movement. Analytical Chart 5.4 Foreground, Middleground, Background Sketches of Bars 23 to 51 of the First Movement. Analytical Chart 5.5 A Detailed Ursatz of the Second Movement. Analytical Chart 5.6 A Detailed Ursatz of the Third Movement. Analytical Chart 5.7 An Alternate Detailed Version of the Ursatz of the Third Movement. Analytical Chart 5.8 A Detailed Ursatz of the Fourth Movement. Analytical Chart 5.9 The Ursatz of the Fifth Movement. Analytical Chart 5.10 A Detailed Ursatz of the Fifth Movement. Analytical Chart 6.1 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 1 to 4. Analytical Chart 6.2 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 5 to 9. Analytical Chart 6.3 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 10 to 14. Analytical Chart 6.4 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 15 to 20. Analytical Chart 6.5 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 21 to 24. Analytical Chart 6.6 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 25 to 28. Analytical Chart 6.7 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 29 to 31. Analytical Chart 6.8 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 32 to 35. Analytical Chart 6.9 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 36 to 42. Analytical Chart 6.10 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 43 to 51.
xi Analytical Chart 7.1 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 1 to 10. Analytical Chart 7.2 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 1 to 10). Analytical Chart 7.3 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 1 to 10. Analytical Chart 7.4 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 1 to 10. Analytical Chart 7.5 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 11 to 22. Analytical Chart 7.6 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 11 to 22). Analytical Chart 7.7 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 11 to 21. Analytical Chart 7.8 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 11 to 21. Analytical Chart 7.9 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 23 to 51 (A Focus on Bars 23 to 26). Analytical Chart 7.10 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 22 to 26). Analytical Chart 7.11 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 22 to 26. Analytical Chart 7.12 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 22 to 26. Analytical Chart 7.13 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 23 to 51 (A Focus on Bars 26 to 32). Analytical Chart 7.14 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement for Bars 23 to 51 (A Focus on Bars 26 to 32). Analytical Chart 7.15 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 26 to 32. Analytical Chart 7.16 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 26 to 32. Analytical Chart 7.17 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 23 to 51 (A Focus on Bars 33 to 37).
xii Analytical Chart 7.18 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 33 to 37). Analytical Chart 7.19 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 33 to 37. Analytical Chart 7.20 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 33 to 37. Analytical Chart 7.21 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 23 to 51 (A Focus on Bars 37 to 51). Analytical Chart 7.22 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 37 to 51). Analytical Chart 7.23 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 37 to 51. Analytical Chart 7.24 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 37 to 51.
List of Analytical Tables Analytical Table 8.1 Statistical Observations for Bars 1 to 51 (Minim Subdivision). Analytical Table 8.2 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 1 to 11. Analytical Table 8.3 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 11 to 21. Analytical Table 8.4 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 23 to 32. Analytical Table 8.5 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 33 to 39. Analytical Table 8.6 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 40 to 51. Analytical Table 8.7 No. of Occurrences Within Each BiP and Intervallic Movement for the First Movement (Minim Subdivision). Analytical Table 8.8 VL Movement across the First Movement (Minim Subdivision). Analytical Table 8.9 Statistical Data for Bars 1 to 11 (Crotchet Subdivision). Analytical Table 8.10 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 1 to 11.
xiii Analytical Table 8.11 Statistical Data for Bars 11 to 21 (Crotchet Subdivision). Analytical Table 8.12 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 11 to 21. Analytical Table 8.13 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 1 to 21 (Crotchet Subdivision). Analytical Table 8.14 VL Movement in the First Idea for Bars 1 to 21 (Crotchet Subdivision). Analytical Table 8.15 Statistical Data for Bars 22 to 26 (Crotchet Subdivision). Analytical Table 8.16 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 22 to 26. Analytical Table 8.17 Statistical Data for Bars 26-32 (Crotchet Subdivision). Analytical Table 8.18 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 26 to 32. Analytical Table 8.19 Statistical Data for Bars 33 to 36 (Crotchet Subdivision). Analytical Table 8.20 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 33 to 36. Analytical Table 8.21 Statistical Data for Bars 37 to 51 (Crotchet Subdivision). Analytical Table 8.22 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 37 to 51. Analytical Table 8.23 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 22 to 51 (Crotchet Subdivision). Analytical Table 8.24 VL Movement (Crotchet Subdivision) in the Second Idea (Bars 22 – 51). Analytical Table 8.25 VL Movement across the First Movement (Bars 1 – 51) (Crotchet Subdivision). Analytical Table 8.26 Statistical Data for Bars 1 to 21 (Crotchet Subdivision). Analytical Table 8.27 Statistical Data for Bars 22 to 51 (Crotchet Subdivision). Analytical Table 8.28 Statistical Data for Bars 1 to 51 (Crotchet Subdivision). Analytical Table 8.29 No. of Occurrences within Each BiP and Intervallic Movement for the First Movement (Crotchet Subdivision).
xiv Chapter 1
Background
1.1 Introduction This study will focus on two major theories, the Neo-Riemannian theory (commonly abbreviated as NRT) and the Schenkerian method and propose that a synthesis of these two theories could provide useful insights into the analysis of Neo-Classical music, using Paul Hindemith’s Piano Sonata No. 1. Hindemith’s background harmonic structure in this work is primarily tonal, inviting the use of a theoretical model that might partake in large-scale melodic reduction, such as Schenkerian analysis. However, as his foreground harmonies are largely post-tonal, this will prove to be challenging if approached by traditional tonal harmonic analysis. An NRT-inspired approach to the foreground harmonies may assist in elucidating the composer’s harmonic language to reveal some components that are attenuated or marginalised in a Schenkerian analysis. The Schenkerian method is commonly known as an effective tool to analyse tonal music, particularly music from the Baroque to the early nineteenth century whilst Neo- Riemannian theory is particularly useful for examining music that is more chromatic, music from the nineteenth-century to selective early twentieth-century works. When used separately, these two methods (Schenkerian and Neo-Riemannian methods) will provide different insights and address different issues within the music and the strength of each analysis is highly dependent on two key factors: the period of the chosen work and the specific analytical focus. A Neo-Riemannian analysis examines the relationship of chords to each other at a foreground level whereas Schenkerian analysis examines the relationship of chords to the melodic and harmonic structures at a background and middleground level. Rather than adhering to the traditional principles of the Neo-Riemannian method, this investigation reveals that drawing out the core elements then using them in conjunction with the Schenkerian method can produce an effective way to analyse music that contains an extended harmonic language yet retains its tonal centricity. Whilst there are few papers that have attempted to integrate NRT and Schenker’s method, a small number of existing studies of this type have been identified and will be presented in this thesis to support the need to undertake this research, to demonstrate how and why the selection of these two methods can be of great use in studying Neo-Classical works.
1 Neo-Classicism is a specific trend of music that occurred before the Great War, with roots embedded in Classicism and Primitivism (the creation of new sounds from old ones by juxtaposing the two) and as a reaction to Impressionism, Expressionism and late Romanticism. In Messing’s words, Classicism and Neo-Classicism are much alike where there is “clarity, simplicity, objectivity, purity, refinement, constructive logic, concision, sobriety, and so on.”1 The term, Neo-Classicism, first emerged through Stravinsky’s music as his work was described “in its essence Tristanesque, romantic” and as Taruskin stated, “it was perhaps the rediscovery of the leading tone, and the reintroduction into his music of the dominant function that proclaimed the self-attachment of Stravinsky's umbilical cord to Western “Classical” tradition.”2 A brief overview of the Schenkerian and Neo-Riemannian theories will be discussed as well as some existing papers that have sought to integrate and synthesise the two theories. This will also be supported by two chapters detailing some brief approaches to analysis and its relationship to performance. Furthermore, as Hindemith was also a theorist, his Craft of Musical Composition provides his thoughts on music and its more specific elements and these have provided the basis to identify the melodic features, perform a comprehensive segmentation and rhythmic reduction of the sonata. The hybrid analytical method will then be presented: firstly, through a preliminary Schenkerian analysis, secondly, segmentation through Hindemith’s compositional ideas, and thirdly, hybrid charts that integrates the Urlinie, pitch collections and Bassbrechung and graphs that illustrates the voice-leading movements against the Urlinie. Subsequently, there will be a discussion of the results and their implications for both performance and analysis: uncovering ways in which the NRT- inspired voice-leading data can enrich the Schenkerian chart and making further observations from using this analytical method.
1 Scott Messing, Neoclassicism in Music: From the Genesis of the Concept Through the Schoenberg/Stravinsky Polemic (Rochester: University of Rochester Press, 1988), xiv. 2 Richard Taruskin, “Review: Back to Whom? Neoclassicism as Ideology” 19th-Century Music 16.3 (1993): 292.
2 1.2 Paul Hindemith Hindemith’s music has been described by scholars as “German to the core” as well as being of a “Neo-Classicist” nature.3 From a German standpoint, his heritage shines through in several ways such as his frequent use of counterpoint and his deep roots in the Reformation (i.e. Lutheran chorales).4 Hindemith also firmly believed that sounds and forms “remain meaningless to us unless we include them in our own mental activity and use their fermenting quality to turn our soul towards everything noble, superhuman and ideal.”5 He also had the idea that a composer’s horizon must continually have the desire to learn, comprehend, incite and inspire and “storming the heavens with artistic wisdom and practical skill must be his least ambition.”6 As one of the early twentieth-century composers amongst other prominent figures such as Stravinsky, Satie and Busoni, who turned to Classicism, Hindemith and the others turned to the Classical ideal, striving to “recapture the spirit of an era when music had not yet begun to call on the other arts for heightened dramatic or pictorial effect, when the art had not yet become preoccupied with personal expression and psychological attitudes.”7 As the musical elements (e.g. melody, harmony, rhythm, texture, orchestration, tonality and form) at the time differed greatly to the seventeenth and eighteenth-centuries, these changes and development brought a new light to the style, partly attributing to its name, Neo-Classicism.8 There was also a revival of absolute forms such as the symphony, concerto, sonata and various types of chamber music. Some of Hindemith’s notable compositional outputs are in chamber music, such as Kammermusik, Der Schwanendreher (‘The Swan Catcher’) and Trauermusik (‘Funeral Music’). In other genres, some of his prominent works also include his opera, Mathis der Maler and the song cycle, Das Marienleben. Hindemith’s compositions are thus a reflection of the label, Neo-Classicism, a reaction against the hypersensitivity and egocentricity of late Romanticism and in Kemp’s words, “against a language which in the social conditions following the 1914-18 war appeared irrelevant.”9
3 Joseph Machlis, Introduction to Contemporary Music (New York: Norton, 1979), 197. 4 Ibid. 5 Paul Hindemith, A Composer’s World (Cambridge: Harvard University Press, 1952), 5. 6 Machlis, Introduction to Contemporary Music, 197. 7 Ibid 160-161. 8 Ibid 161. 9 Ian Kemp, Hindemith (London: Oxford University Press, 2002), 15.
3 Through Hindemith’s “faithfulness” to the laws of tonality, his musical output was heavily inspired by Baroque polyphony and with the strong intent on renewing musical forms of the seventeenth and eighteenth centuries.10 One account of Hindemith’s music states that:
[Hindemith’s] Neo-classical music should become deeply rooted in his creative personality. A distaste for self-indulgent expression and an emphasis on clarity of line, texture, and form remained typical of him throughout his life. Another feature is an affinity with Baroque music, and particularly the music of Bach – that is, with a language not directed primarily towards the expression of ‘personal feeling’. To draw inspiration from music of other historical periods also remained typical of him.11
The Neo-Classical aesthetic has a particular focus on craft and control, characteristics that Hindemith’s early compositions have embodied as he sought to redefine and assert the principles of tonality in the twentieth century.12 As stated by Teachout, Hindemith was an idealist, “one who believed passionately in the power of music to embody visions of a transcendent spiritual order, accessible to all men in all conditions.”13 This ideal then can be reflected in Hindemith’s approach as he believed that music should be composed with intent, for a specific purpose, a concept known as Gebrauchsmusik, “utility or workaday music.”14 He was highly sensitive about the relationship between the performer and composer and he particularly aimed for his compositions to be appealing to both performers and listeners. Hindemith’s concept of Gebrauchsmusik can also be related to the relationship between composer and audience. As the music language of the late nineteenth to early twentieth centuries became more complex and there was a growing emergence of expressionism and atonality, there was a belief that there was a great distance between the composer and audience. Hence, Hindemith’s attempt to rectify this gap in his lifetime can perhaps be seen through his gravitational attraction towards tonality, to compose music that is more “appealing” and “understandable” to audiences.15 His attraction to tonality can also be reflected in his principles in his compositions and theoretical writings and his teachings, in
10 Kemp, Hindemith, 8; Machlis, Introduction to Contemporary Music, 195; Terry Teachout, “The Last German Master,” Commentary 113.1 (2002): 48 11 Kemp, Hindemith, 15. 12 Machlis, Introduction to Contemporary Music, 197. 13 Teachout, “The Last German Master”, 49. 14 Machlis, Introduction to Contemporary Music, 159-160. 15 David Neumeyer, The Music of Paul Hindemith (New Haven: Yale University Press, 1986), 187.
4 his time at Yale University.16 Hindemith’s application of harmony is primarily based on the free use of the twelve tones, resulting in polyharmony.17 However, there is often modal colouring, from his strong passion for past music (e.g. Baroque music). As for rhythm, it can be likened much to the music of the Baroque era, contrasting significantly to other composers of the time such as Stravinsky or Bartók.18 Although Hindemith was well-known for his larger works (i.e. operas, concertos and orchestral works), he also composed three piano sonatas, all of which were written in 1936.19 Initially composed when he was residing in Turkey, it was completed upon his return to Berlin.20 Piano Sonata No. 1 has been described as a reflection of his difficulties with the Nazi regime, drawing its inspirations from a German poem by the nineteenth-century poet Friedrich Hölderlin. In Fierro’s words, the “poet dreams of an idealised ancient Greece, a land once ringing with songs and dances of a happy, highly civilised people on the shores of the blue Aegean, but now in ruins, devastated by wars and oppression.”21 This sonata is ultimately Hindemith’s reflection of his views on Germany, a “product of its moment in history.”22 As stated by Neumeyer, in this period, Hindemith
employed relatively large harmonic and melodic blocks, with a chorale texture as the starting point… the triad is the harmonic point of reference, and harmonic phrases controlled by major or minor triads are often simply juxtaposed with phrases controlled by sonorities developed from augmented or diminished triads.23
Furthermore, Hindemith’s strong commitment to Neo-Classicism became especially apparent at this time as his compositions were strongly influenced by traditional harmonic theory (i.e. Schenker), with an emphasis on linear writing and objectivism.24 This clearly suggests the suitability of a Schenkerian approach in such music. Interestingly, it was during
16 Eckhart Richter, “Paul Hindemith as Director of the Yale Collegium Musicum,” College Music Symposium 18.1 (1978): 20-44. 17 Machlis, Introduction to Contemporary Music, 197. 18 Ibid 197. 19 Neumeyer, The Music of Paul Hindemith, 1999. 20 Geoffrey Skelton, Paul Hindemith: The Man Behind the Music: A Biography (London: Gollancz, 1975), 134. 21 “Hindemith: The Three Sonatas,” Charles Fierro, Charles Fierro, date accessed 28 February 2017, http://charlesfierro.blogspot.com.au/2012/06/hindemith-three-piano-sonatas-by.html; Kemp, Hindemith, 28-29. 22 Ibid. 23 Neumeyer, Music of Paul Hindemith, 187. 24 Machlis, Introduction to Contemporary Music, 199; Neumeyer, Music of Paul Hindemith, 187.
5 these few years of transition where he allowed his “poetic lyricism” to assert itself in his composition, a characteristic that can be seen in Piano Sonata No. 1.
1.3 Existing Studies There are several papers written by scholars on Hindemith’s music, some of which delve into his compositional treatises, some on the application of Hindemith’s own compositional theories to their analyses, and others with a more specific focus on analysing certain musical elements (i.e metre, harmony and texture). More work has been done on Hindemith’s larger works as opposed to his solo pieces. However, there is one article by Harner that analyses Piano Sonata No. 3 but none for the first two sonatas. The analysis of the Third Piano Sonata covers several musical elements: form and thematic usage, “vertical structures”, harmony, tonality, melody and rhythm.25 Harner particularly focusses on how these “vertical structures” (the study of the sonorities, how dissonant, how complex etc.) can be seen across all four movements and from this, how they can inform the performer and listener of the underpinnings of the sonata.26 It is also interesting to highlight Harner’s treatment of the harmonic theory of Hindemith. In order to treat all the notes equally, Harner labels the groups of notes specifically as “vertical constructions” and he seeks to examine the sonorities through “a counting and tabulation… according to the system for defining vertical constructions” as suggested by Howard Hanson.27 The occurrences of pitches throughout the sonata are calculated through groups of two and three tones, its traditional nomenclature (minor 2nd, major 2nd etc.) and Hanson’s concepts. Upon calculating the sonorities, Harner concludes that the “sonata is tertian in concept”, containing 214 major triads, 177 minor triads and 138 traditional seventh sonorities.28 Furthermore, a study by Wildman involves a comparative analysis of Hindemith’s Sonata for Bassoon and Sonata for Tuba, with a focus on melodic or phrase designs, harmony and structure.29 These late works are also discussed alongside the Craft of Musical Composition as they are typical of Hindemith’s compositional framework.30 Similarly, another work by Bedell examines Hindemith’s Clarinet Concerto alongside the Craft of
25 Nevin L. Harner, “Hindemith: Third Piano Sonata. An Analysis” (M.A., University of Rochester, 1962), 1-73. 26 Ibid 86. 27 Ibid 31-44. 28 Ibid 42. 29 Simon R. Wildman, “A Comparative Analysis of Paul Hindemith’s Sonata for Bassoon (1938) and Sonata for Tuba (1955)” (D.M.A., University of Georgia, 2014), 7-33. 30 Ibid 34-49.
6 Musical Composition to observe how his laws of composition can be reflected in his works.31 Bedell concludes that construction of the clarinet concerto was consistent with Hindemith’s laws of composition, particularly in his rules of melody and harmony as set out by the contrasting themes in the first and fourth movements and the step-progressions of the themes in the third movement.32 An interesting study by Kim applies Hindemith’s theories to Niels Bentzon’s Third Piano Sonata, identifying how the work is a reflection of Hindemith’s ideas and examining the relevance of his theory as a tool for analysing the sonata.33 The author concludes that one of the key reasons Hindemith’s tonal theory is applicable to the sonata is that Bentzon utilises rhythmic and melodic devices from the Baroque tradition. The work is unified through motivic development and devices such as ostinato, pedal point and counterpoint are evident.34 Furthermore, a study by Flory discusses the relationship between analysis and performance through Hindemith’s compositions. Flory’s analysis of Hindemith’s Six Chansons takes an approach from a choral conductor’s perspective in providing a rationale for an analytical study for a performance and a practical guide for conductors to prepare the work.35 She identifies that it is imperative for the conductor to have a comprehensive knowledge of Hindemith’s style, “textual purpose,” as well as performing an analysis on the respective pieces “in order to achieve the best possible performance.”36 A different approach by Trombetta investigates the origins of Hindemith’s interest in early music and how it can be reflected in his viola compositions (Viola Sonata Op. 11 No. 5, Op. 31 No. 4, Viola Concerto Der Schwanendreher, Trauermusik for Viola and Strings).37 His findings indicate that Hindemith’s knowledge and practice of early music played a crucial role in his compositional output particularly in his early music techniques such as fugues, chorale settings and cantus firmus-like melodies.38 Whilst some scholars have placed an emphasis on establishing a close relationship between the Craft of Musical Composition and Hindemith’s works, other scholars have
31 Melody Joy Bedell, “The Craft of Musical Composition Applied to Hindemith’s Clarinet Concerto” (MMus, University of Tennessee, 1985), 5-22. 32 Bedell, “Hindemith’s Clarinet Concerto,” 55. 33 Sun Hee Kim, “An Analytical Study: Applying Hindemith’s Tonal Theory to Niels Viggo Bentzon’s Third Piano Sonata, Op. 44” (D.M.A., University of North Texas, 2009), 1-9. 34 Ibid 49-50. 35 Pamela Jean Flory, “Six Chansons of Paul Hindemith: An Analysis in Relation to Performance” (Hons., Butler University, 1970), 14-34. 36 Flory, “Six Chansons of Paul Hindemith,” 34. 37 Domenico L. Trombetta, “Early Music Influences in Paul Hindemith’s Compositions for the Viola” (D.M.A., James Madison University, 2014), 5-41. 38 Trombetta, “Early Music Influences,” vii.
7 investigated how Hindemith manipulates a specific musical element within his compositions. For instance, Uppercue’s study focusses on examining Hindemith’s approach to intervals and presents an analytical method for “Neo-Tonal” music based on Hindemith’s and Etler’s writings, applied to Ludus Tonalis.39 He establishes a theory of “interval resolution”, a gradation that orders intervals from the most stable to the most unstable and how specific intervallic treatments permeate various levels of structure.40His findings indicated that this theory is a starting point for “the analysis of intervallic content and its function within a given setting” and consideration of “all levels of structure” is required to “provide a thoughtful analysis of Neo-Tonal music.”41 A different paper by Bruhn also examines the formal structure of Ludus Tonalis, uncovering its structural devices, symmetry and asymmetry.42 Bruhn discovers that the postlude is a “visual retrograde inversion of the prelude” as frequently stated in the literature and the two fugues “using mirror-reflection strike the eyes of most people who spend time with the score.”43 Similarly, Mak approaches Hindemith’s music from a rhythmic perspective, examining how Hindemith “manipulates metrical conflict in certain passages for particular purposes, for instance, to prepare for a change of tonality or the entry of a subject, to create points of tension, to intensify the build-up of a climax and to provide a link between sections.”44 He discovers that the concepts of metrical consonance and dissonance are a “good way” to categorise the rhythmic interest in Hindemith’s music.45 As there is evidently a gap in the existing studies where some of Hindemith’s works are yet to be examined, analysing his First Piano Sonata for this thesis will also serve as a way towards filling the gap in the literature. There is a need for studies to be carried out that discuss the background structure and how the middleground level details relate to it.
39 Kevin Uppercue, “Modified Contrapuntal Conventions: Stability and Instability in the Neotonal Music of Hindemith” (MMus, University of North Carolina, 2013), 9-37. 40 Uppercue, “Modified Contrapuntal Conventions,” 9-45. 41 Ibid 38. 42 Siglind Bruhn, “Symmetry and Dissymmetry in Paul Hindemith’s Ludus Tonalis,” Symmetry: Culture and Science 7.2 (1996): 116-132. 43 Bruhn, “Symmetry and Dissymmetry,” 132. 44 Yung Cheung Mak, “Formal Functions of Metrical Dissonance in the Music of Paul Hindemith” (M.A., University of British Columbia, 1999), 1. 45 Mak, “Formal Functions of Metrical Dissonance,” 81.
8 Chapter 2
Schenker, NRT and Extended Tonality
As aptly stated by Cook, each analytical approach “creates its own truth through instigating its own perception” and “brings into being a dimension of experience that will co- exist with others.”46 With this in mind, to what extent can Schenkerian analysis be applied to Hindemith? Scholars over the last two decades have sought to analyse music that embodies “extended” tonality (such as Neo-Classical music), but it has proven to be challenging.
2.1 Schenkerian Method The Schenkerian method is a tool that aims to uncover the process of how music is elaborated from the most basic tonal framework (the background), also known as the fundamental structure.47 As stated by Schenker,
The fundamental structure represents the totality. It is the mark of unity and, since it is the only vantage point from which to view that unity, prevents all false and distorted conceptions. In it resides the comprehensive perception, the resolution of all diversity into ultimate wholeness.48
As an analytical tool, the process begins by examining the musical foreground (the surface layer) and the middleground (the layers of elaborations), then “simplifies” the music to reveal the background structure (the deepest layer). Performing a Schenkerian analysis on a piece of early twentieth-century music can have its challenges but the process is very similar to the analysis of a more “tonally centred” repertoire. Although musical factors such as rhythm, motivic features, and durational elements play a significant role in establishing the initial Schenkerian chart, it is more challenging to identify the harmonic features of a work that does not employ harmonies generated from scale degrees and which does not adhere to tonic-dominant relationships at the foreground level. When considering Hindemith’s heavily chromaticised and extended harmonic
46 Nicholas Cook, “Analysing Performance and Performing Analysis,” in Rethinking Music, eds. Nicholas Cook and Mark Everist (Oxford: Oxford University Press, 1997), 239-261. 47 Allen Cadwallader and David Gagné, Analysis of Tonal Music: A Schenkerian Approach (New York: Oxford University Press, 1998); Thomas Pankhurst, SchenkerGUIDE: A Brief Handbook and Website for Schenkerian Analysis (London: Routledge, 2008). 48 Heinrich Schenker, Free Composition (Der Freie Satz): Volume 3 of New Musical Theories and Fantasies/, translated and edited by Ernst Oster (New York: Longman, 1979), 5.
9 language, it is typically misleading to label the foreground harmonies with Roman numerals. A far more useful approach would be to identify the smaller melodic figures, the phrases within a section, and examine the relationship between adjacent chords. Identification of the key notes in the bass lines (e.g. adding tails and stems as per the Schenkerian method) would emerge from a clear understanding of the melodic phrases. The process of identifying all the melodic elaborations such as arpeggiations, linear progressions (3-prg, 4-prg etc.), neighbouring notes, and two-note arpeggiations between voices can also be challenging with this repertoire but uncovering these details will help substantially in revealing all the different layers and voices.49 The next step in performing a Schenkerian analysis (middleground level) focuses on identifying connections and linking up the music into larger spans. These layers are then refined several times to fully uncover the “deepest” layers of the musical structure.
2.1.1 Strengths and Limitations A common criticism of the Schenkerian method is that it is very “subjective;” this method ultimately reflects the analyst’s musical perceptions and intuitions and evidently, despite the benefits of utilising the Schenkerian approach, the analysis will have a narrow focus.50 This would essentially mean that more than one fundamental line is possible for a work (e.g. as shown in the third movement of Hindemith’s First Piano Sonata) and this raises the question of how one would choose one interpretation over another. Whilst it would be useful to establish an Ursatz for each of the movements, it is also worthwhile to be aware of the overall Ursatz, its intermovement connectivity.51 This will in turn fully account for the musical action within the respective movements. It can be argued that Schenker’s techniques of elaboration provide a limited view of the work as the aim is to establish a hierarchical relationship between events, a reduction to the core notes. In the case of this piano sonata, and perhaps for other early twentieth-century music, examining the foreground and middleground details is equally as important as obtaining the fundamental structure. Although this can arguably be stated for other earlier works (ones that can be fully analysed from a Schenkerian approach), it is these elaborations that enrich and provide a
49 Ibid, 61-87. 50Anca Preda-Ulita, “Adaptations of the Schenkerian Analysis to Post-Tonal Music,” Transylvania University of Brasor Series VIII: Performing Arts 6.55 (2013): 85-91. 51 Hindemith’s First Piano Sonata is inspired from the poem, Der Main, by Friedrich Hölderlin. The text describes the poet’s dreams to explore the world and Hindemith’s composition reflects the poet’s feelings. The first movement could depict a lyrical introduction, an instrumental setting to the first two stanzas of the poem. By the fifth movement, the music could depict that the poet has reached his goal, to travel out to sea.
10 comprehensive insight into the music. For instance, the fourth movement contains a variety of different motivic materials and a Schenkerian analysis may not be the most ideal method to reflect its different characters at its surface level. Even if an appropriate Ursatz can be accomplished for each of these movements, Hindemith’s music contains far more “complex” harmonies than earlier music (of the common practice period) and each set of motives and/or melodic materials should be considered in order to obtain a deeper insight as opposed to reducing the music to a small number of key notes. Although there are instances where it is possible to provide Roman numerals for Hindemith’s harmony, it would be more beneficial to develop an approach that reflects the composer’s own harmonic language. This thereby allows the Schenkerian analysis to embody all the chromatic and extended harmonic features of Hindemith’s music. It is also commonly known that Schenker’s theory is essentially monotonal and its diatonic unfolding traditionally does not include modulation. Although local tonicisation can occur in certain instances, these movements have to be centred and related to the Stufe (the tonic). As seen through the examination of each movement of the First Piano Sonata, every section has its own unique key or tonal centre, and if traditional Schenkerian rules are to be adhered to, every movement diverging from its home key will be required to be explained accordingly. In addition, the Ursatz (with consideration of Schenker’s emphasis on counterpoint) determined for each movement have yielded some unorthodox results. Although this could easily be resolved by locating another note of the chord to fit Schenker’s concepts, this would not be a true reflection of the music. It can then perhaps be argued that a strong structural analysis alongside the application of a Schenkerian method would help in making it less subjective. Furthermore, some questions can be raised regarding the effectiveness of the Ursatz within the context of less tonal repertoire (i.e. early twentieth-century music). Another common argument with the concept of the Ursatz is that whilst the Urlinie traditionally unfolds the tonal space in a melodic dimension and the Bassbrechung expresses the harmonic dimension, how can this be demonstrated by a limited number of notes? In addition, it can become especially problematic as Schenker does not view ascending lines (e.g. the initial ascent) as greatly important to one’s understanding of the music. An ascending line could in fact contain some structural significance and help to identify tension and stability. Despite all these challenges and problematic areas, the Schenkerian method can still be relevant to twentieth-century works that contains strong tonal qualities.
11 A more comprehensive insight into the work would ultimately come from the various middleground levels of a Schenkerian analysis. As the details in the middleground level are of most interest to analysts and performers and in order to overcome the subjectivity and its limitations of the Schenkerian approach, one possible solution is the addition of an NRT- inspired approach in conjunction with the Schenkerian method.52 This will help in identifying the notes that should be selected from the foreground level and will support and reaffirm the notes identified for a middleground level chart. In particular, it can be argued that the notes identified in the Bassbrechung within the middleground level do not reveal many details as it essentially absorbs the individual movements between chords. Thus a more nuanced appreciation of the harmonic structure is arguably revealed through an NRT approach, which will enable the examination of the foreground harmonies and the movement between each set of pitches, potentially indicating changes in tension and stability.
2.2 Neo-Riemannian Theory Even though the origins of NRT came from Riemann’s Handbuch der Harmonielehre, scholars such as Lewin, Hyer, Cohn, and Klumperhouwer refined this theory to incorporate functions that sit outside of a diatonic key structure.53 NRT is a method used to analyse chromatic music and triadic textures, particularly in music by Wagner, Liszt, Schubert and Bruckner, to examine the “transformations” as opposed to “relationships” within the harmonies. 54 Although the Tonnetz is one tool that is frequently used to illustrate such transformations, applying this tool to Hindemith’s Piano Sonata is not an appropriate analytical approach. However, as this aspect of NRT relates to post-tonal harmony, it will be discussed further in the Conclusion. Papers have utilised NRT as an analytical approach will be examined to observe how it is used in practice. One such work by Richard Cohn focuses on promoting NRT through the harmonic analyses of late-Romantic triadic progressions.55 He aims to demonstrate that consonant triads have two sets of unique properties where one set can be described as the “primary basis of the syntactic routines of diatonic tonality” and the other set as the “voice- leading potential of motion between triads.”56 Similarly, Broman’s work investigates the pedagogical prospects of the NRT by performing an analysis of Max Reger’s “Traüme am
52 John D. White, Comprehensive Musical Analysis (New Jersey: Scarecrow Press, 1994), 44. 53 David Lewin, Generalized Musical Intervals and Transformations, 1-30. 54 Cohn, “An Introduction to Neo-Riemannian Theory,” 167-180. 55 Richard Cohn, “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions,” Music Analysis 15.1 (1996): 9-40. 56 Cohn, “Maximally Smooth Cycles,” 13.
12 Kamin”.57 Broman believed that NRT could provide “a structure within which to explore issues related to voice-leading connections and set-class consistency” as well as bridging the gap between tonal and atonal techniques in theory pedagogy.58 Similarly, Dmitri Tymoczko’s writings demonstrated how the concept of voice-leading (an aspect crucial to NRT) and minimal voice-leading operations applies not only to chords and chord progressions but to scales and modulations as well.59 The use of measuring voice-leading distances for both chord progression and modulation provides a geometric foundation – especially in relation to performance practice. His theory is justified through his studies of counterpoint from the Middle Ages to the extended tonality of Dmitri Shostakovich. Ramirez’s work also focuses on viewing music from a Neo-Riemannian perspective when investigating Bruckner’s music.60 From his viewpoint, Bruckner’s music has not received the same amount of attention from a Neo-Riemannian approach in comparison to other analytical ones.61 Hence, Ramirez contributes a Neo-Riemannian examination of chromatic-third relations in some of Bruckner’s compositions in the 1880s (Symphony No. 6, Symphony No. 8 and Ecce Sacerdos Magnus), focusing on identifying the non-functional chord progressions, symmetrical divisions of the octave and the temporary suspension of tonic centricity. This illustrates that there is an “evolution in Bruckner’s handling of chromaticism” that has not been discussed in existing literature.62 It is particularly interesting that these papers have focussed solely on using the NRT as a tool to understand the music but they do not directly mention (with the exception of Broman which discusses the pedagogical prospects) how it can be applied to other musical practices such as performance. It is evident upon examining these papers that these methodologies have the potential to aid in performing the work as they provide a different insight into the treatment of harmonies. Thus, it would be highly beneficial to take this into consideration when undertaking this research. The existing studies that have combined both methodologies have not exhausted all the possibilities of this analytical approach. On the whole, based on the papers examined for this thesis, the works chosen for each of the respective author’s studies have mostly focused late Romantic to early twentieth-century works and less so on works that
57 Per F. Broman, “Reger and Riemann: Some Analytical and Pedagogical Prospects,” Svensk Tidskrift för Musikforskning [The Journal of the Swedish Musicological Society] 84 (2002): 13–25. 58 Broman, “Reger and Riemann,” 24. 59 Dmitri Tymoczko, A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. (New York: Oxford UP, 2011). 60 Miguel Ramirez, “Chromatic‐Third Relations in the Music of Bruckner: A Neo‐Riemannian Perspective,” Music Analysis 32.2 (2013): 155-209. 61 Ramirez, “Chromatic‐Third Relations,” 155. 62 Ibid.
13 embody tonal and post-tonal elements. This indicates a need for these methodologies to be tested on early twentieth-century music.
2.3 Integration of NRT and Schenkerian Methods Steven Rings asks,
Does Neo-Riemannian theory represent an ‘alternative’ to such theories or an adjunct to them? Put more pointedly, are Neo-Riemannian and Schenkerian methods in competition with one another, or are they potentially complementary, how might they best interact in analytical praxis?63
Recent scholarship has indeed begun to compare and attempt to integrate NRT and Schenker’s method. One possible example of this can be found in René Rusch’s work which discusses Tovey’s “Tonality in Schubert” and how an understanding of Schubert’s late tonal works can be gained through amalgamating the Schenkerian method and NRT.64 Tovey’s concept of key-relations can function as a “bridge between these two theories because it approximates parsimonious voice-leading operations while preserving chord function within a tonal hierarchy”.65 A graph comparing Schenker’s graph and a Neo-Riemannian analysis was used to support this, solidifying Rusch’s investigations. This study provides a strong foundation for forming ideas of how NRT and Schenkerian methods can work together to reveal Schubert’s use of tonality. Despite the aid of Tovey’s concept of key relations, this suggested “hybrid” analysis primarily involved an explanation of how the notes in the bassbrechung are selected – via the relevant NRT transformations.66 Rusch points out that there is a conflict between contrapuntal voice-leading (Schenker) and parsimonious voice- leading (NRT), which renders the two theories incompatible but one way of resolving this issue will be further examined in the methodology for this project.67 Similarly, Rifkin’s article on a theory of motives for Prokofiev’s music utilises the Schenkerian method and the NRT to provide an insight into the composer’s chromatic
63 Steven Rings, “Perspectives on Tonality and Transformations in Schubert’s Impromptu in E-flat, D. 899, no. 2,” Journal of Schenkerian Studies 2 (2007): 33. 64 René Rusch, “Schenkerian Theory, Neo-Riemannian Theory and Late Schubert,” Journal of the Society for Musicology in Ireland 8 (2012-13): 3-20. 65 Rusch, “Schenkerian Theory, Neo-Riemannian Theory and Late Schubert,” 5. 66 Ibid 17-19. 67 Ibid 19.
14 language.68 Her study has shown that Schenker’s method can only account for the “idiosyncratic chromatic slides” in Prokofiev’s music but the method fails to explain the presence of the chromaticism. It is through exploring Neo-Riemannian principles, the theoretical and analytical implications of the three different types of motives (systemic, functional pitch-class and non-functional pitch-class), whilst considering Schenker’s method that aids in providing an insight into the composer’s music. Rifkin’s study, much like Rusch’s work, has shown that utilising two different analytical approaches can provide a more insightful view of the music we seek to understand. Plotkin’s work on transformational analysis contains elements of the NRT and Lerdahl’s chordal space theory.69 Transformational theory, developed by David Lewin, one of the theorists who contributed to the growth of the NRT, is a theory that treats musical transformations (e.g. transpositions, inversions) as elements of a mathematical grouping, a logical formalisation, which can be used to analyse both tonal and atonal music.70 A specific tool, Filtered Point-Symmetry (FiPS) is used for his dissertation and he explores how this tool can manipulate “iterated maximally even sets over time” and how it has the potential to affect “our conception of musical networks and related analytical techniques”.71 As stated by Plotkin, a “diatonic network is created from triadic nodes connected to each other through parsimonious and stepwise transformations, where the transformations themselves result solely from iterated maximally even operations”.72 An in-depth discussion of the FiPS tool reveals that its analytical landscape contains elements of the NRT and Lerdahl’s chordal space theory. The FiPS tool is then used to analyse Chopin’s E major Prelude (op. 28, no. 9) and the prelude from Tristan und Isolde. Through Plotkin’s analyses and examinations of the theoretical concepts, his dissertation has demonstrated that FiPS is a “promising” tool to analyse late tonal music and that the examination of the fundamental interactions between note distribution and time will provide a significant insight to the music.73 Pieslak’s work compares the different and conflicting analytical approaches, Schenkerian, Schoenbergian and Neo-Riemannian methodologies, to late nineteenth- and early twentieth-century music and he suggests a new model of analysis should be constructed
68 Deborah Rifkin, “A Theory of Motives for Prokofiev’s Music,” Music Theory Spectrum 26.2 (2004): 265-90. 69 Richard James Plotkin, “Transforming Transformational Analysis: Applications of Filtered Point-Symmetry,” (Ph.D., University of Chicago, 2010). 70 Edward Gollin and Alexander Rehding, The Oxford Handbook of Neo-Riemannian Music Theories (New York: Oxford UP, 2011), 516; David Lewin, “Transformational Techniques in Atonal and Other Music Theories,” Perspectives of New Music 21.1/2 (1982): 312-71. 71 Plotkin, “Transforming Transformational Analysis,” v. 72 Ibid v. 73 Ibid 3.
15 from integrating certain elements of the different approaches.74 Pieslak acknowledges that each of these have their strengths and limitations but they will need to be revised in order to construct a “more widely accepted” approach to analyse music of this historical era.75 His investigation consisted of a thorough discussion on the structure of the Schenkerian, Schoenbergian and Neo-Riemannian analytical methods. This then leads into applying these methods in practice by analysing three works, Schoenberg’s “Lockung” (Op. 6/7), Debussy’s “Les sons et les parfums tournent dans l’air du soir” and Scriabin’s “Enigme” (Op. 52/2).76 Pieslak then critiqued the process of the analyses and he firmly believes that a new methodology should reveal “in what capacity a work can be linked with the music written before it was composed, but also allow a work to be examined on its own terms, free of a schematic process.”77 The addition of a Schoenbergian approach to Schenkerian and Neo- Riemannian methodologies can be regarded as ‘unusual,’ but this may prove to be useful upon analysing the works that contain extended tonality. New insights can be gained from the analyses through the help of performances assessed against Schoenberg’s motivic approach, the composer’s writings, and in understanding the historical context. Sayrs’ work delves into an examination of theories that can be used to analyse Wolf’s songs.78 As Sayrs states, late nineteenth-century music “inhabits an ambiguous realm of mixed diatonic and chromatic tonality” and this poses as a problem for music theory as the analytic tools used to address it are not suitable.79 It can also be deduced that this will also pose as a problem for early twentieth-century music. Sayrs utilises the Schenkerian method as well as “neo-traditional” theory, in viewing the three functions (tonic, subdominant, dominant) as labels rather than transformations, to address this issue, and acknowledges that these methods alone will not suffice.80 Neo-traditional theory has the advantage of creating comprehensibility through understanding relations between chords themselves as opposed to the Schenkerian method and traditional theories where the focus is on relating the chords back to the tonic. However, in certain cases, chords need to be related back to the tonic in order to fully understand the music. Her overview of the analytic results has shown the ramifications of reconceptualising the Ursatz and she explores the relationship between the
74 Jonathan Robert Pieslak, “Conflicting Analytical Approaches to Late Nineteenth- and Early Twentieth- Century Tonal Music: A Meta-Theoretical Study” (Ph.D., University of Michigan, 2003). 75 Pieslak, “Conflicting Analytical Approaches,” 239. 76 Ibid 53-143. 77 Ibid 245. 78 Elizabeth Paige Sayrs, “Approaches to Wolf: Schenker, Transformation, Function” (Ph.D., Ohio State University, 1997). 79 Sayrs, “Approaches to Wolf,” ii. 80 Ibid 6-19.
16 “equal division of the octave” and Schenkerian theory. She also suggests “dividing” as a transformation, in order to account for the chromaticisms encountered in the music within the Schenkerian framework. This in turn creates a bridge between the traditional Schenkerian method and the neo-traditional theory.81 As will be later demonstrated in the methodology, Sayrs’ study has been particularly illuminating in emphasising the need to treat the chords as their own “entities” as opposed to relating them all back to the tonic. Using both the Schenkerian and Neo-Riemannian approach can be challenging and potentially problematic but as shown through these few works (Sayrs, Plotkin, Pieslak, Rifkin and Rusch), it can in fact provide useful perspectives on the music. It is also interesting to point out that both Sayrs' and Plotkin's works expand on the Schenkerian approach or the NRT through combining it with another approach, where Plotkin's work combines NRT with Lerdahl's theory and Sayrs' work combines the Schenkerian method with Neo-traditional theories. Baker’s work on some selected sections of Wagner’s Parsifal explicitly states the use of Neo-Riemannian and Schenkerian approach for his investigation.82 The Neo- Riemannian approach in Baker’s investigation focuses on creating an “inclusive model” that is capable of “analysing any parsimonious connection between two common practice sonorities.”83 To do this, the author establishes context (introducing the opera, Gesamtkunstwerk, performance history), how this work has been previously analysed, reviews and extends the NRT, extends the Schenkerian approach for late-Romantic music, before proceeding to analyse five different scenes. His work has shown that applying both NRT and Schenkerian approach is insufficient to analyse Parsifal and they do need to be modified and extended to become a more appropriate analytical tool to analyse chromatic passages.84 Baker has suggested that it would be interesting in future research to compare and contrast the hexatonic and octatonic harmonic motion in parsimonious passages in the opera to non-parsimonious passages, to assess whether Wagner uses parsimony in a “super leitmotivic” manner and how diatonicism and chromaticism can be seen in the opera.
81 Ibid 162. 82 Steven Scott Baker, “Neo-Riemannian Transformations and Prolongational Structures in Wagner's ‘Parsifal’” (Ph.D., Florida State University, 2003). 83 Baker, “Neo-Riemannian Transformations,” xv. 84 Ibid 152-155.
17 2.4 Expansion of Schenker and NRT Although there have been some attempts by theorists to create a “hybrid” method that can elucidate compositional elements that elude or challenge traditional analysis, this particular amalgamated approach has not been attempted before. Although the Tonnetz can be modified to accommodate to Hindemith’s harmonies, it is evident that there is still no clear link between these diagrams and a more traditional analysis. Although a Schenkerian view of a Neo-Classical work can be accomplished, the harmonic details will evidently be incomplete, especially on a middleground level. As the foreground harmonies are post-tonal and Hindemith’s music cannot be approached by a traditional Roman numeral analysis, an NRT-inspired approach will assist in supplying the missing harmonic component, and this will then enrich the middleground level charts. Thus, as a way for NRT to assist with this, it is more pragmatic to examine the individual voice-leading movements between each chord or between broader pitch collections. In doing so, this extends the typical procedure of NRT (in utilising the Tonnetz, labelling transformations etc.) and will emphasise the finer harmonic details within the music. The idea of examining voice-leading movement belongs to Transformational theory, a branch of music theory established by David Lewin through his work, Generalized Musical Intervals and Transformations.85 This theory focuses on the intervals or types of musical motion that can be described as transformations, as elements of a mathematical group and encompasses NRT as well. The resulting analyses from these are effective in a visual and metaphorical manner as they illustrate how one musical event is transformed into another as an audible process in a piece of music. Whilst Lewin’s transformational theory is heavily influenced by Hugo Riemann, he reconceptualises Riemann’s approach by reordering the relationship between objects (triads) and processes (functions). Interestingly, Lewin’s meaning of function has more mathematical meaning (in that he seeks out transformations rather than following the archetypal harmonic progressions) but Riemann approaches function from a categorical stance. Originating from Cohn’s “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions,” some factors that are particularly significant in the analysis of late Romantic music include higlighting common tones and
85 Lewin, Generalized Musical Intervals and Transformations, 1-30.
18 maximally smooth voice-leading movement.86 Cohn stated that one set of “unique properties” consonant triads have
concerns the voice-leading potential of motion between triads, may be characterised in group-theoretic terms without any appeal to tonal centres, diatonic collections, harmonic roots and the like, and is the basis of many of the syntactic routines of chromatic music.87
This potential of voice-leading movement was later discussed and developed by Douthett and Steinbach who established a criteria to illustrate these “symmetries inherent in parsimonious structures.”88 The visual representation of “parsimonious” graphs is one way to observe the interaction between parsimony and the “modes of limited transposition,” a useful tool to reveal the “complexities of late nineteenth and early twentieth-century voice- leading.”89 Similarly, Straus and Roeder further explore voice-leading movements in terms of similarity to different pitch class sets in succession. Straus explores the idea of a “total” voice leading movement from one chord to the next, as opposed to a traditional view, the interval multisets.90 This will thus account for all the “possible destinations” in subsequent chord, examining the “overall voice-leading gesture”, “the sound envelope” and the “sonic environment.”91
Chord X Chord Y Chord X Chord Y
Figure 2.1 “Traditional” and “Total” Views of Voice Leadings from Chord X to Chord Y.
86 Cohn, “Maximally Smooth Cycles, Hexatonic Systems,” 12. 87 Ibid 13. 88 Jack Douthett and Peter Steinbach, “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition,” Journal of Music Theory 42.2 (1998): 241. 89 Douthett and Steinbach, “Parsimonious Graphs,” 260. 90 Joseph N. Straus, “Total Voice Leading,” Music Theory Online 20.2 (2014): 1-9. 91 Straus, “Total Voice Leading,” 2.
19 Straus also attempted to generalise the voice-leading systems through three key criteria: uniformity (where the voices would move by the same intervallic distance - traditional transposition), balance (where the voices move by the same index number - traditional inversion), and smoothness (the extent to which the voices travel the shortest possible distance).92 On the other hand, Roeder proposes a different perspective on voice- leading in atonal music where he utilises vectors to present and illustrate the individual movements among chords and his analysis focuses on examining the voice leading movements in the pitch space.93 Furthermore, Hook continued to develop these concepts by creating a group structure of triadic transformations,
92 Joseph N. Straus, “Uniformity, Balance, and Smoothness in Atonal Voice Leading,” Music Theory Spectrum 25.2 (2003): 305-352. 93 John Barlow Roeder, “Voice Leading as Transformation,” in Musical Transformation and Musical Intuition: Essays in Honor of David Lewin, ed. Raphael Atlas and Michael Cherlin (Dedham: Ovenbird Press, 1994), 41- 58. 94 Julian Hook, “Uniform Triadic Transformations,” Journal of Music Theory 46.1/2 (2002): 57-126. 95 Dmitri Tymoczko, “Set-Class Similarity, Voice Leading, and the Fourier Transform,” Journal of Music Theory 52.2 (2008): 251-272. 96 Clifton Callender, “Voice-leading Parsimony in the Music of Alexander Scriabin,” Journal of Music Theory 42.2 (1998): 219-233. 97 The “S” (Slide) relation is obtained through a LPR Transformation: Leading-Tone to Parallel to Relative Transformation. 98 Callender, “Voice-leading Parsimony,” 232. 99 Yeajin Kim, “Smooth Voice-Leading Systems for Atonal Music” (Ph.D., Ohio State University, 2013), 1-129. 100 Kim, “Smooth Voice-Leading,” 61-128.
20 being grouped by pitch-class sets’ string interval contents also contain a strong consideration of motives, how listeners hear the music, acknowledging the role cognitive psychology in this method.101 A work carried out by Lerdahl and Krumhansl discusses how voice-leading is one of the factors that contributes to the theory of tonal tension.102 They state that the four components necessary for a “quantitative theory of tonal tension” consist of the following: 1. A representation of hierarchical (prolongational) event structure. 2. A model of tonal pitch space and all distances within it. 3. A treatment of surface (largely psychoacoustic) dissonance. 4. A model of voice-leading (melodic) attractions.103
Whilst the idea of that certain pitches tend strongly or weakly towards other pitches has been recognised in music theory, scholars such as Bharucha explain the phenomenon for the urge for a less stable pitch to resolve to a subsequent and more stable pitch.104 Furthermore, it is interesting to observe how the basic space interrelates with the anchoring strength of the melodic attraction, where the increase of the anchoring strength aligns with the growing amount of distance between notes.105 From these studies, it is evident that one way to extend or adapt these existing ideas from a tonal perspective is to examine the relationship between successive pitches of simultaneously moving parts or voices, calculating this voice-leading movement alongside a typical Schenkerian chart.
101 Ibid 17-19. 102 Fred Lerdahl and Carol L. Krumhansl, “Modeling Tonal Tension,” Music Perception 24.4 (2007): 329-366. 103 Lerdahl and Krumhansl, “Modelling Tonal Tension,” 330. 104 Ibid 336. 105 Ibid 337.
21 Chapter 3
Analysis and Performance
Although an analysis of any given work will produce a significant amount of information and data that nuances the details of the composition, an ongoing issue raised by many over the last few decades is the relevance of analysis. In the study of Hindemith’s First Piano Sonata, the relationship between analysis and performance will be first considered through the analysis of recordings. This will then inform the analytical method and the interpretation of the analytical data.
3.1 Approaches to Analysis and Performance The relationship between analysis and performance is an ongoing issue that has been widely discussed over the last two decades. Some scholars have encouraged analysts in stimulating an exchange of ideas between the two “competing” disciplines, some have tried to reconcile these two opposing forces in establishing a “dialogue” between the two, whilst others have attempted to justify how the focus on one particular musical element or the combination of several different elements are of great assistance in creating a deeper understanding of a work. As highlighted in Cook’s “Analysing Performance, Performing Analysis”, “one should make analysis true through, rather than true to experience.”106 Furthermore, analysis, as emphasised by Lewin, “is not an aid to perception, or to the memory of perception; rather, we are in the very act of perceiving.”107 It is crucial to note that whilst theoretical models provide the basis for each respective analysis, the description of the theory will carry its own “assumptions”.108 As any analysis might be considered subjective by others there is a growing need for analysts to demonstrate the implications of their analysis for other practitioners in other disciplines, particularly in performance. It has been stated by the renowned musicologist and performer, Donald Tovey, that “performers should understand what they play.”109 Whilst this statement is debatable, there is existing literature that argues from both sides, with one side that promotes a strong need for analysis for performers and the other with the suggestion that it is a performer’s analysis that
106 Nicholas Cook, “Analysing Performance and Performing Analysis,” 253. 107 Lewin, “Music Theory, Phenomenology, and Modes of Perception,” 327-392. 108 Cook, “Analysing Performance and Performing Analysis,” 254. 109 Donald Francis Tovey, A Companion to Beethoven’s Pianoforte Sonatas (London: Associated Board of the Royal Schools of Music, 1931), iii.
22 can be of use to an analyst. Views that strongly promote the vital need of analysis for performers can be traced back to Berry’s Musical Structure and Performance and Cone’s Musical Form and Musical Performance.110 However, there are other scholars such as Dunsby, Howell, Rink, Schmalfeldt, and Yih who have worked towards creating a balanced relationship between performance and analysis, as opposed to the prescriptive approach taken by the aforementioned scholars. They also worked towards demonstrating how a performer’s analysis is of vital importance in understanding the work.111 How might one even begin to address this issue? As Fisk pointed out, why does it always start with analysis?112 How can theory (the idea of analysing and examining the details within the music) be of assistance to performers? How would it work the other way around? Can a performer’s analysis inform a theorist’s analysis of the work? As summed up by Cook, one such approach by Berry promotes a ‘path from analysis to interpretive decision’, ‘findings of analysis and consequent outlets in performance,’ and these findings are then expressed in performance.113 Likewise, in Narmour’s article, “On the Relationship of Analytical Theory to Performance and Interpretation,” he argues that formal analyses are necessary for performers as they will perform considerably ‘better’ when the analytical theory is applied.114 It is evident that Berry and Narmour approach the music from analysis to performance, but what if it were to be reversed, approaching this from performance to analysis instead? It has been argued that when performers study a piece of music, they will gain its “meaning” but when analysts study the music, they will gain its “structure.”115 According to Yih, it is vital for performers to understand the “structural” effects of the music as this will help to develop intuitive inner hearing and to reach informed decisions for specific
110 Wallace Berry, Musical Structure and Performance (New Haven: Yale University Press, 1989); Edward T. Cone, Musical Form and Musical Performance (New York: W.W. Norton, 1968). 111 Jonathan Dunsby, “Guest Editorial: Performance and Analysis of Music,” Music Analysis 8/1-2 (1989): 5-20; Tim Howell, “Analysis and Performance: The Search for a Middleground,” in Companion to Contemporary Musical Thought, eds. John Paynter, Tim Howell, Richard Orton and Peter Seymour (New York: Pendragon, 1992), 692-714; John Rink, “Review of Berry,” Music Analysis 9/3 (1990): 319-39; Janet Schmalfeldt, “On the Relation of Analysis to Performance: Beethoven’s Bagatelles Op. 126, Nos. 2 and 5,” Journal of Music Theory 29/1 (1985): 1-31; Annie Yih, “Connecting Analysis and Performance: A Case Study for Developing An Effective Approach,” Gamut 6.1 (2013): 277-308. 112 Charles Fisk, “Analysis, and Musical Imagining. I. Schumann’s Arabesque,” College Music Symposium 36 (1996): 59-72. 113 Cook, “Analysing Performance and Performing Analysis,” 239. 114 Eugene Narmour, “On the Relationship of Analytical Theory to Performance and Interpretation,” in Explorations in Music, the Arts, and Ideas: Essays in Honor of Leonard B. Meyer, eds. Leonard B. Meyer, Ruth A. Solie and Eugene Narmour (Stuyvesant: Pendragon Press, 1988), 317-340. 115 Yih, “Connecting Analysis and Performance”, 277.
23 performance techniques such as phrasings.116 Furthermore, understanding the “temporal position” of certain pitches on both local and broader levels in conjunction with the structural effects will provide performers an “informed” and “intuitive” interpretation of the work, which will be effective in creating the overall mood of the performance.117 In the bigger picture, as suggested by Narmour, the study of music theory should not only help performers in demonstrating how these works are structured but how they fit into their stylistic and historical context. Music theory should “endow performers with the means to discover how different interpretations alter the listener’s perception and understanding of living works as art.”118
3.2 Schenker and Performance A small number of papers have utilised a Schenkerian approach, with a common recurring theme of its use for performers. One such work is by Asada whose objective was to analyse Scriabin’s Sonata No. 9.119 This study promotes the idea of utilising Schenker’s method as a performance tool and suggests significant implications particularly for performers as the method helps to determine where the climax of the piece occurs and the respective roles of each note.120 Similarly, Everett’s study strongly promotes the notion that the Schenkerian approach is well suited to analyse the feeling of grief in Schubert’s Winterreise.121 By performing this analysis on the songs in Winterreise and considering the lyrical content, Everett is able to demonstrate the specific motives and figures that illustrate the idea of grief. Another such work that promotes the use of the Schenkerian method to analyse music is by Plum and Drabkin.122 They also support the notion that performing the Schenkerian analysis will help improve the performer’s approach to the music as well as clarifying the voice-leading structure for listeners, performers and researchers. The essay provided a way to standardise the criteria by which Schenkerian voice-leading analyses are produced, providing an explanation of the passing passages rather than treating them as an ambiguity. The notion that the Schenkerian method is useful for performance is further
116 Yih, “Connecting Analysis and Performance,” 277. 117 Ibid 301. 118 Narmour, “On the Relationship of Analytical Theory,” 317. 119 Chizuko Asada, “Schenkerian Analysis of Sonata no. 9, Op. 68 by Alexander Scriabin” (M.Mus., California State University, 1997). 120 Asada, “Schenkerian Analysis of Sonata no. 9, Op. 68,” 37-38. 121 Walter Everett, “Grief in ‘Winterreise’: A Schenkerian Perspective,” Music Analysis 9.2 (1990): 157-75. 122 Karl-Otto Plum and William Drabkin, “Towards a Methodology for Schenkerian Analysis,” Music Analysis 7.2 (1988): 143-64.
24 reinforced in Swinkin’s work which strongly encourages the close ties between Schenkerian analysis and performance.123 The concept of applying analysis to performance has been discussed by many theorists, ranging from Janet Schmalfeldt’s work on Beethoven’s Bagatelles to Nicholas Cook’s study on “Analysing Performance and Performing Analysis.”124 Whilst Schmalfeldt’s research provides one indication in which analysis and performance can work together, much more work will be required to assess its effectiveness in practice. The results from the analysis could build on Schmalfeldt’s work to help inform performers as to how they would approach learning the music – to understand the harmonic language, where the work is situated within the broader historical context and to understand how detailed investigations of particular sections can influence their playing (e.g. in shaping the phrases).
3.3 A Schenkerian/Formenlehre Approach? The benefits of performing a Schenkerian and formalistic analysis as a way to assist performers has been supported by several scholars such as Yih and Samson as well as key musical figures such as Alfred Brendel. Yih strongly argues that an effective approach can be developed to connect analysis and performance through employing the various facets of the Schenkerian method.125 As suggested by Rink, performing a Schenkerian analysis requires four musical factors to be considered: formal divisions and functional processes of the work; the “constituent” motives (interspersed within the music from small phrases to bigger units); examining the “starting effect, culminating point” and ending effect within each phrase and its consequent phrase; and dynamic, temporal, expressive and articulation markings.126 One will then be able to observe the various motives, in Schenkerian terms, particularly from a foreground to middleground level.127 Yih also stated that certain Schenkerian elements such as continuity, interruption, delayed arrival, sustained momentum, weakened responses, overlapping of
123 Jeffrey Swinkin, “Schenkerian Analysis, Metaphor, and Performance,” College Music Symposium 47 (2007): 76-99. 124 Janet Schmalfeldt, “On the Relation of Analysis to Performance: Beethoven’s “Bagatelles” Op. 126, Nos. 2 and 5,” Journal of Music Theory 29.1 (1985): 1-31; Nicholas Cook, “Analysing Performance and Performing Analysis,” in Rethinking Music, eds. Nicholas Cook and Mark Everist (Oxford: Oxford UP, 1999), 239-262. 125 Yih, “Connecting Analysis and Performance,” 277-308. 126 John Rink, “Analysis and (or?) Performance,” in Musical Performance: A Guide to Understanding, ed. John Rink (New York: Cambridge University Press, 2002), 48; Yih, “Connecting Analysis and Performance”, 278- 279. 127 Yih, “Connecting Analysis and Performance,” 279.
25 phrases can be explained through analogies and she believed that these effects can be felt in the body. In understanding the formal divisions, one will learn about the directional information within the music, which will in turn help in developing phrase decisions.128 For instance, making phrase decisions stem from understanding the antecedent and consequent phrases and how an interruption in the Urlinie indicates a break in the continuity and flow of the phrase. Evidently, through performing a Schenkerian analysis, one will expand upon their knowledge on the music’s structural effects such as how the events unfold and lead to the preparation for cadences. This aligns with Schenker’s idea of the descending progression and the acquisition of a sense of “energy and pull” within the music.129 Additionally, certain melodic details will emerge from a Schenkerian analysis and this can include the identification of certain motives and how the melodic features (such as suspensions and voice exchanges) work with or against the chords. A direct correlation can also exist between the Urlinie, the dynamics and articulation markings. It is anticipated that the hybrid analytical method developed from this project will be of further assistance in performance practice. Alfred Brendel believed that performing Schenkerian analyses will help provide an insight into the music for performers.130 In the examination of Beethoven’s Piano Sonata Op. 2 No. 2, Brendel stated that he followed Schenker’s recommendation as a guide for performance directions where he used both hands for the broken octave triplets in the first movement as well as paying attention to the motivic connections established in the middleground Schenkerian chart.131 Furthermore, whilst he believes that it is important for every performer to “know enough about traditional harmony and counterpoint,” part writing, and the rudiments of music theory, he believes that it is perhaps more vital for the performer to establish their own thoughts and perceptions about the “atmosphere”, “character” and “poetic ideas.”132 Whilst Brendel supports that the findings obtained from a musical analysis are useful at times for a performer, he states that analysis should not be taken as the “key” to an insight into a “great performance.”133
128 Ibid 285. 129 Ibid 289. 130 Alfred Brendel, Alfred Brendel on Music (London: JR Books, 2001), 23-24. 131 Brendel, Alfred Brendel, 220. 132 Ibid 368. 133 Ibid.
26 On the whole, the use of formal analyses is supported by Samson, in needing to understand the music’s structure.134 Arnold Schoenberg presents a different perspective that formal analysis is “overrated” as it simply shows “how” something is done not “what” is done.135 Additionally, the use of a Schenkerian approach for performance has been criticised by Lester as this approach “downplays the thematic aspect and concentrates on underlying voice-leading structures.”136 As stated by Cook, each analytical approach will bring its “own truth through instigating its own perceptions, bringing into being a dimension of experience that will coexist with any number of others.”137 However, its “validity” can be dependent on other factors. Interestingly, whilst there are a number of papers that discuss how the Schenkerian approach may or may not be applicable to performance practice, there are much fewer papers that suggest how NRT can be of use to performers. This thesis will examine which elements from this method can be of use in performance practice.
3.4 A “Performative” Approach As pointed out by Lester through examining studies conducted by notable analysts such as Berry, Cone, Howell, Schenker, and Tovey, their analyses are not validated “by referring to a singular performance.”138 Therefore, Lester suggests that performances should be referred to “in order to get at the essence of the pieces they analyse.”139 Through his examination of two recordings of Mozart’s Sonata K. 331 by Horowitz and Kraus, Lester raises some interesting questions as to which musical elements should be brought to the front and which ones are crucial to musical form. His findings in the Minuet uncovered “whether tonal closure occurs at the same time as rhythmic and thematic closure.”140 Although Hindemith’s Piano Sonata does not conform to typical tonal closures, it can be observed that rhythmic and thematic closures do occur within each key section. The idea of connecting analysis and performance by comparing several different performances of the same work (by different performers) has also been investigated by scholars such as Narmour and Yih. Yih in particular, suggests that an examination can be
134 Jim Samson, “Analysis in Context,” in Rethinking Music, eds. Nicholas Cook and Mark Everist (Oxford: Oxford University Press, 1997), 35-54. 135 Ibid. 136 Lester, “Performance and Analysis,” 213. 137 Cook, “Analysing Performance and Performing Analysis,” 261. 138 Joel Lester, “Performance and Analysis: Interaction and Interpretation,” in The Practice of Performance: Studies in Musical Intepretation, ed. John Rink (Cambridge: Cambridge University Press, 1995), 197-216. 139 Lester, “Performance and Analysis,” 199. 140 Ibid 202.
27 carried out to observe how these performers begin the work, shape their phrases, approach the musical motives and their approach to the direction of the music. She also proposes the following questions that can be investigated:141 1. Why do certain notes have specific significance? 2. How does repetition have an impact on the music? 3. What is the structural effect of particular notes and/or rests?
The idea of analysing recordings can also be supported by Narmour, as he believes that listening to recordings should be the primary way to learn about the pieces, allowing analysts to immerse themselves in and experience the music.142 One strong suggestion by Lester proposes that at least two recordings are required, and should be referred to when validating an analysis. By paying attention to the recordings, this will help in assisting in distinguishing between “analytical decisions involving indisputable aspects of structure which should not be contradicted by any analysis or performance.”143 The analysis of such performances will then provide the essence in enhancing one’s understanding of the music- theoretical issues within the music. He also proposes that the idea of a metre and phrase focussed analysis (led by Schachter) as well as a durational and voice-leading analysis in conjunction with the analysis of recordings will be useful. Barolsky and Klorman have also suggested that to “navigate the treacherous dialectic” between performance and analysis, musical recordings will need to be studied, with a focus on the following:144 1. Improvisation – the combination of performance, composition and analysis into “one integrated process.” 2. Rehearsal – the process of interpreting the players’ “marked” scores for analysis 3. Play – understanding the “impulse” that is critical to musical participation.
Similarly, Sutcliffe’s analysis of Scarlatti’s keyboard sonatas describes the composer’s musical language through its phrase rhythm, opening and closure, use of
141 Yih, “Connecting Analysis and Performance,” 277-308. 142 Narmour, “On the Relationship of Analytical Theory,” 331. 143 Lester, “Performance and Analysis,” 212. 144 Daniel Barolsky and Edward Klorman, “Performance and Analysis Today: New Horizons,” Music Theory Online 22.2 (2016): 1-4.
28 sequences and the idea of repetition and rationality.145 This is then validated through references and at times, criticisms of recordings. Sutcliffe notes that some performers take “too many rhythmic liberties” and some are “chronically under-aware of the implied cross- rhythms …. Unless they are clearly indicated by the notation.”146 Through Sutcliffe’s knowledge of the context (social, political and cultural environments), his various views on different performances of the keyboard sonatas and examination of the works of his contemporaries, he presents a view that is of great help to one’s “understanding and performance of any composer and his music.”147 Therefore, it is proposed that analysts should incorporate performances as “an important ingredient of the analytical process.”148 In the near future, a gradual shift towards an “account” of a piece should be encouraged, to seek how it draws upon analytical and characterological description of musical events by using “descriptive” terms to encapsulate the character. If there are disagreements on the analyses of a piece, there will be performances that “disagree with one another” and it will become vital for both analysts and performers to further investigate these differences to gain a deeper insight to the music. As aptly stated by Lester,
Taking note of performances as part of the analytical process will assist in distinguishing between analytical decisions involving disputable aspects of structure which should not be contradicted by any analysis/or performance, and those analytical decisions that are interpretative.149
145 Dean W. Sutcliffe, The Keyboard Sonatas of Domenico Scarlatti and Eighteenth-Century Musical Style (Cambridge: Cambridge University Press, 2003), 145-187. 146 Sutcliffe, Keyboard Sonatas, 177. 147 Mark Kroll, “Reviews: “The Keyboard Sonatas of Domenico Scarlatti and Eighteenth-Century Musical Style,” Notes 61.1 (2004): 147. 148 Lester, “Performance and Analysis,” 211. 149 Ibid 212.
29 3.5 Moving Past Formal Analyses It has been suggested that there is more that can be explored in creating a relationship between analytical theory and performance, perhaps moving towards creating a balance between formal analysis and its opposing counterparts.150 For instance, in each of Eugene Narmour’s description of the varying musical parameters, he establishes a strong interplay of elements as well as demonstrating how this would have an effect on the listener and the performer, thus creating an approach in highlighting how analysis plays a role in a listener’s and performer’s experience of the music. Narmour establishes a strong interrelationship between harmony and rhythm, stating that it is crucial towards an understanding of the effect of a passage and why it must be played a certain way. In the case of melody, Narmour implies that “the larger a melodic interval, the more implicative it is; and the smaller a melodic interval is, the less implicative it is.”151 This could suggest a correlation between the idea of a greater increase in tension with a larger melodic interval and a smaller amount of tension alongside a smaller melodic interval. Furthermore, with consideration to the Gestalt principle of continuation, it is interesting to point out that smaller intervals generally tend to “imply continuation in the same direction” and large intervals tend to imply a reversal of direction.152 A strong interrelationship can then be created between the elements of harmony, rhythm and melody, supported by an example from Handel’s Overture to Messiah where double-dotting the rhythms “considerably alters the strength of melodic (and harmonic) implication(s).”153 This study thus demonstrates the need to consider other musical elements in analysis, not just melody and harmony. A different approach by Rothstein suggests four approaches as an alternative to the formalistic ones where other missing musical elements will be acknowledged in the process: thematic and motivic analysis, metrical analysis, phrase analysis and voice leading analysis.154 In addition, he recommends “character” analysis, where the motifs and the dramatic elements are treated as vital components to the understanding of the music.155 For Rothstein, he believes that performers provide listeners with the experience of the work
150 Narmour, “On the Relationship of Analytical Theory”, 317-341. 151 Ibid 328. 152 Ibid. 153 Ibid 330. 154 William Rothstein, “Analysis and the Act of Performance,” in The Practice of Performance: Studies in Musical Intepretation, ed. John Rink (Cambridge: Cambridge University Press, 1995), 217-240. 155 Rothstein, “Analysis and the Act of Performance,” 222.
30 without the analytical understanding but the experience itself will provide the listener with an avenue towards understanding.156 Another alternative to formalistic analysis is the idea of the role of imagination. Fisk suggests that a performer’s analysis can serve as a basis for performance studies, as there is a strong correlation between a performer’s technique and the notion of “imagination.” 157 He believes that imagination is the key to an improved approach to music analysis and it is a performer’s analysis that can draw on articulate analytic awareness and the assessment of the music’s character as a necessary supplement to more “objective” analytical observations.158 The aim of this approach would then be to identify the aural shape and musical gesture and thus it can be argued that theorists will gain more from the performer’s modes of musical awareness than performers can gain from the explicit analytic awareness of theorists. Fisk also identifies several components within performance that are vital within an analysis, to account for a performance perspective: arm movement, arm-weight drop and release, the control of the “thumb”, separate hand practice, “bringing out” inner voices and pulsation. It could be a possibility for future analyses to embody a formenlehre approach as well as incorporating interpretations by a selected number of performers. This will be considered in the study of Hindemith’s Piano Sonata No. 1. The idea of imagination as a concept for performers can initially be traced back to Elisebeth Le Guin’s Boccherini’s Body: An Essay in Carnal Musicology, whose work has been described as a “quantum leap forward” in establishing a discourse that pays a significant amount of attention to performance.159 In a case study of Boccherini’s String Quartet in E major Op. 15 No. 3, Le Guin juxtaposes two different analyses, one that bears a strong resemblance to a descriptive and traditional approach, and the second, incorporating members of the quartet involved in the recording, to deliver a detailed discussion on the physical aspect of performing, by identifying the physical difficulties that are involved in delivering the music.160 As it is known that performance involves “negotiating” between the demands of physical gesture and sound, Le Guin’s ground-breaking work demonstrated one way of combining these components. On the whole, this body of work has in a way provided the
156 Rothstein, “Analysis and the Act of Performance,” 218-219. 157 Charles Fisk, “Analysis, and Musical Imagining. I. Schumann’s Arabesque,” College Music Symposium 36 (1996): 61. 158 Fisk, “Analysis, and Musical Imagining I,” 61. 159 James A Winn, “Review: “Boccherini’s Body: An Essay in Carnal Musicology,” Studies in Romanticism 45.4 (2006): 644. 160 Elisabeth Le Guinn, Boccherini’s Body: An Essay in Carnal Musicology (Berkeley: University of California Press, 2006), 223-53.
31 basis for scholars to undertake further research into musical gestures and imagination as part of performance analysis. Alternatively, Lester suggests the use of linear analyses, to depict “metric and hypermetric levels along pitch levels” and as a way to connect metre and phrasing.161 According to Schachter, durational analyses in conjunction with Schenkerian analyses can also have an impact on how performers would approach the music. In the case of Chopin’s Prelude Op. 28 No. 3, the additional layer of a durational analysis helped performers locate the beginnings and endings of larger rhythmic units and phrases.162 As Lester states, there should be a shift from merely finding the structure of a piece to investigating different and potentially multiple strategies for interpreting pieces.163 Similarly, Rothstein also argues that a rhythmic reduction of a work will be vital for performers through his examination of Strauss’s “Blue Danube.”164 In the long run, if there is to be a balance between analysis and performance, as Cook stated, these two “competing” facets need to be seen as “interlocking modes of musical knowledge” and they should be utilised “simultaneously and interactively, not in succession.”165 Much like Cone’s argument that music analysis lies somewhere between description and prescription, it may well be the case that a practical model to bridge analysis and performance may lie in between a performer’s analysis and a combination of different analytical approaches. Although more work is evidently needed in discussing how NRT in particular can be of use for a performer, on the whole, the idea of creating a dialogue between these two “competing” fields still needs to be explored. As it has been supported by various academics that Schenkerian analysis has relevance for a performer, it can thus be suggested that if NRT is integrated and combined with the Schenkerian method, more details will emerge, perhaps vital information for both the analyst and performer.
161 Lester, “Performance and Analysis,” 203. 162 Carl Schachter, “Rhythm and Linear Analysis: Durational Reduction,” in The Music Forum Vol. 5, ed. Felix Salzer (New York: Columbia University Press, 1980), 197-232. 163 Lester, “Performance and Analysis,” 214. 164 William Rothstein, Phrase Rhythm in Tonal Music (New York: Schirmer Books, 1989), 8. 165 Cook, “Analysing Performance and Performing Analysis,” 248.
32 3.6 Performance Recordings of Hindemith’s Piano Sonata No. 1 As previously stated, one way to bridge the approach to analysis and performance is through the analysis of recordings by performers. A comparison of two different recordings of the Sonata will be examined, identifying the performer’s stylistic approach and focussing on two particular moments in the music where the interpretations of the performers greatly differ. This will be accompanied by a discussion of what Schenkerian and NRT analysis has to offer in light of this. Whilst it is evident that these two mediums will offer different perspectives to the music, this assessment will demonstrate that listening to the recordings is one useful tool with the potential to enrich the analysis. At certain instances, it will be worth taking a closer examination of where the analytical data disputes the performers’ interpretation and this will in turn raise further questions and possibilities of how one should approach that particular moment in the music. It may also be the case that the analytical data will suggest that a particular note or phrase should be emphasised or the performer’s approach to a particular moment suggests that there are missing details in the analytical charts, which could then result in a direct correlation to the analysis. Whilst it is evident that utilising these two different mediums will enrich one’s insight into the music, how will these comparisons and discussions be carried out? A balance between the two will be attempted in the following discussion. Whilst it would be beneficial to use more recordings to create well-informed statements, for the scope of this study, two contrasting recordings will be examined, one by Glenn Gould and another by Sviatoslav Richter. An initial listening to these recordings strongly indicate that they are two distinctly different interpretations of the Sonata. Gould’s interpretation to the Sonata can be described as rather “introspective” as he approaches the phrases, indicated by the respective slurs, as one singular idea, as a “closed” phrase. 166 Gould’s unique interpretation focuses on these individual units, resulting in a sense of appreciation for these individual units. This can then pose as a challenge for the listener to identify the climactic moment of the phrase or section, within the overall structure. One example of this can be seen at bar 7 where the music yearns to reach the high B in bar 8 but instead, an emphasis is placed on rounding off the inner voices. Performed significantly slower than its stated tempo, a “contemplative” feel is thus evoked from Gould’s performance, a different interpretation with consideration to the poem that inspired the work.
166 Paul Hindemith, Piano Sonatas Nos. 1-3 (Gould), Sony Classical 074645267029, 1992, Compact disc.
33 Furthermore, there is a great amount of flexibility in Gould’s approach to rhythm through the modifications of basic pulses. Richter’s interpretation of the Sonata is significantly different to Gould’s in his approach to the tempo, phrase structure, rhythm and use of rubato.167 It moves at a quicker pace than Gould’s, with less fluctuation in the rhythm and there is a clear sense of the climactic moment within each section. Richter’s use of rubato bears a strong correlation to the overall melodic arch of the respective phrases (i.e. increasing in tempo as the music intensifies in both harmonic tension and surface activity) – used more sensitively than Gould and with a flexible approach to rests. Climactic moments can be heard more distinctly in this interpretation especially towards the end of the two key ideas (bars 16 to 22 and bars 33 to 37). There was also a clear distinction between the characters of the first and second idea. Richter’s interpretation of the second section sounds almost “subdued”, significantly different to the march-like feel evoked from the first idea (from the consistent crotchets in the bass). It will become evident upon the examination of the recordings that this is a necessary tool for performers and analysts as it will reveal certain elements that are not immediately apparent in analysis. In the case of Hindemith’s First Piano Sonata, some observations have been made based on the performer’s approach to specific melodic figures. Some attention has been given to the phrasing and how the performers have interpreted the slur markings. For future studies, a more thorough investigation can be carried out in examining the factors that determine a phrase: will these be determined solely through the use of slurs? What fingering should the pianist use in order to create a “rounded” phrase? Is it necessary for every phrase to “taper off”? How should slurs be used as an expressive device?
167 Paul Hindemith, Richter: Live in Kiev Volume 5 & 6, TNC Recordings H1465-66, 2002, Compact disc.
34 Chapter 4
Analytical Method
A method of analysis can thus be created that is appropriate for Neo-Classical composers such as Hindemith, and potentially other post-tonal composers, one that embodies a significant amount of Schenkerian characteristics yet draws on NRT-inspired elements to obtain a detailed harmonic analysis. If the use of one method creates one dimension of experience, it will be interesting to examine how the co-existence of two different methods will assist in the understanding the music and how this can be used to assist performers. This chapter will begin with a brief discussion on performing the segmentation of the music which involves ideas from Hindemith’s Craft of Musical Composition. This will then lead into a calculation of intervallic distances between chords, an application of the data as a form of harmonic analysis which can expand and refine the preliminary Schenkerian charts and a discussion of how the use of these data can suggest analytical interpretations that go beyond Schenker.
4.1 The Craft of Musical Composition According to Kemp, Hindemith was particularly interested in overcoming two “major, interlinked” problems: “how to answer students’ requests to ‘explain contemporary music and his own in particular, how to provide contemporary music suitable for amateurs.’”168 This in turn led to the creation of The Craft of Musical Composition, one of several theoretical works. His main objective in the treatise was to seek out an organised musical language that “will embrace both twentieth-century harmonic developments and the vocabulary of traditional harmony.”169 This was approached from an acoustical view, understanding the natural characteristics of tones, developing new scales (Series 1 and 2), reorganising chord groups according to their harmonic tension, and taking a different perspective to the theory of melody.170 This particular theoretical writing can be perceived to be a rationale, where it is partially scientific and intuitive. However, it is crucial to note that these theories are attractive to some people due to roots being drawn from the laws of Nature and it may not appeal to all
168 Kemp, Hindemith, 15. 169 Ibid 35. 170 Paul Hindemith, The Craft of Musical Composition (London: Schott, 1941), 14-197; Kemp, Hindemith, 35- 39.
35 theorists. These ‘Nature’-based theories have a tendency to have the “ring of truth about them, especially to those who seek a repudiation of atonality and twelve-note music.”171 For instance, Hindemith believed that his new insight into scales were of “divine provenance” due to their application and discovery. The Craft of Musical Composition, in of three volumes, is essentially Hindemith’s writing on musical theory as well as a teaching guide. His first book laid the theoretical foundations, the second provided some writings on its practical curriculum, including two- part writing and the third consolidates the first two volumes as well as adding some writings on three-part textures. Unlike other theorists of his time, his writings described the natural quality of the tones, investigated these sounds in relation to acoustics and physics and attempted to establish the fundamental relationships between tones.172 Some highlights in Hindemith’s work are his emphasis on “intuitive listening”, his theoretical writings on melody, including how it should be constructed and in particular, his thoughts on the concepts of melodic degree-progression and step-progression.173 He believed that these concepts are “indispensable for the analysis of existing melodies, in which one always begins with the determination of the harmonic content as the cruder ingredient, extracting the degree-progression and then seeking for step-progressions.”174 This is reinforced in Hindemith’s later writings (Craft III) where he especially proposed that each of the musical elements has a unique function in each layer of structure. Melody in particular “generates” the most details even though it lies closest to the surface.175 The melody can be extended through the use of thematic motivic connections as well as step progressions.
4.2 Rhythmic Reduction and Segmentation Although a rhythmic reduction is embedded within a Schenkerian analysis, in order to fully justify which chords or pitch collections should be further investigated from a NRT perspective, it will be necessary to have a thorough understanding of Hindemith’s harmonic language. For this study, step progressions will be chiefly examined instead of degree progression as the aim is seek the main notes in a melody (step progression) to support the rhythmic reduction, as opposed to locating the succession of roots in a larger harmonic
171 Kemp, Hindemith, 39 172 Paul Hindemith, The Craft of Musical Composition (London: Schott, 1941). 173 Hindemith, Craft of Musical Composition, 175. 174 Ibid 197. 175 David Neumeyer, The Music of Paul Hindemith (New Haven: Yale University Press, 1986), 30.
36 context (degree progression), although the degree progressions will still play some role in the following analysis. Step progression, according to Hindemith, is the primary rule of “melodic construction” where the “main” tones of a melody must move in “seconds”. They should identify all the melodic activity within a passage and longer range connections within a section or across the entire work. As illustrated below, Hindemith performed a melodic analysis on a ballad by Guillaume de Machaut, “Il m’est avis”, utilising his concepts of step progression, degree progression and locating the main voice.
Example 4.1 An Excerpt from Hindemith’s Melodic Analysis of de Machaut’s “Il m’est avis”.176
When applying this concept to the set repertoire, it is critical to remember that not all the pitches require harmonic support – some pitches may be supported by notes from a chord but some pitches may act as non-choral tones. As Neumeyer stated, “the step progression is not to be equated with Schenker’s Zug line.”177 Step progressions consist of a series of notes that only moves in one direction, they do not need to “outline a particular interval” and they can occur in other voices, not only within the “principal upper voice”.178 They reveal the “core” notes, eliminating the embellishments and repetitions. Slurs are to be used to indicate tied notes as well as consonant skips and main chordal movement. It is Hindemith’s belief that a “well-constructed melody may have four or more step-progressions.”179 It is also worth noting that the use of step progressions was also employed in Neumeyer’s five-staged analytic method where the “melodic activity” (step progressions and arpeggiations) is analysed after identifying the structural levels and the harmonic activity.
176 Hindemith, Craft of Musical Composition, 204. 177 Neumeyer, Music of Paul Hindemith, 67. 178 Ibid. 179 Hindemith, Craft of Musical Composition, 193.
37 Furthermore, in generating step progressions, it will be necessary to understand Hindemith’s thoughts on what comprises a non-harmonic or non-chordal tone. His chapter on “Non-Chord Tones” describes the following classifications which informed the segmentation of the first movement:180 1. Returning tone: When one tone moves to another tone for a short time before returning to its original tone. 2. Passing tone: A stepwise movement from one chordal tone to another. 3. Suspension: A succession of two intervals, the first of which is held over to the second, creating tension in conjunction with the second chord. 4. Unprepared suspension or Neighbouring tone: A tone that occurs a second above or below the primary chord tone and resolves to a note from the chord. 5. Neighbouring tone left by leap: A movement to a note whose “relation to the rest of the chord is less close than the original chord tone” and the leap occurs just before the second chordal tone.181 6. Neighbouring tone approached by leap: This differs slightly from the previously mentioned statement where the leap must be approached from the first chord. 7. Anticipation: The opposite of suspensions, appears where one or more tones of the second chord is introduced “too soon”, a “premature satisfaction of the listener’s curiosity”.182 8. Unaccented free tone: An unstressed note that does not belong to either of the stated chords. 9. Accented free tone: A rhythmically stressed note that occurs “on” the chord and is usually resolved back to its chordal tone by a leap.
Through the understanding of Hindemith’s analytical method, one will be able to identify the core notes and corresponding melodic embellishments, and this can be one important factor in segmenting the music. Whilst Hindemith’s writings have set the foundations, segmenting a piece of music requires more than just one fixed rule, it is not an exact science. Besides a comprehensive view of melodic elements, other musical elements will need to be considered and these can include register, duration and motives, which work with one’s musical sensitivity and perception. Utilising Hindemith’s particular perspective
180 Hindemith, Craft of Musical Composition, 165. 181 Ibid 172. 182 Ibid.
38 would greatly help in justifying the segmentation undertaken, helping to reduce subjectivity and bias on the part of the analyst. Following some of Hindemith’s main tenets, in the case of Piano Sonata No. 1, two different levels of rhythmic reduction can be drawn from the music, in minims (or dotted minims or semibreves, if there is a change in time signatures) and in crotchets. Despite the lack of a time signature, it can be observed that the first movement in particular, alternates between quadruple and triple time. By performing a rhythmic reduction on two levels, this could be perceived as a continuation from Hindemith’s idea of degree and step progressions, acknowledging that there is more than one layer of analysis, one on a broader scope (degree progression, minim level) and one that is more focussed (step progression, crotchet level). It is then imperative to note that not every bar will have the same number of beats as this will depend upon the data produced from uncovering the step progression. The rhythmic and motivic elements may suggest four crotchet beats in some bars, but others may suggest three crotchet beats. Brackets can be used to indicate beats that can be implied (due to the “time signature”) but are not necessary in the reduction.
4.3 Voice-Leading and Intervallic Movement and BiP Collection Instead of using the Tonnetz as a graphical representation to depict the transformations of the chord progressions, the highlighted chords or pitch collections (drawn from the rhythmic reduction) will be written on a single stave, in a close position, with their integers directly above the notes. Subsequently, the amount of intervallic movement between each set of pitches will be determined by the smallest number of semitones. “Minimal” movement has been placed as a priority as one of NRT’s core principles is to seek maximally smooth motion from one chord to the next (as mentioned earlier in Straus’ work), bearing a strong resemblance to a typical SATB harmony exercise, where there is an emphasis on smooth voice-leading (VL).
39
Table 4.1 Characteristics of the VL Movement from 0 to 6. VL Movement Description 0 Common tone 1 Increase/decrease by a semitone 2 Increase/decrease by a tone 3 Increase/decrease by a minor 3rd 4 Increase/decrease by a major 3rd 5 Increase/decrease by a perfect 4th 6 Increase/decrease by an augmented 4th/diminished 5th
Pitch Collection 1 Movement Pitch Collection 2 Fs 6 2 E 4 A 9 0 Fs 6
0 A 9
Figure 4.1 Calculating the Intervals Between Two Sets of Pitch Collections.
Upon calculating the amount of movement between each pitch collection, the data can then be categorised in three different ways to examine its role and possible effect on the music. 1. The “unordered” combination of numbers between each voice within the pitch collection. 2. The “ordered” combination of numbers between each voice within the pitch collection (from smallest to largest), known as the “basic interval pattern” and abbreviated as “BiP”. 3. Total amount of intervallic movement between each pitch collection.
The first set of data, the “unordered” combination of numbers, is essentially an unaltered presentation of respective voice-leading movement between each pitch collection. But it is the organisation of the second set of data, the “ordered” combination of numbers, where interesting observations can be made as these ordered sets of numbers can then be compared to other sections of the piece. The third type of data, the total amount of intervallic movement, comprises the total of the respective voice-leading movements within each pitch collection. This data will later be particularly useful in creating a graph that charts the amount of harmonic movement across the entire piece.
40 The second and third sets of data can then be arranged into a table, listing the range of intervallic movement between each pitch collection, the number of occurrences, the respective BiP and the specific number of occurrences of each. This will be done on a local level (key sections and ideas) as well as on a general level so that one can examine the frequency of a particular BiP across different sections of a piece. For example, if one set of BiP is more frequent than others, it is worth closer examination. This could potentially have an effect on the idea of tension and release within the phrase structure. For instance, building upon Narmour’s ideas, it could be hypothesised that a series of uniform intervallic movements could indicate a sense of harmonic stability and more varied intervallic movements could evoke a sense of instability.183
Table 4.2 An Example of Data Categorisation.
Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences
4.4 Visual Representations Two different types of visual representations will be used to illustrate the relationship that can be established between the Schenkerian and Neo-Riemannian approaches. The first of these will bear some resemblance to a typical Schenkerian chart whilst the other is in the form of a graph, a visual display of the data gathered from the pitch collections.
4.4.1 Schenkerian and NRT Chart A modified graph has been designed to combine the core elements of the Schenkerian analysis and the NRT-inspired approach. In order to integrate the groups of pitch collections, the Urlinie and the Bassbrechung, the various sets of pitch collections are placed on a separate system between the Urlinie and the Bassbrechung, linking each respective point with chords and bar numbers.
183 Narmour, “On the Relationship of Analytical Theory,” 321-334; Eugene Narmour, The Analysis and Cognition of Melodic Complexity: The Implication-Realization Model (Chicago: University of Chicago Press, 1992).
41 Urlinie
Pitch Collections
Bassbrechung
Figure 4.2 An Example of a Modified Schenkerian and NRT Chart.
By placing these pitch collections on their own stave in the middle system, one will be able to examine how the Urlinie is supported by the progression of pitch collections as well as the Bassbrechung. The addition of this middle system to a typical Schenkerian chart is critical in that it demonstrates the movement from one pitch collection to the next, the “vertical” harmonic movement (to obtain the “Amount of movement between each chord”) as well analysing the individual voice-leading movement within the pitch collections (to obtain the “BiP”). Hence, this additional system will help in enriching the details of the initial Schenkerian chart. It is also imperative that when sketching these pitch collections, they should be constructed in a manner that will allow the reader to visually see the close proximity of one chord to the next: depicting notes that are in common with the subsequent pitch collection and by utilising red arrows to depict any movement. Furthermore, a table will be inserted directly below this chart detailing the data obtained from calculating the various aspects of voice-leading and intervallic movement against the bar numbers of the piece (i.e. unordered combination of numbers, BiP and total number of intervals between each chord). Two different sets of Schenkerian and NRT charts will be needed, one with the “bigger” picture (the identification of minim beats) and another with “smaller” details (the identification of crotchet beats). Much like a Schenkerian chart where there is a clear relationship between foreground and background, producing two different sets of charts (with different focuses) will be useful in illustrating how the intervallic movement differs when looking at minim chords in contrast to crotchet chords. In calculating these movements between the pitch collections, this will thus substitute for a traditional harmonic analysis and the results can then aid in enriching the analytical chart.
42 4.4.2 Intervallic Movement Graphs Line graphs are then utilised to express the number of intervals between each pitch collection. The “x” (horizontal) axis will represent the quantity that will change periodically with time, the bar numbers and the highlighted minim or crotchet beats whilst the “y” (vertical) axis will represent the physical quantity, the amount of intervallic movement, ranging from the smallest to the largest number of intervals. As two different Schenkerian/NRT charts will be designed, two different graphs will be required, one with the identification of minim beats and another with the crotchet beats. More graphs will be required with a crotchet beat segmentation as more data points would have been obtained from further subdivision.
4.4.3 A Relationship between the Urlinie and the Data Points One possible way to combine the Schenkerian and the “Intervallic Movement” graphs is to plot the notes gathered from the Urlinie on the line graphs. As there are two distinct levels of rhythmic reductions, minims and crotchets, the Urlinie from the detailed background level analysis will be inserted into the graph with the division of “minim” beats and the Urlinie from a middleground level analysis will be inserted to the graphs with the subdivision of “crotchet” beats. Whilst observing the background level analysis and the subdivision of “minim” beats will provide a comprehensive view of the movement between the key chords and a comparison to the phrase structure, observing the middleground level analysis and the subdivision of “crotchet” beats will provide a closer view of the movement between each pitch collection within the smaller phrases. The letter names will be added as labels on the data points, dotted curved lines act as prolongations and solid curved lines represent neighbouring movements. Linear progressions (3,4,5-note progressions) and connections between key notes will also be illustrated on the graphs. This will provide a significantly different insight, a visual representation depicting the relationship between the melodic (Urlinie) and the harmonic (identified pitch collections) elements in the music. For instance, it will be particularly interesting to examine the shape of the graph when there is a prolongation of a note – if there is a significant increase or decrease in the “amount of movement between each chord”, how does this impact one’s perception of the music? Could this suggest that an additional note should be added to the Urlinie and the Schenkerian chart? The selection of the note should also be treated carefully, but it is imperative to observe that not all the additional notes need to be weighed against their connection to the Urlinie. Other movements such as consonant skips or other skips can be
43 added to the final Schenkerian chart if the analysis of the intervallic movement suggests that they are “significant” (increases or decreases), and one can hear the note playing a significant role within a phrase. Thus, to truly obtain a detailed Urlinie, particularly in the context of early twentieth-century music, the application of this NRT-inspired approach will be extremely useful. The amalgamation of this method with a Schenkerian approach will enable a detailed and well-justified interpretation and analysis at a middleground level of analysis.
4.4.4 Mean, Median and Mode A statistical view of the graphs, employing the concepts of mean, median and mode are uncovered to obtain information about the transformations between each pitch collection from the data points on each of the respective graphs. 1. Mean: By calculating the mean, this will reveal the average of the sets of data points, the intervallic movement that appears the most frequently. The voice- leading changes within the uncovered mean will then be further examined to observe the particular BiP – e.g. if it is the same each time, if it plays a structural role in the music. If it reoccurs at the highest point of a phrase, would it be significant? Does this apply to every case? 2. Median: By calculating the median, one will be able to uncover the middle value of the data set (when it has been arranged in ascending order). Whilst this can produce similar results to the mean, calculating the median can be useful when there are “extreme” values in the data points as it will not be affected by the extreme values. 3. Mode: By calculating the mode, one will be able to make observations based on the most frequently used data point. This can be done on a broad level as well as segmenting the music to its corresponding key ideas or sections and phrases. It may be the case that a larger data point can be found at the climactic section in comparison to the beginning of the movement or that different modes may be discovered for phrases that bear a strong resemblance.
The use of statistics can be utilised for the overall view of the movement as well as subdividing the music into its respective key ideas or sections and phrases. If certain phrases contain a significantly larger number than neighbouring phrases, this could potentially influence one’s perception as well as suggesting a re-evaluation of how it would be placed
44 within a larger context – how it has an impact on the neighbouring phrases, the respective section and the piece. As a way to reveal further insights into the composer’s approach to harmony going beyond Schenker, this statistical data can be utilised alongside the data obtained from the voice-leading and intervallic movement (refer to 4.3) to shed light on the most and least common use of BiP and voice-leading movement. Furthermore, correlations can be made between harmonic regions and particular types of intervals. For instance, it may be the case that a smaller interval type correlates with a “stable” harmonic region and a larger interval type with an “unstable” harmonic region. These “stable” and “unstable” harmonic regions are established through musical factors such as rhythm, melodic contour, phrasing, motivic relationships.
45 Chapter 5
Application of the Analytical Method Part I: Preliminary Schenkerian Analysis
The first part of this chapter comprises linear analyses of Hindemith’s Piano Sonata No. 1. These preliminary Schenkerian charts do not include any notes derived from an analysis of foreground harmonies. The analysis is derived from musical factors such as melodic contours, metric emphasis, rhythm, motivic relationships, textural changes, dynamics, phrase markings and basic background harmonies (as these are traditionally tonal and do not require any special analytical techniques for assessment). The core notes of the Urlinie and Bassbrechung as well as significant embellishments are identified in the respective charts. The second part will discuss these graphs, detailing the assessment of these musical factors from my listening responses and discussing which aspects of the music are included in the initial Schenkerian charts.
46
5.1 Application
5.1.1 Whole Sonata
Analytical Chart 5.1 Ursatz of All Movements of Piano Sonata No. 1.
5.1.2 1st movement
Analytical Chart 5.2 A Detailed Ursatz of the First Movement.
47
Analytical Chart 5.3 Foreground, Middleground, Background Sketches of Bars 1 to 22 of the First Movement.
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Analytical Chart 5.4 Foreground, Middleground, Background Sketches of Bars 23 to 51 of the First Movement.
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5.1.3 2nd movement
Analytical Chart 5.5 A Detailed Ursatz of the Second Movement.
5.1.4 3rd movement
Analytical Chart 5.6 A Detailed Ursatz of the Third Movement.
50
Analytical Chart 5.7 An Alternate Detailed Version of the Ursatz of the Third Movement.
5.1.5 4th movement
Analytical Chart 5.8 A Detailed Ursatz of the Fourth Movement.
51
5.1.6 5th movement
Analytical Chart 5.9 The Ursatz of the Fifth Movement.
Analytical Chart 5.10 A Detailed Ursatz of the Fifth Movement.
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The preliminary Schenkerian charts of the five movements from Hindemith’s Piano Sonata No. 1 are discussed in this section, highlighting the key findings and difficulties in performing a Schenkerian analysis, with an emphasis on the first movement.
5.2 Discussion From a broader perspective, the entire work can be described as an overall arch of tension spanning from the first to the final movement, where each of the movements can be perceived to be unfinished and the true moment of resolution can only be heard at the end of the fifth movement. Despite the sonata’s close relationship to Hölderlin’s poem, the work has been described by some as more of an “instrumental correlative” than a “programmatic depiction.”185
Whole Sonata (Analytical Chart 5.1) Upon examination, one can find the themes from the first movement in the fourth movement and the character of the second movement in the fifth movement. Although each of these movements are of different tonalities, it is particularly interesting to observe that an Ursatz can be sketched for the entire sonata, where the Urlinie descends from # (Cs) to a f@ (Bf) and finally to ! (A). This is also supported by an unconventional Bassbrechung, A-G-A, as opposed to the typical tonic-dominant-tonic progression. Each of these identified notes is selected according to the established tonality at the beginning of the respective movements as well as from an understanding of the key areas within their sections (e.g. modulations). In the first movement, the sense of an A major tonality is established in the opening chord, a single A in the bass and Cs in the upper melodic line. A clear relationship to the minor dominant can be heard in the second idea (bars 22 to 51), E minor. Similarly, in the second movement, a clear Cs major tonality is emphasised in the opening bars and reaffirmed by octave Cs on both treble and bass lines. The Cs in the Urlinie is also reinforced in the bass but this is marked in brackets as the core 3-note Bassbrechung comprises of A-G-A against the descending Urlinie. However, in the third movement, a strong Bf tonality can be heard within the music. This thus suggests that Bf will be in the Urlinie, which will be reflected as a f@ when examining it from an overall perspective. As will be discussed, instead of a dominant relationship to A, G was identified in the Bassbrechung, from the second beat of bar 2. From an overall perspective, this G will have a step connection to the tonic which can
185 “Piano Sonata No. 1,” Malcolm MacDonald, Hyperion, last modified 2013, http://www.hyperion- records.co.uk/dw.asp?dc=W14764_67977 53 arguably be perceived as appropriate for a Schenkerian chart. The interval established between the Bassbrechung and the Urlinie then forms a minor 3rd, following from a major 3rd and perfect 8ve in the previous movements. In the fourth movement, A is identified in the Urlinie without a note in the Bassbrechung. Due to the nature of this movement and its strong relationship to the first movement, one can observe that the structure of this is reversed where the first idea from the first movement appears in the second idea and vice versa. As a result, the Urlinie is significantly different to the first movement where it descends from $ to !. It is also challenging to identify the different key areas in the movement as the notes in the Bassbrechung do not conform to the archetypal Schenkerian progression (of tonic-dominant- tonic). And as for the fifth movement, a clear sense of an A major tonality can be heard in its opening and final sections. This is then reinforced by the presence of A in both the treble and bass lines in the first bar.
First Movement (Analytical Charts 5.2, 5.3 and 5.4) The first movement of the sonata acts like an introduction, a prelude to the work and this particular interpretation differs greatly from a conventional Urlinie where it moves from # to @ without reaching its point of resolution (!). These two key points have been determined due to its structure where the kopfton, #, marks the beginning of the first idea (bars 1 and 11) whilst the next key note, @, appears in bar 23, coinciding with the beginning of a new idea. The selection of these two notes can then be further justified as the key note #, Cs, is situated in the upper voice of the treble line and key note @, B, occurs on the first beat of the bar. It is worth highlighting how @ is reinforced continuously throughout the second section (see Analytical Chart 5.2: bars 27, 31, 33, 37, 46) and despite the slight shift to Bf, a f@ in bar 31 (suggesting a temporary change in tonality), this quickly moves back to B (@) in bar 33 to reinforce the climactic moment of the movement. These particular notes have been chosen due to their metric placement (being situated on the first beat of the bar) and their role in developing the melodic movement within the section. For instance, identifying B in bar 27 reinforces its previous counterpart in bar 23 and reaffirms the fact that bars 27 and 28 are a reiteration of bars 23 and 24, an octave higher than their first appearance. Although the identified Bs in bars 31, 33 and 37 all fall on the first beat, these notes can almost be described as a pedal point for the treble line. Highlighting the slight chromatic shift to Bf emphasises the temporary change in tonality, marking the transition to the climactic moment of the section. Similarly, the identified B in bar 37 introduces a new section, the coda, with its short melodic motive reiterated three times and thus emphasises B in the upper voice. The 54 same can be stated with the identification of B in bar 46. It is thus evident that these identified notes, B, all reaffirm the E minor tonality of the second section, establishing a dominant relationship to the first section, A minor. As previously stated, the Urlinie does not resolve to ! and as seen in Analytical Chart 5.2, the melodic line ascends at the end to E. D, the subsequent note identified after B, was selected due to its metrical placement as well as its role in leading up to the final moment of the movement, as a pre-dominant function. In the overall structure, the ascent from B to D to E suggests that the movement is not truly complete and that there is a sense of yearning for the music to segue to the next movement. It is also worth highlighting how the melodic elements identified in the detailed Ursatz enrich and support the kopfton. Two sets of neighbouring movements can be located in the first statement of the first idea: a lower neighbour movement (Cs-B-C) in the first phrase (bars 1 to 5) and an upper neighbour movement (Cs-D-Ds-Cs) in the subsequent phrase (bars 7 to 10). This connects the second statement back to the restatement of the first phrase in bar 11. In the first lower neighbouring movement, Cs-B-C, it is worth noting how B and C were identified. As bars 1 to 4 can be described as a musical statement comprising two smaller phrases, the last note of the statement, B, also coincides with the starting note of the subsequent phrase, almost creating a link between the first and second musical statements. The identification of C as the last note of the lower neighbouring movement can be justified from a structural standpoint as it can be perceived that C (in the upper voice of bar 5) acts as a form of closure to the first musical statement. In the second set of neighbouring movements, Cs-D-Ds-Cs, it is worth highlighting how D has been selected. Although this is not immediately apparent upon initial listening, it can be argued that there is a strong presence of D in the bass in bar 7 and the Fs in the upper voice can be perceived as a pedal point. Ds is then identified due to its metrical placement (on the first beat of the bar) as well as its structural role where it occurs as the last note of the phrase. Establishing the connection from D to Ds is especially important in a Schenkerian chart as this will reveal to the analyst of the possibility that there is a slight change in tonality, a point of harmonic interest. Subsequently, there is a prolongation of Cs, which can be seen from bar 11, flattening slightly to C (in bars 13 and 19) before descending to A. Cn can be identified particularly in bar 13, as this clearly marks a sharp change in tonality and the notes prior to this can be perceived to be pre-empting the strong downbeat. Although this downbeat occurs on beat 2 as opposed to the archetypal beat 1, it is through other musical factors such as rhythm and melodic contour that have suggested its significance in a Schenkerian chart. The connection 55 of Cn can also be seen in bar 19 on the last quaver beat. It can be argued that the identification of Cn is particularly important as it occurs just before the ascent to the highest point of the phrase and it pre-empts the Bf in bar 20. The following note A can then be justified due to its structural role as the last note of the section and through the tie across to the first beat of bar 21. The notes in the Bassbrechung are identified from “traditional” principles (in avoiding consecutive fifths and octaves) and Hindemith’s musical language (which is heavily influenced from tonal theory) as well as other factors such as rhythm and voicing. For instance, upon initial analysis in bars 1 to 5, there is a moment in the music where consecutive octaves occurred as B was not added to the Schenkerian chart. A closer examination of the opening bars revealed that there is a clear structural significance of B on the third beat of bar 4 in both treble and bass lines as that particular moment marked the end of the first melodic statement. It is also interesting to highlight another unconventional feature in the second idea as there are several instances where a dissonant interval is formed between the treble and bass lines (e.g. bars 32, 37 and 49). Although it is evident that there are fewer notes identified in the Bassbrechung than the Urlinie, there is a need for the notes selected in the Urlinie to be in the Schenkerian chart as they play a structural role in the music. A closer inspection of the process can then be seen in Analytical Charts 5.3 and 5.4, demonstrating every step taken to obtain the fundamental structure of the first movement from the foreground to the background levels. The foreground level (the bottom system), essentially contains all the noteheads stripped from their stems. The various melodic devices are identified such as linear progressions, neighbouring notes and arpeggiated figures. The following system, the middleground level, highlights the immediate prolongations established from the foreground, the larger phrases and key notes that “sum” up a phrase or section. It can be highlighted that there is an archetypical closed progression (tonic-pre-dominant- dominant-tonic) in the first idea, bars 7 to 10. As seen in the Bassbrechung, D is established as the tonic area, A as the “subdominant,” Cs as the “dominant,” before resolving back to the tonic, D. Although it is evident that A and Cs are not the subdominant and dominant of D, these notes are of significant value due to their metrical placement and role in the phrase. As illustrated in Analytical Charts 5.3 and 5.4, the subsequent system above the middleground level is the detailed Ursatz and the top system depicts the overall Ursatz of the entire sonata.
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Second Movement (Analytical Chart 5.5) With the second movement, one striking feature is the identification of * as the kopfton, a number that is less frequently used in conventional Schenkerian analyses. However, unlike the first movement, there is a complete descent to ! at the end of the movement. Much like the latter, there are some “irregular” intervals between the Urlinie and Bassbrechung but these notes are essential to identify the key notes and melodic contour. As stated earlier, this movement is of a Cs tonality and the kopfton (*) can be justified as Cs due to its first appearance in the opening bar. The open notehead, Cs, is also reiterated in bar 13 as it restates fragments of the opening idea (in bars 1 to 11), strongly establishing a relationship between its two appearances. When examining the inner movement, there are two sets of linear progressions (the first of which is a 3-prg and the second, a 4-prg) which branch out from the key note Cs, with a strong support by the dominant in the bass (Gs). In this case, the appearance of Gs follows the archetypal tonic-dominant relationship and the passing notes are supported by Gs, providing a strong harmonic support for the passing notes. With the first 3-prg, the Bf and A in the Urlinie have been selected due to their structural role within the musical statement. Bf is significant in marking the start of the second phrase in bar 5 due to its metrical placement on the very first beat of the bar and through the 2-note chromatic figure upbeat, as this short descending figure Ds-Dn acts as an anticipation to the following bar. As for A, this note occurs at the end of the climactic moment of the first statement, “phrasing” off, and its significance is further emphasised by its metrical placement on the first beat of bar 9. The slightly longer linear progression in the second instance occurs under the reiteration of the first musical idea (bars 1 to 12). This could be of a structural significance as the second can be perceived as an extension from the first, introducing contrasting material as a bridge to the development. The descending notes, B, A and Gs, are situated in the “coda”-like passage from bars 21 to 26. Each of these notes occurs on the first beat of the respective bars (bars 21, 23 and 26) and they all either mark the beginning or end of a musical figure. The development section pivots around the D minor tonality. This is strongly established in the very first bar (bar 27) with D heard on the first beat in the upper voice of the treble line, reinforced by notes of the D minor chord and through its dominant prior to bar 27 (on the last beat of bar 26), creating a sense of yearning to resolve to its tonic note. D in the Bassbrechung was obtained from the second beat, in the middle voice. As the notes in the bass line have both melodic and harmonic functions, C in the inner voice of the first beat is the leading tone of D, thus giving more importance to D in the second beat. On a broader 57 scope, an upper neighbouring relationship can be established between the two * (Cs) in bars 1 and 60, the latter also having a structural function, in marking the beginning and the recapitulation. It is also evident through an examination of this movement that the development is missing a substantial amount of detail. As D is the only identified note from bars 27 to 49, this suggests that it has a strong presence throughout the entire development with only a slight deviation to Ef/Ds at bars 50 and 59, the climactic moment of the section. Interestingly, the bass note D remained the same for the entire section, despite the slight chromatic changes in the Urlinie. It therefore becomes evident that the recapitulation will contain the remaining key notes - some of which occur within a very short span of time and it can be challenging at times to locate these notes. Much like the previous instances, these key notes are primarily selected due to their metrical placement (located on the first beat of the bar) and their role within a phrase (starting or last note of a phrase). However, it is interesting to highlight the musical function of the closed noteheads, f& and %. Although the first appearance of & in bar 70 plays a structural role within the phrase in pre-empting the climax, its connection to Bf is crucial as it signifies a change of tonality, the beginning of a wider use of register and sonorities. The location of % occurs in bar 79, between ^ and $ and is unlike the other key notes, as G is essentially a passing tone without the support of a bass note. Furthermore, due to the frequent use of consecutive octaves across the treble and bass lines, there were several instances where a note in the Bassbrechung could not be designated to every key note in the Urlinie. However, it can be pointed out that D in the Bassbrechung in bar 79 is particularly prominent as it acts as a pedal point in the music. There is also an interesting relationship between the Bassbrechung and Urlinie on @ where a strong dominant chord would typically precede the final chord but the notes in bar 86 suggest the use of chord vii. On a broader scope, in sketching the Ursatz and identifying the key notes, this helps in reaffirming the distinct sections of this movement. As it is in ternary form, * is sustained over the first section (A) as well as the development (B) and the descent begins in the recapitulation (A1).
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Third Movement (Analytical Charts 5.6 and 5.7) An overall examination of the third movement has revealed that there are two possible fundamental structures, the first of which would begin on * and the second on %. As it is known that * is used less frequently than # or %, other plausible alternatives were explored. The main difference between these two possibilities is that with the application of % as the kopfton, the first 114 bars will be perceived as an initial ascent whilst if * is the kopfton, this acknowledges the first section, bars 1 to 113, as being a core part of the music. If the first interpretation (beginning on %) were to be taken as the fundamental structure, this may have an impact on how one would approach the piece from a performer’s perspective. As the initial ascent is a technique introduced by Schenker as a way to delay the “introduction of the tension” to the music, it can be perceived that the musical movement preceding bar 114 acts as an introduction. There are potentially several flaws in viewing % as the kopfton. From a structural view, within the first 114 bars, there are two distinct sections with two different thematic materials, divided into bars 1 to 60 and bars 61 to 113. The stemmed notes, Bf, C, Cs, D and F can be clearly identified in the first 114 bars. However, identifying E was more challenging and it is only considered in order to fulfil the complete 5-prg from Bf to F. In this specific context, as C and E are passing notes and Bf, D and Fs can essentially be described as the core notes. This could mean that it might not be entirely necessary to locate these passing notes, to force the music to fit Schenker’s approach. Similarly, a connection is made with F to Fs, from bars 96 to 110, which suggests that there is a relationship between these bars. Thus this particular section can potentially be seen as a transitionary passage to the kopfton (%), the climactic moment of the initial ascent. This would therefore result in the musical tension beginning at bar 114, reducing the first section to an introduction, and could arguably be perceived as a less significant section. Alternatively, a more plausible interpretation of this movement involves establishing the kopfton as *, which would imply that the previously suggested kopfton in bar 114 is %. This alternative interpretation would acknowledge that the opening bars are crucial in adding to the musical tension. As seen in Analytical Chart 5.7, by acknowledging that Bf (*) is a core part of the movement, this aids in reinforcing the Bf tonality particularly in the first 40 bars. Additionally, by adding a stem to D in bar 61, this could indicate a structural change in the music as there is a change of tonality, marking the beginning of a new sub-section. It is also interesting to observe that even though there is an overall shape of a descent from *, the
59 opening 104 bars depict a gradual ascent to A. This could then suggest that the musical action from the beginning is “driving” towards bar 104 and gradually descending to Fs in bar 114. From bar 114 onwards, both interpretations of the movement yielded the same results. Much like the first two movements, most of the identified key notes are supported by linear progressions, neighbouring notes and in certain instances, their enharmonic counterpart. It can be highlighted that there are in fact several candidates for ! but this interpretation suggests that ! is at bar 270, as this particular point in the music marks the beginning of the true beginning of the recapitulation. Two other Bfs have also been designated as open note heads as they play a specific structural role, the first at bar 237 depicting a brief hint of the opening material, and the second at bar 316 marking the closing statement of the movement. Similarly, there are other instances in the other key notes that support !, which are of a lesser structural significance and are indicated by a crotchet. Although these are less significant than the notes with designated open note-heads, it is particularly important that these are shown on a Schenkerian chart as they demonstrate that there are more than just a small set of important notes as well as providing room for further alternatives.
Fourth Movement (Analytical Chart 5.8) Identifying the fundamental structure for the fourth movement is particularly challenging and as it is significantly different to the previous movements, this has resulted in creating a unique Ursatz. From a thematic perspective, although the fourth movement bears a strong resemblance to the first movement, the thematic materials are placed in a reversed order where the second idea of the first movement is presented, followed by the first idea. The Ursatz illustrates the Urlinie moving from % to !, Bf to E. However, as Bf or B cannot be seen in the opening notes, it can be perceived that this movement is a continuation from the third movement, resembling a segue and Bf (!) can be interpreted as % in the fourth movement. Furthermore, as the thematic materials are reversed, the opening of this movement sounds much like a development section. In the first idea, A in the Urlinie appears like a pedal point and most of the melodic activity occurs in the Bassbrechung. Like the earlier statements, each of these notes (bars 9, 13, 18 and 22) have been selected due to their metrical placement as well as the use of register (e.g. doubling of a note an octave lower to create emphasis and resonance). In the next section (bars 24 to 33), the notes identified in the Ursatz are much like the first movement where they play a key role in the phrase (as the start or last note), located on the “strong” beat of the bar and through their type of rhythm. Furthermore, it is only at bar 24 60 and its subsequent repetition at bar 34 where there is a sense of stability, strongly indicated by the familiar melodic motives. This again raises some questions on the effectiveness of the Schenkerian approach as this movement does not conform to the # or % or * pattern. However, using this method provides a partial framework for its structure and one is able get a sense of how the tension is unfolded across the movement. It can be highlighted that a strong E major tonality can be established towards the end despite a f@ (F) and D in the Bassbrechung as # contains a Gs with the support of E, before ending with E in both parts. This reaffirms that notion that the Schenkerian method is still applicable in Hindemith’s First Piano Sonata as there is a sense of tonality arising from Hindemith’s unique harmonic language that employs both tonal and atonal elements.
Fifth Movement (Analytical Charts 5.9 and 5.10) The derived Ursatz (as shown in Analytical Chart 5.9) for the final movement of the sonata bears a strong resemblance to an Ursatz for a typical piano sonata in that it contains the overall shape of #-@-!, with an unresolved @ in the development. Much like the previous movements, each of these key notes identified on the chart were selected due to their metrical placement, their structural role, and rhythmic prominence. There are also several instances where unorthodox intervals can be seen between the Urlinie and the Bassbrechung, such as minor seconds, diminished fourths, and augmented seconds. Furthermore, viewing this chart on its own without a visual representation of the musical score clearly demonstrates how this method condenses and reduces much of the melodic and harmonic movement into a few selected key notes. This can be seen especially in the development (as reflected in the detailed version of the Ursatz) as a significant portion of the music has been dismissed and seen as an elaboration of the dominant. However, the Ursatz for this movement does help in establishing an understanding of the structure of the work. One can even observe that a strong relationship can be established between the exposition and recapitulation as they are both labelled as Cs on the Urlinie (as seen in bars 1 and 193).
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5.3 Strengths and Limitations From uncovering the detailed Ursatz for each of these movements, it is evident that it is possible to apply the Schenkerian approach to early twentieth-century music, particularly a specific scope of works by composers that employ “traditional” harmony as well as the use of dense and extended tertian harmonies. Whilst this may be possible for Hindemith’s music, it may not be the case for all early twentieth-century music. However, in the case of this piano sonata, it can be established that there is a tonal centre in each of the movements. Even if all of the appropriate accidentals are not utilised, it can be heard within the musical action that there is a sense of grounding to the relevant key. From a broader perspective, in considering the work’s programmatic inspiration, to be able to derive a #-@-! Urlinie for the entire sonata is exceptional, as each of the movements contains very different characters and structures. The Schenkerian method is extremely valuable in this respect as it demonstrates how all the movements can be bound together as one cohesive work as opposed to the idea of five separate and unrelated movements. Furthermore, even though the Ursatz for some movements does not resemble a traditional Ursatz, this challenges the analyst to view the bigger picture, to perceive the work as one unit. One example can be seen particularly with the first movement where the Urlinie moves from #-@. This could potentially suggest that the first movement could segue to the next movement. With consideration of its programmatic implications, this movement could act as an introduction, setting up the framework of the sonata. Although some movements have proven to be challenging to derive their fundamental structure, it is possible to perform a Schenkerian analysis for the entire work due to a strong remnant of tonality in Hindemith’s music. This will provide a deeper insight into the structure of the work, particularly in larger movements (such as the third and fifth). Although the application of this method does not help in truly defining the individual movement’s tonality and their archetypal cadences and chord progressions, a hierarchical relationship can be established through various techniques of elaboration: identifying the core pitches, establishing neighbouring movements and the relevant linear progressions. In certain instances, it was also possible to apply the archetypal counterpoint principles to the middleground and background levels of analysis. Furthermore, Hindemith’s writings emphasise the use of step and degree progressions and this coincides with Schenker’s ideas on Auskomponierung (elaboration) and the prolongational or Stimmführungsschichten (voice- leading) levels. This in turn, aids in illustrating how a series of notes can contribute to the sense of stability and tension. Linear connections (e.g. passing notes) can thus be formed, 62 statements can be made regarding how each of these connections can be related in the overall structure, and hence, allowing the development of a sense of “structural hearing” to gain an understanding of the music. From the examination of all the movements (with an in-depth analysis of the first movement), uncovering a detailed interpretation of the fundamental structure is challenging but not entirely impossible.
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Chapter 6
Application of the Analytical Method Part II: Segmentation (First Movement)
The first part of this chapter presents the identification of the harmonic units in the first movement. Hindemith’s theoretical ideas from the Craft of Musical Composition (such as step and degree progressions and concepts of melody) as well as consideration of other unique aspects of the music (such as texture) are applied during the segmentation process. Two levels of segmentation have emerged from this process: crotchets and minims. The second part of this chapter will present a discussion of this process.
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6.1 Application
Analytical Chart 6.1 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 1 to 4.
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Analytical Chart 6.2 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 5 to 9.
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Analytical Chart 6.3 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 10 to 14.
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Analytical Chart 6.4 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 15 to 20.
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Analytical Chart 6.5 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 21 to 24.
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Analytical Chart 6.6 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 25 to 28.
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Analytical Chart 6.7 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 29 to 31.
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Analytical Chart 6.8 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 32 to 35.
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Analytical Chart 6.9 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 36 to 42.
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Analytical Chart 6.10 Segmentation, Rhythmic Reduction, Pitch Collections and Calculating VL Distance in Bars 43 to 51.
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6.2 Discussion
Bars 1 to 4 The first four bars of the first movement can be divided into two main phrases that are also marked out by Hindemith’s articulation and slurring patterns. The first phrase occurs in the first two bars and the second in bars 3 to 4. In the treble line of the first two bars, there are three different layers of step progression (SP) and one neighbouring movement. The longest progression can be seen in the “alto” line represented by E in bar 1 with an ascent to Cs at the end of bar 2. Two shorter 3-note SP can be seen in the upper voice, the first of which begins on the first note, descending to A on the third beat of the first bar and E on the second beat of the first bar with an ascent to Gs on the second beat of the second bar.
Urlinie
Bassbrechung
Melodic Embellishment
Figure 6.1 Identifying the Melodic Features in Bars 1 to 4.
It is particularly interesting to note that B on the second half of beat two would conventionally be regarded as an embellishment but the application of Hindemith’s melodic principles of SP has highlighted its structural role within the phrase. There is also a lower neighbouring movement in the treble line (E-Ds-E) spanning from the second beat of the first bar to the last note of the phrase in next bar. As for the bass line, there are two simultaneous lines both beginning on the tonic note, A, on beat 1. The first of these is sustained till the end of the phrase in bar two. The second comprises a descending 8-note figure with its final note coinciding with the last note of the phrase. Furthermore, the notes sketched from this SP
75 resembles the results gained from a Schenkerian perspective as the key notes in the Urlinie, Cs-Ds-E, are supported by a Bassbrechung of A-B-A, supporting the clear closed phrase shape. As for bars 3 and 4, there is a lower neighbour movement, much like the first two bars with three SPs. The first SP occurs at the beginning of the phrase, ascending from A to C and a similar SP can be seen on the last three notes of the phrase, descending from D to B. A longer SP can be identified at the climax in the inner melody where C descends to Fs. In the bass line, there is one clear ascending line, moving from D to B with a smaller 3-note SP moving from D to Fs (inner melody). It can be pointed out that the identification of the 3- note SP in bar 4 in the treble line can also be reflected in a Schenkerian view of the same passage, which in turn suggests that there is possibly a relationship between Hindemith’s concepts and Schenkerian principles, where step progressions can be seen as a form of prolongation within Schenker’s concepts. It could also be hypothesised through these initial bars that the SPs play a structural role in defining the subphrases (e.g. bars 1 and 2, bars 3 and 4).
Segmentation Schenkerian Chart
Figure 6.2 3-note Step Progression (SP) in Bar 4.
From the SPs, two different layers of rhythmic analysis can be justified, one with minim beats and the other with crotchet beats. The first layer establishes the identification of the main beats through strong minim pulses and this can be seen across the entire movement. The opening note of the movement, located on the first beat, provides a strong sense of a down beat, solidifying the tonality. It can then be argued that the third beat of the bar is the next principal beat. This is due to the subsequent quaver rest in the melody, giving the beat slightly more emphasis. The following Cs on the last quaver of the beat then has an impact on the start of bar 2 as the note can be described as a form of “anticipation,” in turn giving the first beat of bar 2 some emphasis. Subsequently, whilst one can expect that beat 3 in bar 2 76 will contain more emphasis, utilising Hindemith’s harmonic language to identify SPs reveals that it is bass A on beat 4 that holds more structural significance than B. As A is the “tonic” note as well as the starting note of the descending SP, it strongly indicates the end of the phrase. This can also be supported by observing the rising melodic contour in the treble line, stepwise descending bass line and its phrase marking. However, it could be argued that beats 3 and 4 could possibly function as a “cadence” to the tonic chord, where beat 3 could depict the highest point of the phrase, containing a significant amount of tension and beat 4 resolves this tension by arriving on a tonally stable chord, “releasing” the tension of the phrase. This would then suggest that both beats are equally important and as this minim level of rhythmic reduction only accounts for the first chord, both chords will be investigated through the next layer of analysis, the rhythmic reduction at a crotchet level.
Figure 6.3 Observing the Cadence in Bar 2.
However, whilst these two bars contain strong minim pulses, the SPs can also suggest another layer of analysis, by dividing the minims into crotchet beats. It is possible to identify four crotchet beats per bar as a result of the descending SP in the bass alongside similar rhythmic movement in the treble clef. It is worth noting that the pitches gathered in these bars at a crotchet level are unaltered whilst major or minor or seventh chords are drawn at a minim level. For instance, the notes on the first beat of bar 2 consist of D-Fs-Gs-A, but in the context of A major, Gs can be regarded as an embellishment based on Hindemith’s principles and observations of the music. Therefore, a D major chord can be drawn at that particular
77 moment. This same principle is applied to all the other “minim” chords for the entire movement. Even though bars 3 and 4 are similar to bars 1 and 2, there are several interpretations in identifying the main beats. It can perhaps be perceived that there is an emphasis on E (bass line in the third beat of the bar 3). At this particular point, the appearance of this note evokes a sense of stability due to its duration as a dotted crotchet and its role in creating a “driving” horizontal movement, propelling the music to the next key note, the first beat of bar 4. In bar 4, the main beats fall on the first and third beats, resembling the structure of the descending 3-note progression (treble line) where the first and third notes can be perceived to be the core harmonic tones and the middle note (Cs) acts as a passing tone, in accordance with Hindemith’s concept of non-essential tones. This is further reinforced by its metric displacement, as Cs appears as a quaver on the second half of the second beat.
Figure 6.4 Further Observations in Bars 3 and 4.
It is then worthwhile noting on a crotchet level that the first two beats in bar 3 have been omitted as the notes (in the treble of bar 3) can be perceived to be playing a role in “anticipating” the subsequent note (G on beat 3). This is due to the absence of bass notes and the lack of metric emphasis where the use of a dotted crotchet followed by a quaver accelerates the music towards a more harmonically “stable” moment. However, from a Schenkerian perspective, B (first beat of bar 3) is particularly significant as that note is prolonged to the end of the phrase. The strong crotchet pulses in these bars are reaffirmed by the ascending bass line, supported by the descending inner voice of the treble line, essentially moving in contrary motion to the bass. On the whole, initial observations reveal that the
78 opening bars of the movement establish the key of A, through the prolonged “tonic” note and its SPs and are thus reflected in the Schenkerian chart.
Bars 5 to 10 The first of the two phrases in this section, bars 5 and 6, are a sequence and presents two melodic ideas that bear a strong resemblance to one another. SPs are not present but instead, slightly “longer” connections are made between notes. Neighbouring movements can be seen on beat 2 of these bars and thus suggest that the first beats are the principal notes. Horizontal connections can be seen in the inner and outer voices where A on the first beat of bar 5 can be seen to be driving towards C on the third beat. Similar observations can be made with the other three neighbouring movements with an additional descending 3-note progression, G to Ef in the bass line of bar 6. In the broader structure, horizontal connections can be made from the first note of bar 5 into the next bar as this ties the two melodic ideas together. As stated earlier, even though these two bars can be described as a sequence, there is a melodic difference where bar 6 contains a slightly larger interval (perfect 4th) than bar 5 (minor 3rd).
A – C Bf - Ef m3 P4
Figure 6.5 Horizontal Connections in Bars 5 and 6.
The second phrase, bars 7 to 10, comprises two prolonged tones and a series of SPs. In bar 7, two clear descending figures can be seen in both the treble and bass lines and the Fs
79 in the treble line is sustained to the start of bar 8. Drawing the SP in bar 8 was more complicated but it can be argued that A (last note of the triplet) is an embellishment thus forming a stepwise descending motion from B to E. The SPs in bar 9 occur within the inner voices of the treble line, the lowest of which continues to extend to the start of bar 10 and similar observations can be seen in the bass line as well. The overall structure thus demonstrates how the notes of bars 7 to 10 can be connected from one to the next, thus creating a relationship between the melodic ideas. When making larger connections within phrases and between notes, it is worthwhile observing that the notes in bars 3 and 4, A and B, could potentially play an important role in forming connections as they could potentially connect to C in the subsequent bar (bar 5, beat 3). This would mean that D would be the next note in the sequence but instead, it moves to Ef (bar 6, beat 3), thus breaking the stepwise motion. It can even be argued that the significant harmonic change to Ef reaches over the next few bars and can be connected to bar 10 in its enharmonic form (Ds). Furthermore, one could interpret that there is a strong return to the A major sonority in bar 9, almost pre-empting the final moment of the section. Therefore, bars 9 to 10 can arguably be described as a summation of the harmonic movement in the opening idea.
Figure 6.6 Uncovering the Larger Connections in Bars 2 to 10.
Much like the first four bars, the rhythmic reduction in these bars produced a rather consistent set of minim beats. As mentioned, bars 5 and 6 are a sequence and as the inner neighbouring movement could be perceived as non-chordal tones, giving emphasis to the subsequent beat, this reaffirms the main beats for these two bars. Identifying the main beats in bar 7 could be problematic due to two reasons: the strong sustained Fs and the descending SPs. If Fss are taken to be the main tones, this will continue the “main” chordal pattern created in the earlier bars. However, this pattern is broken in bar 8 where there is a change in metre from 4/4 to 3/4, resulting with one principal chord for the bar. The identification of this beat can be further reinforced by the last notes of the SPs in both the treble and bass lines but as the statement of the chord sounds “unfinished,” this can be seen as a form of anticipation to the subsequent melodic figure. In the context of A major, the root of this chord can
80 presumably be Gs, which is the leading note of A, containing a strong need for resolving to its tonic. It is also worthwhile noting that although a SP can be formed with the subsequent notes in bar 8, it was not sufficient to label these as a “beat.” As these notes are unaccompanied, the principal chord on the first beat of bar 8 is then further emphasised and the same notes could also be perceived as embellishments that pre-empt the “strong downbeat” E, in the next bar.
Figure 6.7 Step Progressions and Rhythmic Reduction in Bars 5 to 9.
On another level, the beats in bar 7 could be perceived through each vertical set of sounds, acknowledging both the “strong” chordal tones (reaffirmed by the Fs) and the “weaker” non-chordal tones. These non-chordal tones can be strongly identified by their rhythm as they appear in quavers. Similarly, with the sequence in bars 5 and 6, whilst it is acknowledged that the second beats of these two bars are lower neighbouring movements, these notes can be examined on a more detailed level, at the crotchet level of segmentation. A more detailed rhythmic reduction of bar 9 has also produced a similar problem as there could be two possibilities. If this passage were to be guided strongly by E, a strong remnant of the tonic sonority, this bar could be divided into two main beats, as Cs and Fs (2nd and 4th beats) within the upper voice could act as embellishments to the E, where the first could be a consonant skip and the second as an escape note. However, a closer examination of the SPs on both treble and bass lines indicates that there is a need to include Cs in the rhythmic reduction as it is strongly supported by other pitches. In fact, there is a strong structural significance for these notes as each line is approaching the end of its respective linear
81 progressions in bar 10. Moreover, in bar 9, the Cs and A in the second half of the second beat are also part of the A major sonority which suggests that its immediate predecessors in the first half of the second beat (G and B) are embellishments. The bass entry in this bar appears at the start of the second beat, aligning with the embellishments but it could be argued that these notes have been metrically displaced and could in fact be part of the first beat of bar 9, reinforcing the A major chord.
Bars 11 to 16 As these bars bear a strong resemblance to the opening bars, numerous SPs can be drawn in their familiar material (bars 11 and 12) as well as their extended ideas (bars 13 to 16). In bars 11 to 12, upon examining the opening melodic figure, there are two SPs in the treble and bass lines. In the treble line, it can be observed that the first SP, a three-note figure (from Cs), includes the consonant skip (B), and thus reinforces the idea that an analysis of step progressions will reveal the significance of an embellishment in the broader structure. The second SP can be seen from E (second beat) in the same bar and it stretches to Gs in the subsequent bar, pre-empting the end of the small sub phrase. Similarly, a step wise motion can be seen in the bass line from A of bar 11 descending to Cs of the sub phrase in bar 12 and an ascending three-note figure from the same starting note to Cs. It is evident through these two bars that the identified SPs greatly contribute to shaping the start and end of the sub phrase.
Repeated Material Extended Ideas
Figure 6.8 Identifying the Melodic Ideas in Bars 11 to 16.
Several short SPs and neighbouring movements can be seen between the next two bars. In the treble line of bar 13, the first SP begins on the very first note of the phrase, E, and descends to C, drawing out the significance of the non-chordal tone, D. The second SP begins
82 on the first beat of bar 13 and ascends to B in the subsequent bar, the second last note of the phrase. The lower neighbouring movement appears in the inner voice of these two bars, spanning from the first beat of bar 13 into 14. It is evident that Hindemith’s idea of SPs has revealed that each note has an important structural role. An analysis of step progressions is crucial in assisting with the rhythmic reduction of the music. The identified notes are not immediately apparent when simply reading the music at a surface level. The bass line yielded similar results where the first SP begins on Gs (upbeat to bar 13) and extends to the very last note of the phrase in bar 14. In addition, another layer of SP can be found in the bass line, beginning on C in the upper voice at the start of bar 13 and ascending to E. The last note of the phrase is further reinforced by the upper neighbouring movement in the lower voice, from Ef to E. An additional SP can also be located starting on the same Ef and reaching over to G in the next bar, the anacrusis leading into the next phrase. Whilst the SPs from the beginning acknowledged all the notes that are located on the “down beats”, the findings from the next two bars indicate a different arrangement. As bars 15 and 16 are a sequence, the identified SPs from the first phrase will be similar to the next phrase. The first SP begins on the very first note, G, and descends to an Ef, disregarding Bf on the first beat of bar 15. The same descending figure can be observed in bar 15 and it also disregards the first beat of bar 16. It can be seen that the downbeats in this case are not necessarily notes that are part of the SP and they play an auxiliary role in forming part of the melodic decorations of the phrases. There is one descending SP in bar 15, from C to Bf. Interestingly, bar 16 yielded a different finding where it is comprised of a Cs sustained to the beginning of the next phrase. However, sketching the SP in the bass line revealed a deeper relationship between these two bars as there is a much longer progression connecting Gf, the second beat of bar 15 to the very first beat of bar 17. From an overall perspective, the roles of the treble and bass lines vary in these bars, but they both can be unified in forming the phrase structures. The rhythmic reduction for bars 11 to 16 presents a strong appearance of crotchets but it could be argued that a broader division can be established through minims. Minim beats can be established on the first and third beats of bar 11 and at the start of bar 12. As bar 11 is much like bar 1, the first beat and third beat have been marked as the main pulses. However, there is only one main pulse in bar 12 and this was determined through the presence of the last quaver in bar 11 in the melody. The appearance of the Cs as an “off-beat” gives the following note more emphasis as well as the lack of supporting notes on the third beat, which suggests that an additional minim pulse might not be necessary in this case. Whilst there is a
83 temporary change of metre in bar 13, the strong minim pulse is not located on the first beat, but rather on the second beat. A stronger sense of the downbeat is more evident on the second beat as the pitch collection forms a strong Af major chord, establishing a stronger pulse and the notes before the second beat can be interpreted to be a form of “anticipation.” The appearance of the bass in bar 13 on the second half of beat one also suggests that more emphasis should be given to the second beat. In the following bar, a minim pulse can be located on the first beat as it coincides with the peak of the crescendo. Much like bar 12, a minim beat on the third beat is excluded in the rhythmic reduction due to the lack of supporting notes in the harmony. The same findings can then be seen in the subsequent bars, which bear a strong resemblance to bars 13 and 14.
Figure 6.9 Step Progressions and Rhythmic Reduction in Bars 11 to 16.
A closer examination of bars 11 to 16 reveals that crotchets can be formed on every beat. There are some cases where further investigation has to occur in order to place these securely as a crotchet beat. For instance, it can be argued that the basic rhythm of the second half of bar 12 is simply two crotchets and Ds is allocated an extra quaver beat to create melodic and rhythmic interest within the music. Similar comments can be made in bars 13 and 14 and it is worth highlighting that deriving crotchets in the subsequent bars requires a synthesis of the upper and lower SPs.
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Bars 17 to 22 Longer SPs can be seen in the climactic moment of the first idea, divided clearly into two sub phrases, bars 17 to 19 and bars 20 to 22. In the treble line, there are three SPs, the longest of which spans in the inner voice from the very first note, Cs, to D in bar 19. A smaller SP can be seen from the first note of the first beat of bar 17 in the melody to Bf, in the subsequent bar. The last of the three begins on the second beat of bar 17 and stretches over a bar to rise to an A at the end of the phrase. In the bass, the longest SP begins on Cs, half a beat earlier than the treble and descends to Bf at the end of the phrase. A much shorter SP can be seen at the start of bar 17, Bf, and descends to G. An interesting observation can be made at this particular moment where another SP can be seen within Bf-G. This SP occurs within the inner voice of the harmony, beginning on C (second beat of bar 17) and descends to A (first beat of bar 19). In the next phrase, there are no SPs in the bass line but a connection can be made between the pairs of notes (as shown through the use of slurs). In the treble line, three SPs can be seen, the first of which encompasses the first note of bar 20, C (assuming that the triplet prior to this acts as an anticipation to the subsequent beat) and descends to A, the very last note of the phrase. Another SP can also be traced from the last note of the short melodic idea, Af (second beat of bar 20) and descends to F, the first beat of the subsequent bar. A longer SP can also be seen in bar 20, where it begins on F, incorporating the important notes in the melody and descends to A, the last note of the phrase.
1st Phrase 2nd Phrase
Figure 6.10 Identifying the Two Phrases in Bars 17 to 22.
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From a broader perspective, the rhythmic reduction in bars 17 to 20 could be perceived as a series of minim and dotted minim pulses in bars 21 to 22. This can be justified through the presence of the quaver upbeat, especially in bars 17, 18 and 20, where it can be described as an anticipation to the first beat of the respective bars. Additionally, in bar 21, a minim beat is located on the second beat rather than the first beat as the statement of the previous phrase concludes on the first beat of the bar. This in turn indicates that the subsequent minim beat is located on the last beat of bar 21 and stretches to the first beat of bar 22. It can be observed that the principal beats in this section have a direct correlation to the shape of the phrases, reinforcing their structural role within the music. Despite the lack of indicators of the change in metre, the principal beats are drawn according to the melodic shape of the music.
Figure 6.11 Step Progressions and Rhythmic Reduction in Bars 17 to 22.
However, a closer examination with a consideration of the SPs strongly suggests that the rhythmic reduction could be better perceived as crotchets as this will account for Hindemith’s use of ascending and descending stepwise motion and its vertical and march-like character. The only exception to this idea can be seen in a couple of examples in bars 19 and 21. The triplet in the last two beats of bar 19 plays an auxiliary role and it can be viewed as an embellishment or anticipation to the first beat of bar 20. Similarly, the two beats identified in bar 21 are deduced from the bass notes, the two significant pulses of the bar.
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Bars 23 to 26 As the new section of the movement contains a contrasting idea, the individual notes of the SP occur one per bar instead of one per beat SP (as seen in the first idea). In the treble line, there are two 3-note SPs, one that can be traced from the first note of each of the short melodic figures and the other, from the highest note of the respective melodic figures. Further movement can be seen within these few bars: the sustained E across all 4 bars and the chromatic inflection from B to Bf (bars 23 to 25) and D to Df (bar 26). Similar results can be seen in the bass line, where the first two 3-note SPs begins at the start of the short melodic figure and the other comprising the highest note of the respective melodic figure. Additionally, two descending 3-note SP can be seen between bars 25 and 26, the last sub phrase, using the same starting notes as the earlier mentioned SP (bars 23 to 25). The slight variation of the SP, where bars 25 to 26 descends as opposed to the ascending figure, could play a structural role in shaping the phrase, reinforcing the end of the phrase.
Figure 6.12 Step Progressions in Bars 23 to 26.
It can be observed that there is a greater amount of rhythmic flexibility in the second idea, through the presence of longer notes and more use of rubato, resulting in the music moving in a “horizontal” manner, differing greatly from the “vertically” oriented first idea. This is more apparent in Richter’s interpretation than Gould’s of the passage. As a result, there is a significant difference in deducing the rhythmic reduction as one semibreve can be drawn from each of these bars. These chords are thus determined through the bass line where the key note is raised by a semitone in each bar. Furthermore, the short melodic figures in the
87 treble line mirror the change of harmonic movement in the bass with slight changes to the starting notes in each of the figures. Upon closer examination, these semibreve beats can be further subdivided into crotchet beats. This is determined through the removal of passing tones and an understanding of the metric placement (e.g. bringing forward quaver notes that have been shortened by the presence of a dotted crotchet beat). For instance, in bar 23, acknowledging that E in the bass is a prolongation and the first crotchet beat comprised of B (treble, first beat) and G (bass, last quaver of the first beat). The second beat then comprises the notes that are immediately located on the beat whilst the third beat comprises Bf (treble) and F (bass, second half of the beat) and the last beat consists the notes immediately seen on the beat. This same process can then be repeated in the subsequent bars.
Figure 6.13 Step Progressions and Rhythmic Reduction in Bars 23 to 26.
Bars 27 to 32 The first three bars of this section, bars 27 to the first beat of bar 29, are very much a repeat of the previously stated melodic figure and both the bass and treble contain the same SP and prolongations. Whilst there is a strong resemblance in the SP to bar 26 in the bass, the treble line consists of a series of prolonged tones: Fs (eventually to Gf) and As. Despite the lack of SP in the treble and the emphasis of E in the bass, the “intensity” of the phrase is driven by lowering the notes in each of the short melodic figures by a semitone. Whilst the next bar contains no step progressions in both the treble and bass, connections can be made between the notes. Gf, the first note of the phrase (bar 30, last beat), can be connected to the start of the next phrase (bar 31, last beat) and there are slight chromatic inflections in both the inner and outer voices. A consonant skip can also be seen within the first and second beats of bar 31. Similarly, a consonant skip can be seen in the first two notes of the phrase, Gf and Ef, whilst the other notes can be treated as an arpeggiated figure, thus reinforcing the importance
88 of Ef. In bar 32, two 3-note SPs can be traced in the treble line, both in the inner and outer voices, where one begins on the second half of the first beat and the other on the second beat. A chromatic inflection can also be observed from Bf to A, the last note of the phrase. Likewise, the bass consists of a consonant skip from the previous bar, Gf to Ef and the subsequent notes can arguably be heard as an auxiliary arpeggiated figure. These bars are much like bars 23 to 26, where the SPs and horizontal movement are determined by the start and end of the phrases.
Figure 6.14 Step Progressions in Bars 27 to 32.
Much like the opening bars of the second idea, one principal chord can be formed in each bar and further subdivisions can be drawn from applying the same principles in bars 23 to 26. The removal of passing tones and consonant skips in the treble as well as a closer examination of the arpeggiated figures in bars 31 and 32 have provided more details for crotchet subdivision (where the second half of each beat can be omitted).
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Figure 6.15 Step Progressions and Rhythmic Reduction in Bars 27 to 32.
Bars 33 to 36 Within these four bars, the climax of the movement, there are a number of step progressions as well as other melodic features: prolongations, neighbouring movements and consonant skips. These bars can also be further subdivided into two melodic figures with a short transitional passage to connect the two. In the anacrusis leading up to the opening of the first phrase (bars 32 to 33), there is a consonant skip from Fs to B in both parts. In the broader picture, B can be perceived to be a prolongation where it begins from the first beat of bar 33, through the anacrusis and downbeats in the next phrase to the last beat of bar 36. The inner movements within B are of a homorhythmic nature and the treble and bass lines move in contrary motion. It can be observed that descending SPs can be seen in the inner movement of the treble line, from As to Ds and Fs to B. Similarly, this is echoed in the bass with ascending SPs from Cs to G and Fs to C. Immediately after the SPs in both parts, upper neighbouring movements can be seen in the treble and lower neighbouring movements in the bass. The appearance of neighbouring movements in both the treble and bass lines plays a
90 structural role in concluding the sub phrase. It can then be noted that there are two 3-note SPs in the transitional passage leading up to bar 35, supported by a consonant skip in the bass. As the rest is very much identical to the aforementioned bars, the same SPs and neighbouring movements are therefore identified with different starting notes.
1st Phrase 2nd Phrase
Figure 6.16 Identifying the Phrases in Bars 33 to 36.
Upon segmenting these bars through identifying the SPs and making connections in a larger framework, the rhythmic reduction of these few bars can be interpreted in three different ways. One, based on the “principal” beats; two, with the subdivision of crotchet beats; and three, acknowledging all the vertical sets of pitches, accounting for the “strong” and “weak” beats. When considering the melodic contour of the phrase, the principal beats in these bars are located on the first beats in bars 33 and 35. The emphasis of these principal chords can be reinforced by the anacrusis leading up to the respective beats. There is a sense of stability established with the declamation of these chords. It can also be argued that the emphasis on these beats is due to the change of metre as well as a lack of stability in bars 34 and 36. On a more detailed level, the rhythmic reduction can be interpreted as a series of crotchets and perhaps as quavers as well. Much like bars 7 to 8 in the first idea, the off-beat quavers can be perceived to be passing tones and the strong pulses are located “on” the beat. As each of these vertical set of sounds play a critical role in heightening the tension of the climactic moment, it is worth investigating every set of sounds as opposed to analysing these via a crotchet beat subdivision. The data is obtained by analysing every quaver and the SPs are determined by the melodic contour. If this passage were to be analysed through crotchet pulses, the first set of pitches (Fs-Cs-Fs-As) would be dismissed as mere passing tones and subsequent quavers that do not occur on the down beat would be regarded as “non-chordal”
91 tones. But as each of these sets of pitches form a “chord” in its own right, it would be more effective to analyse this passage on a quaver level as opposed to crotchets. Likewise, the same concept is applied to the transitional passage towards the end of bar 34 where the passing passage in the inner voice of the treble alongside the arpeggiated bass forms its own individual set of chords.
Figure 6.17 Step Progressions and Rhythmic Reduction in Bars 33 to 36.
Bars 37 to 51 The coda and ending of the first movement can be subdivided into four phrases, bars 37 to 39, 40 to 42, 43 to 46, and 47 to 51. The first of these acts as a “concluding” statement to the climax (bars 37 to 39), the second acts as a statement of a melodic figure that recycles rhythmic elements from earlier moments in the movement (bars 40 to 42) and the third and fourth phrases are much like the second, but beginning on B and G respectively, a major third lower each time (from Ef (Ds) in the second), representing a descending arch to convey the end of the movement.
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Concluding Fragment to the Climax Melodic Figure 1
Melodic Figure 2 Melodic Figure 3
Figure 6.18 Identifying the Melodic Ideas in Bars 37 to 51.
In the first subphrase, SPs are apparent within the inner voices of the treble lines whilst the upper voice can be perceived as a prolongation of B, the dominant note of the second idea (E). This prolongation is also supported by the bass line where the notes, C, E and D can be seen to stretch over bars 37 to 39. The SPs within this are shorter compared to its earlier counterpart with 3-note progressions in each instance. Whilst the first SP at the end of bar 36 incorporates all the notes as they ascend by step, it is interesting to observe how the subsequent descending SPs are determined. It can be perceived that F on the second half of beat 2 in bar 37 could be an embellishment, as more emphasis would be given to the previous note, the dotted crotchet, but it can also be seen as an anticipation of the following notes, E and D, thus forming a descending SP. The lower note of the two inner voices, C, would then descend to A, regarding F as a passing tone. As bar 38 is the same as bar 37, the same SPs are identified. It can be seen through the inner voices of the treble that two distinct interpretations have been revealed through the application of SPs and certain notes that initially appear as passing tones do play a significant role in the music.
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Figure 6.19 Step Progressions in Bars 37 to 39.
Bars 40 to 42 can be further divided into three smaller phrases as each of these contains a significantly different rhythmic character. In the arpeggiated passage of bar 40, although no SPs are traced in either parts (as they both contain the same notes), the first note, Ef can be connected to Af. Subsequently, in the treble, the same Af is also the beginning of a SP, where it ascends to Ds, connecting the last note of the arpeggiated passage (bar 40, beat 2) to the last chord of the phrase (bar 42, beat 1) and the same Ds also forms the first note of an upper neighbouring movement. Within the inner voices, a SP can be seen at the start of bar 41, descending from Gf to Ds. An upper neighbour movement can also be seen between the anacrusis to the SP (F) to the second note of the SP. Similarly, in the bass line, a SP is located in the lowest voice, from F to C. It can be highlighted that the use of enharmonic equivalence is applied in this SP as an initial reading of these notes does not fit its archetype within the SP. An upper neighbouring movement can also be seen between the last note of the arpeggiated passage (bar 40, beat 2) and the second beat of bar 41.
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Figure 6.20 Step Progressions in Bars 40 to 42.
SP (Bass) F Ef Cs C An Alternate View F Ef Df C Table 6.1 An Alternate View of the SP.
Bars 43 to 46 are much like bars 40 to 42 and can be divided into three sub phrases. The arpeggiated idea reappears in bars 43 and 44, a third lower than its precedent, (acknowledging its enharmonic equivalence) and whilst there are no SPs, the first note B can be connected to E. A SP then begins on the same E and ascends to B, forming a connection between the arpeggiated passage (bars 43 and 44) to the last chord of the phrase (bar 46). The last note of the SP, B, also forms the first note of an upper neighbouring movement. Similarly, another SP can be seen in the inner voice where it begins on Cs (the last note of bar 44) and ascends to Gs (bar 46, beat 1), and this SP can be perceived as supporting the first SP in connecting the two melodic ideas. In the bass, an upper neighbouring movement can be seen from the last note of bar 44 to the last beat of bar 45 and a short SP begins at the start of bar 45, spanning to the end of bar 46.
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Figure 6.21 Step Progressions in Bars 43 to 46.
Similarly, the next four bars are much like their predecessors with an additional bar to finish the movement. The familiar arpeggiated idea appears a third lower and thus a connection is formed between G and C. The very same C then marks the beginning of a SP where it ascends to G in bar 50. A smaller SP can also be traced in the inner voice of the treble line from the last note of bar 49, Bf to the very last note of the movement, Gs. An upper neighbouring movement can also be identified from the last note of bar 48 to bar 50. In the bass line, two SPs can be traced from the same note, G, where the first SP ascends to C whilst the other SP descends to D. Slurs have been added in bars 50 and 51 in both treble and bass lines as there is a strong connection between the second last chord to the last chord of the movement.
Figure 6.22 Step Progressions in Bars 47 to 51.
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In this final section where the time signature has shifted to triple time, the rhythmic reduction from a broader perspective could be perceived as dotted minims. Whilst this applied to the first three bars where the (implied) C dominant seventh chord is repeated at the start of each bar, the subsequent bar does not follow the pattern. A minim beat is identified instead as the arpeggiated figure in bar 40 can form a chord and a strong pulse can be heard on the second beat of the bar. Whilst the rest of the movement is much like the aforementioned examples, a slightly different result can be seen in bars 45 and 50 where it was particularly challenging to identify a major or minor chord. As a “broader” level of analysis (through minims) entails primarily diatonic chords, in order to perform a closer and in-depth analysis, this particular set of notes will instead be examined through a deeper level of rhythmic reduction where they will be analysed as “pitch collections” on a crotchet level.
Figure 6.23 Step Progressions and Rhythmic Reduction in Bars 37 to 51.
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On a more detailed level, a crotchet pulse can be located on almost every single beat and this is further strengthened by the presence of repeated tenuto indications in addition to the sequence of repeated musical ideas. However, unlike the broad overview of chords in the previous paragraph, no crotchet pulses were identified in the arpeggiated passages. Although it can be argued that if combined, the notes could form a “chord”, a deeper layer of insight into this passage provides a strong hint that these arpeggiated figures move more “horizontally” than “vertically” as they essentially act as an anticipation of the subsequent bar. The non-chordal tones identified in bars 42 and 46 are not included in the crotchet pulses as they are essentially neighbouring tones whereas the first and last notes have a tendency to be more significant.
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Chapter 7
Application of the Analytical Method Part III: NRT-Inspired Voice-Leading Data - Completing the Schenkerian Chart
This chapter presents the following: 1. A series of Schenkerian charts integrated with NRT-inspired VL (voice- leading) calculations between chords at minim and crotchet levels. 2. A series of graphs depicting the intervallic movement and its correlation to the Urlinie 3. A discussion of the findings suggested by the charts and graphs and suggestions of ways in which the analysis can be applied in performance, through the assessment of two recordings of the Piano Sonata, performed by Glenn Gould and Sviatoslav Richter.
The presentation of these analytic charts, graphs and the corresponding discussion will be segmented into smaller phrases and key sections: 1. Bars 1 to 10 2. Bars 11 to 22 3. Bars 22 to 26 4. Bars 26 to 32 5. Bars 33 to 37 6. Bars 37 to 51
The discussion will assess the data from the NRT-inspired voice-leading approach with the middleground level Schenkerian charts. The following questions will be considered: Are there patterns in the data that seem to match features of the Schenkerian chart? Does the prolongation of a particular note in the chart correlate with a “uniform” set of intervals in the data (a sequence of similar-sized intervals)?
As it is evident that musical elements such as dynamics and sequences play a significant role in a listener’s perception, it is therefore not sufficient to simply discuss the changes in intervallic motion based on the harmonic movement. Thus, from building upon
99 the initial observations of various musical features that are reflected in the preliminary Schenkerian charts, suggestions can be made regarding the relationship between the data and tension, resolution, and stability. These musical features can include: A rise/fall in the melodic contour An increase/decrease in rhythmic activity An increase/decrease in dynamics Phrase markings Motivic structures
Furthermore, a close examination of the data has revealed that there are “significant” moments in the data (e.g. one large interval among a group of small ones) that are not represented by a corresponding note in the initial Schenkerian chart. This then prompts for the following points to be considered: In harmonic regions or phrases that might be considered “stable” (as understood through musical factors such as rhythm, melodic contour, phrasing, and motivic relationships), do these correlate with a particular numerical pattern or an emphasis on a particular interval type (e.g. “smaller intervals”)? In harmonic regions or phrases that might be considered “unstable” (as understood through the musical factors described above as well as pressing on towards a climactic moment, or approaching the end of the phrase or climactic moment), are there correlations with other numerical patterns in the data and can this be correlated to a particular interval type? If there are such moments in the data that do not correlate with a feature on the chart, upon further listening to the specific phrase in which this “significant” harmonic moment occurs, can this be heard as significant? Is the moment particularly distinct upon a closer inspection of the harmonic context? If the moment can be heard as “significant” for harmonic reasons, a note from the pitch collection could then be justified for inclusion in the final analytical chart. What will form the basis of selecting the most appropriate note? Will this be guided by Schenkerian principles such as priority to the treble and bass voices, prolongations via scalic movement towards and/or away from a note etc.?
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How might the unusual moments, such as a region that sounds “unstable” relate to moments that can be described as stable? What might be the implications for a performer?
The idea of a “significant” moment also had to be defined. In this case, a significant moment in the graph can arguably be the occurrence of a number larger than 3. This can be supported through NRT principles as whenever a chord is transformed from one to the next, the movement is by a semitone (1) or a tone (2), as shown in Fig. 7.1. It can even be argued that in terms of pitch content, a difference of 1 or 2 represents the “transformation” of one chord into another but a difference of 3 or more represents a movement to a distinctly different chord. However, the actual “significance” of any intervallic difference heavily depends on its context. For instance, in the progression of 2-1-2-2-3-2-1, 3 might stand out. But in the case of 3-4-5-4-1-3-3, 1 would be the most significant in the progression.
Figure 7.1 C major Chord and its Neighbouring Transformations on the Tonnetz.
Table 7.1 Examples of NRT Transformations.
Transformation Notes Movement Leading Tone Transformation CEG EGB Moving C to B by a semitone (1) Relative Transformation CEG ACE Moving G to A by a tone (2) Parallel Transformation CEG CEfG Moving E to Ef by a semitone (1) (Letters in bold indicate common tones across the two chords)
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To further demonstrate how an analytical view might be linked with interpretation in performance, the following questions will be considered in the discussion in this chapter and in Chapter 8: To what extent do the interpretations by Richter and Gould correspond to the preliminary analytic results? Have the performers’ interpretations confirmed the assessment of which notes are considered analytically significant? Do the performers bring out other aspects of the music that were not considered upon initial examination?
Several moments within the music are selected for closer examination, to assess the differences between the two recordings, to assess what the analysis reveals in any particular passage, and how this information might enlighten analysts and performers.
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7.1 Bars 1 to 10
Analytical Chart 7.1 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 1 to 10.
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8
Bf 7
D Cn A 6
C B
5
Cn Ds Bf 4 A
Bn Number Number ofIntervals B B D E 3
Cs 2 Cs B
1 B
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
First Idea Second Idea Bar Numbers Analytical Chart 7.2 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 1 to 10).
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Analytical Chart 7.3 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 1 to 10.
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9
B 8
4-prg Dn 7
Ds Cn 6 N 3-prg E B Ds 5
s C E 4 s D C
Number Intervals of Number B 3 Ef
2
1
0 1 2 3 4 5 6 7 8 9 Bar Numbers Analytical Chart 7.4 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 1 to 10.
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Discussion (Bars 1 to 10) Calculating the number of intervals between each chord at a background and middleground level has evidently produced different sets of data. Several observations can be made when examining the first four bars of the music to a minim level of rhythmic reduction alongside a background level of a Schenkerian analysis. As the overall melodic contour in the opening beats contains a descending idea, this is correlated with a decrease in the intervallic distance between the first and second chords within the first bar, which is then followed immediately by an increase. Although the second chord in the descending idea contains an E, the descending data points from 4 to 3 reinforces the fact that E is merely an embellishment and B is in fact the key note in the second beat. It can thus be stated that in this particular instance, the intervallic decrease aligns with the melodic descent in the music. This also reinforces the idea of having a smaller intervallic change at the start of the movement as a way to establish stability. Although bars 1 to 4 are essentially one musical statement, they can be further subdivided into two smaller phrases, bars 1 and 2 and bars 3 and 4. These are shaped by their slur markings and it can be implied that within each phrase, there is a build up to a “high” point, before drawing to a close. However, the data from bars 2 and 4 depict a slight increase of intervallic distances from 1 to 3, suggesting more harmonic movement. The use of crescendo and faster rhythms also contributes to a sense of increased intensity within the two phrases. As the data point at the beginning is the same as the end of the phrase, it can perhaps be argued that these bars form one phrase and the repeated intervallic movement of 3 suggests that there is a relationship between the first and second subphrases. However, upon further investigation, the number of intervals between each chord at a crotchet level of rhythmic reduction matched to the middleground Schenkerian chart yielded slightly different results. As bars 1 and 2 can also be described as an antecedent phrase to bars 3 and 4, this melodic idea ends on what may appear as an “unfinished” chord to listeners (despite the appearance of the tonic chord) and this is supported by an increase in the data points. It can be seen that through plotting the Urlinie against the respective data points in bars 1 to 2, the increase in the intervallic movement correlates with the initial prolongation, Cs-Ds-E. And as stated in the methodology, it is plausible to make an assumption that the “large” increase in intervals between Cs and Ds correlates with the tension and instability heard in the phrase. It can be perceived that there is an increase in momentum from the harmonic rhythm between the starting note, Cs on the first beat of bar 1 to the Ds, the third beat of bar 2. This is further reinforced by the repeated and sustained A in the bass line as
107 well as its descending scalic figure where the arrival of B (beat 2, bar 2) coincides with the highest moment of the phrase (Ds). The bass note B is supported by the Ds in the melody and without the following beat, the music feels incomplete and filled with tension without any resolution. With consideration of the following beat and its representation in the Urlinie as E, there is a small decrease in the intervals on the graph to correlate with a fulfilled cadence, the moment of resolution of the phrase. In the consequent phrase (bars 3 and 4), one can hear a decrease in the register of the melody yet the final chord of the phrase sounds incomplete. This could act as a suggestion for performers that this phrase may be connected to the subsequent phrases as an unresolved moment generally suggests that the phrase has yet to be formally completed. As represented in the initial Schenkerian chart, a descending 4-note progression, E to B, in bars 2 to 4, has been identified and this is supported by a contrasting set of data as the total number of intervallic movements between chords denotes a general increase in data points against the descending note progression. As these four notes do coincide with the conclusion of the first musical statement, it can be suggested that there might be a decrease in the intervallic movement, correlating with the end of the phrase. This “significant” increase of 3, whilst challenging the notion that the approach of the end of the phrase would contain a smaller intervallic movement, could play a much bigger structural role, as the movement is driving to reach the next phrase, potentially signifying that the cadential moment at bar 4 is not truly “complete”. It must be highlighted that although the movement between each voice within a chord moves in “smaller” steps (0, 1, 2 or 3), it is through the combination of these movements that the total distance between each chord or pitch collection is calculated.
Table 7.2 Total Amount of Intervallic Movement Between Each Chord. 4-note progression E D Cs B Intervallic Movement 5 4 4 8 Individual movement -1 0 +4 Overall movement +3
The final notes of the opening statement in bar 4, D-Cs-B, also clearly establish a descending SP and supported by an increasing set of data points (4-4-8). As stated earlier, this moment in the bar suggests an end to the subphrase yet the large intervallic movement suggests otherwise - the possibility that there is a stronger connection to subsequent bars. These data points also match the notes where the cadence comprises the “tonic” chord, A-Cs-
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E with an added Gs to B-Fs. This can be likened to an imperfect cadence, an incomplete moment that yearns to be resolved or as I-V in E major. These opening bars strongly establish the tonality of A, reinforced by Cs and as shown on the initial Schenkerian chart, this leads to C, as one can hear the end of the first idea and the start of a new phrase. It is therefore interesting to observe the overall neighbour note movement spanning from Cs in the first bar to C in bar 5. The intervallic distances between the chords that surround the lower neighbour note, B, span from the beginning of bar 3 to bar 4. This is depicted on the graph as an increase that moves from 3 to 5 to 8. The role of B in this particular instance is rather interesting as it alternates from being an inner voice to an outer voice.
Example 7.1 Lower Neighbour Note B in Bars 3 and 4.
One can hear that these opening bars are incomplete, suggesting that these bars are merely an introduction, an unfinished opening statement which wants to lead to the following bars. This is supported by the findings in the graph where the overall contour from Cs (the first note in bar 1) to C (the third beat in bar 5) rises from 4 to 8 (B) before decreasing slightly to 5. This reinforces the idea that a higher number of intervallic movements would denote instability and harmonic movement.
Table 7.3 A Neighbouring Movement and its Corresponding Data Points in Bars 1 to 5. Bar 1 4 5 Neighbouring Movement Cs B C Data Point 4 8 6
In the following phrase, one can hear that its opening bars, 5 and 6, are a sequence and this is supported by an increase in the data points from 2 to 4 from the graph depicting the minim level of rhythmic reduction to the background level Schenkerian chart. As the reiteration of a melodic figure generally denotes more emphasis, this suggests more intervallic movement within the music. In turn, the repetition in bar 6 contains more
109 harmonic intensity and should be emphasised as it plays a significant role in anticipating the subsequent bar. With consideration to the recordings as well as the increase in dynamics and shorter note values, it can also be stated that the next moment, the beginning of bar 7, marks the climactic point of this phrase, with the support of an intervallic movement, 6. Although the overall movement from the identified minim chords in bars 5 and 6 increases by 2, a number that can be perceived to be less significant, it is the examination of chords at a crotchet level that reveals a bigger increase of 3 between the two bars.
Table 7.4 Data Obtained from a Minim Subdivision in Bars 5 and 6. Bar 5 6 Data Point 2 1 4 3 Individual Movement -1 +3 -1 Overall Movement +2
At the start of bar 9, the familiar A major sonority can be heard once more, preceded by a descending melodic figure. The intervallic data depicts a decrease at the start of bar 9, from 3 to 1, coinciding with the A major sonority. This decrease correlates with the idea of the release of tension, supported by a familiar and “stable” chord. However, one can hear that the end of the first idea at bar 10 sounds unfinished and this might be perceived to be like an interrupted or imperfect cadence. This is reinforced by the data through a significant increase to 4, perhaps a suggestion of instability and a sense of heightened tension that is not yet resolved. It can thus be suggested that in the context of the opening idea, an increase of intervallic movement by 3 (from 1 to 4) can arguably be significant as most of the preceding movement in this passage is by 1 or 2.
Table 7.5 Data Obtained from a Crotchet Subdivision in Bars 5 and 6. Bar 5 6 Data Point 6 6 4 4 3 7 Individual Movement 0 -2 0 -1 +4 Overall Movement -3
However, the data gathered from crotchet beats at a middleground level significantly contrasts with and almost contradicts the earlier discussion. The sequence in bars 5 and 6, indicated by C and Ef on the Schenkerian graph, illustrates a decrease in the data points on the graph as opposed to an increase as discovered in the background level analysis. When
110 examining the music, as it is the beginning of the new phrase, it can be observed that the melodic ideas have a strong correlation with the overall arch of the data points. The arch decreases initially, thus suggesting stability and allows room for the intervals to increase significantly as the music develops and intensifies, illustrated in the following bar to data point 7. This observation can be useful particularly for a performer, suggesting that the context of these two bars can be examined in two ways, through their overall and individual voice-leading movements. This could suggest for the performer that the first melodic figure in bar 5 will be slightly more emphasised (i.e. more weight given to the notes – perhaps with a higher dynamic level) than its similar appearance in bar 6. But the data obtained from the individual voice-leading movement suggests that towards the end of bar 6, momentum can be created to align with the resulting data by increasing the dynamics and tempo. In bar 7, there are two different layers occurring at the same time: a descending stepwise melody supported by two minims. As these two minims are located on the first and third beats of the bar, this suggests that there is a metrical emphasis on these beats. When the music is placed alongside the data, one can observe that the data points supporting the descending figure reaffirm the emphasis on the first and third beats. Smaller intervallic movements (3) can be observed on “passing tones,” thus reaffirming the idea that the first and third chords should be given slightly more emphasis. This is also supported by the rhythm as the second and fourth chords are on quavers, which can then be perceived as a “weak” beat compared to its “dotted crotchet” counterpart, which tends to be given more emphasis. Thus, the overall contour of the data points mirrors and supports the descending SP. Table 7.6 Data Obtained from a Crotchet Subdivision in Bar 7.
Bar 7 Data Point 5 3 4 3 Individual Movement -2 +1 -1 Overall Movement +2
Subsequently, the climactic moment of this phrase can be heard in bar 9 with its key notes as highlighted in the Urlinie, E (in bar 9) to Ds (in bar 10). Although the movement between these two notes is lowered by a semitone, the data suggests an increase in the intervallic movement. The action within the music can be correlated to the data as the increase coincides with the “end” of the phrase, which is unresolved and can be perceived as a strong propellant to the next phrase. This correlation between the music and the data
111 obtained from a crotchet subdivision level is very much like the results obtained from the background level, where both depict an increase in the intervallic movement. On a broader level, when examining the upper neighbour idea with the key notes D (bar 7, beat 1) to Ds (bar 10, beat 1), a different observation can be made as this is reflected as a decrease in the data points, moving from 7 to 5, disputing the earlier statement that there is in fact an increase towards the end of the phrase. This decrease can be perceived as an anomaly as the end of the phrase is on an “unfinished” chord and one might expect an increase in the data points on the graph to correlate with the “urge” for the music to lead to the next section. However, on a more detailed level, it can be argued that the decrease of data points strongly suggests that this phrase marks the end of the first thematic statement. By highlighting these details, the performer’s interpretation of the music can be enriched through an awareness of the melodic and harmonic movement of the music within its phrases as well as understanding how this will play in the overall structure, as a phrase and section.
Table 7.7 Overall Description of the Data Points in Bars 5 to 10. Bars 5 to 10 Background level An increase in data points – to lead onto the next phrase. Middleground level A decrease in data points – acknowledging the cadence in the phrase.
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7.2 Bars 11 to 22
Analytical Chart 7.5 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 11 to 22.
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8
Bf 7
D Cn A 6
C B
5
Cn Ds Bf 4 A
Bn Number Number ofIntervals B B D E 3
Cs 2 Cs B
1 B
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
First Idea Second Idea Bar Numbers Analytical Chart 7.6 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 11 to 22).
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Analytical Chart 7.7 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 11 to 21.
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9
8
A 7
Bf 6
n C Cn 5
s Cn f Fs C B 4 Fs
Number of Intervalsof Number Cs
3 Ds E
2
1
0 10 11 4-prg 12 13 14 15 16 17 18 19 20 21 Bar Numbers Analytical Chart 7.8 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 11 to 21.
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Discussion (Bars 11 to 16) In bars 11 to 16, it can firstly be observed that the features identified are depicted in the initial Schenkerian charts, and the subsequent subdivision of rhythms, particularly on a minim level, have a strong correlation to the gathered data points. As bar 11 bears a strong resemblance to bar 1 in that it reiterates the opening idea, one could predict that there should be a decrease in the intervals to suggest a sense of stability in opening a new phrase. However, the data suggests otherwise as it increases from 2 to 4. Even though the initial number, 2, is the same in bars 1 and 11, as the music is moving towards more “unstable” harmonies, there is a variation in its subsequent number sequence. The highest data point for these bars is 6 in the first beat of bar 14, and it is interesting to point out that the increase of 3 from the previous chord correlates with the role of dynamics at this point. One can observe that the crescendo from bar 13 drives to the first beat of bar 14, and this could suggest that these notes in the bar should be given more emphasis. It is also curious to note that following the increase of intervallic movement, it immediately decreases to 3, arguably acting as a gesture that elegantly completes the phrase and supports the musical features that build up the tension in anticipating the next phrase.
Example 7.2 Phrasing and Shaping in Bars 13 and 14.
When examining how the melodic movement (as reflected on the middleground level of a Schenkerian analysis) correlates to the intervallic movement in bars 11 to 16, it is the inner voices that provide a deeper insight into the overall structure. It is interesting to note that the initial ascent, Cs-D-E (bars 11 to 12) remains on the same data point, 3. Furthermore, these notes are also part of an ascending 4-note progression, moving from Cs to Fs. As there is an increase in intensity in these bars, attributed to the ascending melodic figure and quicker rhythms, this correlates to the increase in data points on the graph (3-3-3-4). The increase also coincides with the end of the second subphrase, strongly suggesting that this particular
117 moment is incomplete and one can perceive a gradual increase in harmonic tension through the inner melody. It is also interesting to observe that Fs is prolonged over two bars and it is supported by the same data point, 4. This could potentially suggest that this note (which can be argued to be “unstable” or incomplete) sustains the harmonic tension in preparation for a more intense moment in the music (bar 17).
Gradual Build up in Harmonic Intensity
Example 7.3 Prolongation of Fs in Bars 14 to 18.
It can be observed that the second subphrase (bars 13 and 14) develops the opening materials (as stated in bars 11 and 12) and is supported by the data point, 5, a higher number than bar 11. The background level Schenkerian chart and its corresponding minim level segmentation also reinforces this increase of data points, indicated by C, a prolongation of the kopfton Cs (from bar 11). It can be further examined that the 4-note progression (Cs-Fs) from bars 10 to 13, the inner voice within the passage is supported by an increase in the data points, bearing a strong resemblance to the outer voice, where the data points of the prolonged Cs-Cn increases from 3 to 5. This also reaffirms the data obtained from the 4-note progression where the increase in data points play a significant structural role in driving the music to the next pivotal moment. In turn, it can be perceived that the movement from Cs to C denotes a “false” sense of resolution as one would normally attribute a chromatic decrease to be a release of tension. Furthermore, as these subsequent bars can be interpreted as an extension of the initial theme, the fact that it is reflected on a higher point suggests more harmonic intensity and reinforces the notion that the music is propelling towards a climactic moment.
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Table 7.8 Observing the Melodic Movement and its Corresponding Data from a Minim Subdivision in Bars 11 and 12. Bar 11 13 Note Cs C Movement (by semitones) -1 Data Point 3 5 Movement (by semitones) +2
When examining the Urlinie from the background level, it is interesting to observe how the kopfton (Cs) is sustained and stretched over these five bars on the graph and how this relates to the accompanying intervallic movement. As the opening statement is extended and contains larger intervallic movements, this is thus supported by an increase in the data points but there was a slight decrease at bar 16 on Cs. As Cs can be identified in both the treble and bass lines, it can be argued this particular moment has a dual function. One, the decrease coincides with the descending SP in the bass line, and as the bar contains a strong Cs sonority, this could arguably be the last note of the phrase. Two, the decrease plays a bigger structural role in preparing for the following bars, which contain more harmonic movement to build up to the climactic moment of the first idea. In bars 16 to 21, there is a strong correlation between the background level of a Schenkerian analysis and the data points on the graph. As there is only one principal chord in each of these bars, the data is generated mainly from the first beat of each bar. It is firstly interesting to observe that whilst one can perceive bars 17 and 18 to precede the climax, the graph indicates that they are on the same data point. This could suggest that whilst one can hear the growing harmonic intensity between every set of sounds in these bars, this is represented by the same data point, 3, which can possibly be described as “maintaining” the momentum before increasing to reach the climactic moment of the section. Bars 19 and 20, the climactic moment of the phrase correlates with the largest data point, 5, and this is subsequently followed by a melodic passage depicting a gradual decrease in dynamics and register. This decrease is supported by a slightly smaller intervallic movement, 4, correlating with bar 21, and it can be observed that these bars contain data points that are much like the melodic contour within the music - increasing when there is more harmonic movement, decreasing to correlate with a release of tension, and possibly to mark the end of a phrase or section. When comparing the middleground level to the data points, it can be observed that there is a strong resemblance to the data obtained from the background level as the data
119 points from bars 16 to 21 have increased. By identifying the key notes, it is interesting to observe how the kopfton, #, is sustained in these few bars before moving through a descending 3-note progression to reach a point of resolution (A). The data points on the graph where # is prolonged in bars 16 to 18 before moving to ! (A) depict an increase in intervallic movement. This can be perceived to be an anomaly as one would expect based on previous observations that when approaching a resolution, the end of the phrase should coincide with smaller intervallic movement. It can perhaps be speculated that the significant increase plays a bigger structural role in driving the music to the next section. The increase of intervallic movement can primarily be found towards the end of the phrase, between bars 20 and 21 on @. This strongly suggests that although Bf is a passing tone between Cs and A, the particular moment where Bf arrives should be given more consideration, perhaps with more emphasis. In addition, there are two descending arpeggiated figures in bars 19 and 20, similar to a sequence. As Bf is the first note of the repeated arpeggiated figure supported by G and C in the bass and it is placed on a “down” beat, this motivic pattern suggests that Bf is a chordal tone, not a passing note. This specific observation can be particularly useful for a performer as the touch given to a chord on a “down” beat can be significantly different to a passing tone on a weak beat, in its attack, execution, or voicing.
Table 7.9 Data Obtained from a Crotchet Subdivision in Bars 16 to 21. Bar 16 18 19 20 21 Urlinie # @ ! Key note Cs C C Bf Bf A Data Point 4 5 4 4 (6) 7 Overall Movement +3
Example 7.4 Descending Arpeggiated Figures in Bars 19 and 20.
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Additions to the Urlinie (Bars 11 to 21) There are two significant movements on the graphs in bars 11 to 21 that are not accounted for in the initial Schenkerian chart: bars 14 to 15 and bars 16 to 17. In bars 14 to 15, there is a sharp increase of 4 without the support of a note from the Urlinie. Upon closer examination, when considering both Schenkerian principles and understanding the various musical features that can be attributed to tension or release, there are two possible notes that would be appropriate for this data point: C or Bf. It can be argued that Bf is implied and should be inserted into the graph, as this is a note that is prominent from one’s listening experience, and it is situated on the first beat of the bar. Initial observations of these few bars suggest that Bf was not included in the initial Schenkerian chart due to two factors: phrase marking and bass support. In this particular phrase, indicated by the slurs, G is the first note and Bf is the second. As it is a common perception for the first note within a slur to be slightly emphasised, this can result with Bf (the second note of the phrase) to be perceived as less structurally important despite its location on the first beat of the bar. This is also reinforced by the lack of support in the bass and by the fact the first entry of the bass only appears on the second half the first beat of bar 15. As a result, by adding Bf to the final Schenkerian chart, this creates a lower neighbouring movement from C to Cs in bars 13 to 16. Whilst one could argue that perhaps G on beat one of bar 13 should be considered for inclusion to the final chart, the note is not supported harmonically in the bass and other factors such as its shorter note value and soft dynamics suggest more emphasis on C instead.
Example 7.5 A Lower Neighbouring Movement in Bars 13 to 16.
However, in bars 16 to 19, there is only one note that would be appropriate for inclusion in the graph and Urlinie, D. This is mainly due to the following reasons: its metric placement on the first beat of the bar and that both recordings emphasise the first beat of the bar. This is further reinforced by Cs (the anacrusis in the treble to bar 19) and thus gives D more emphasis. D also has a Schenkerian prolongation in the inner voice, beginning on the middle C at the end of bar 16 and leading up to D in bar 19. The addition of D to the Urlinie
121 will create an upper neighbouring movement from Cs to C, spanning across bars 16 to 19. This was not reflected in the initial Schenkerian chart as the foreground harmonic factors were not considered for the initial analysis. In this case, D would seem the most appropriate note for inclusion, a view which is also strongly supported by the performers’ interpretations of the work.
Example 7.6 Addition of D to the Bars 16 to 19.
There is also a large decrease in intervallic movement at bar 15 without a note on the Schenkerian chart assigned to the data point. A close examination of the harmonic context reveals that this moment can be described as “significant” and therefore, a note should be considered for inclusion in the Schenkerian graph. When considering the music, there are three possibilities: Cf, Ef or Gf. Gf appears to be the least likely option when considering Schenkerian principles as it cannot be connected to its surrounding notes. Thus, the note most suitable for inclusion could be a Cf, a note in the inner melody as opposed to the Ef in the outer voice. Whilst this adheres to Schenker’s principles, it can be perceived that drawing out the Cf gives prominence to the inner melody of the bar, C – Cf – Bf. This could possibly be important to the harmonic movement in the bar prior to the build-up of the climactic moment. By including the Cf, this can then be connected to Bf and in turn, sustains the neighbouring note for another beat. This new addition could also potentially be an example of voice exchange where the inner voice reaches over and thus becomes more prominent than Ef on the beat.
Example 7.7 The Inner Voice in Bars 15 and 16.
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7.3 Bars 22 to 26
Analytical Chart 7.9 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 23 to 51 (A Focus on Bars 23 to 26).
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8
Bf 7
D Cn A 6
C B
5
Cn Ds Bf 4 A
Bn Number Number ofIntervals B B D E 3
Cs 2 Cs B
1 B
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
First Idea Second Idea Bar Numbers Analytical Chart 7.10 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 22 to 26).
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Analytical Chart 7.11 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 22 to 26.
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10
D 9
8
E Fs
7
6
G 5 (@) B
4 Number of Intervalsof Number
3
2
1
0 22 23 24 25 26 Bar Numbers Analytical Chart 7.12 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 22 to 26.
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Discussion (Bars 22 to 26) In the opening statement of the second idea, one principal chord can be drawn from each of these bars. It can be observed that when comparing the music (identified Urlinie at a background level) to the intervallic movement, the uncovered data has a strong correlation to the surface level details of the music. Firstly, the repetition of the melodic figure in bars 23 to 26 can be closely reflected in the data as there is minimal movement between each figure. Secondly, the end of the phrase in bar 26 (x2) is supported by a slight decrease in the data points. This suggests that the data points can play a structural role in reinforcing that this phrase marks the end of the first statement of the new melodic idea. It can be observed that the three subphrases within these bars are all interrelated as the second and third subphrases develop from the first (marked as ‘x’ below). One can also perceive that due to the development of the melodic fragment as well as the increase in dynamics, the first two subphrases are “driving” towards the last subphrase of this new melodic idea.
Table 7.10 Data Obtained from a Minim Subdivision in Bars 23 to 26. Bar 23 24 25 26 Melodic Idea (x) x x1 x2 Intervallic Movement 3 3 2
Example 7.8 Melodic Fragment “x” and its Extensions in Bars 23 to 26.
There is also a sharp increase in the intervallic movement between bars 26 to 27, from 2 to 6 and it can be perceived that this increase plays a structural role within the music. As this particular moment marks the transition to the reiteration of the opening statement (bars 23 to 26) at an octave higher, the significant increase in the data points reflects the contour of the section.
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Table 7.11 Data Obtained from a Crotchet Subdivision for the Key Notes in Bars 23 to 26. Bar 23 24 25 26 4-prg D E Fs G Data Point 9 7 7 6 Individual Movement -2 0 -1 Overall Movement -3
Table 7.12 Data Obtained from a Crotchet Subdivision in Bars 23 to 26.
Bar 23 24 25 26 Data Point 9 6 8 6 7 6 6 7 7 6 4 8 6 6 5 Movement between -3 +2 -2 +1 -1 0 +1 0 -1 -2 +4 -2 0 -1 each data point
It can also be observed that the ascending 4-note progression in the inner melody, D- E-Fs-G in bars 23 to 26 is supported by a decrease in the data points (from 9 to 6) both at the background and middleground level charts. This is particularly interesting to observe as this suggests that the gradual build-up of intensity (through the ascending melodic figure) can be supported by smaller intervallic movements and it is not necessary for all “build-ups” to be supported by larger movements, thus suggesting that not all smaller intervallic movement has to represent stability and lack of tension. In this instance, other factors like the increase in dynamics and the use of faster note values play a significant role in building up the tension. There is a sense of harmonic cohesion in these bars through the minimal movement between each pitch collection. Furthermore, the key note B (as supported by data point 4) is prolonged for a series of bars but it is interesting to observe that the inner melody (as stated previously) significantly contrasts the data point of B as it is located on higher data points. Unlike the data gathered from the minim level of analysis, four sets of pitches are gathered in bars 23 to 26 and all individual movements are supported by the fluctuation in data points. This strongly reinforces the idea that the harmonic intensity in these few bars is driven by the inner melody as opposed to notes that appear on the outer layers of the music.
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Additions to the Urlinie (Bars 22 to 26) In these bars, there is one significant increase in the data points in the graph that is not supported by a note in the Urlinie. An increase of 4 can be seen at bar 25, in between the identified “inner” notes of the Schenkerian graph, Fs and G. It can be heard that this particular moment is significant and a note should be considered for inclusion in the final chart. A sense of heightened tension is evoked from this particular moment as it occurs in the middle of the phrase and its appearance as the third reiteration and extension of the melodic figure (as established at the start of the section). As the pitch collection that surrounds this increase comprises of C, A and Bf, it can be hypothesised that Bf can be added to the Urlinie. Although the note differs slightly, where the note is connected from B to Bf, this new addition will sustain the initial key note from bar 22. The addition of Bf can be further justified by its appearance in the music as the note is given a longer duration than the other notes in the bar. This in turn suggests that Bf has a particular structural significance as well.
Example 7.9 Prolongation of B to Bf in Bars 23 to 26.
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7.4 Bars 26 to 32
Analytical Chart 7.13 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 23 to 51 (A Focus on Bars 26 to 32).
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8
Bf 7
D Cn A 6
C B
5
Cn Ds Bf 4 A
Bn Number Number ofIntervals B B D E 3
Cs 2 Cs B
1 B
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
First Idea Second Idea Bar Numbers
Analytical Chart 7.14 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 26 to 32).
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Analytical Chart 7.15 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 26 to 32.
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12
10
Gf Fs 8
A
3-prg Fs
D 6 E Fs A B
B Number of Intervalsof Number
4 B Bf N
2 B
0 26 27 28 29 Bar Numbers 30 31 32 Analytical Chart 7.16 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 26 to 32.
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Discussion (Bars 26 to 32) The data obtained from comparing the intervallic movement of the principal chords to the Urlinie in bars 27 to 32 revealed a significant increase on the graph and can be described as one of the largest shifts across the entire movement, correlating with how these bars play a profound role in the overall structure of the second idea. In addition, the initial melodic material in these bars bear a strong resemblance to bars 22 to 26 but it appears an octave higher, suggesting an increase in intensity. This gradual build in tension is supported by other musical elements such as a wider range of register and dynamics and helps in propelling to the climactic moment of the section. However, when examining bars 27 to 29, as this is a reiteration of earlier materials (but an octave higher), this correlates with the minimal movement within the data points and in turn, is associated with a sense of stability. It can also be observed that the intervallic movement between bars 27 to 29 also bears a strong resemblance to bars 23 to 25 as it utilises similar numbers, 3 and 2.
Example 7.10 First Appearance of the First Statement of the Second Idea.
Example 7.11 Second Appearance of the First Statement of the Second Idea.
It is also worthwhile highlighting that the climactic moment of this section is supported by significant movement in the graph, increasing from 2 to 7. It can be argued that the appearance of 2 prior to this moment can be strongly attributed to the series of short melodic and harmonic figures that shift slightly each time (applying minimal movement). The increase in intensity to bar 31 is supported by the appearance of repeated melodic and
134 rhythmic figures and a greater use of dynamics. It can even be stated that the data reinforces the use of repetition, an expressive device that has a large role in contributing to the sense of urgency, to build up the intensity to the next section. As bar 31 to the first beat of bar 33 can also be perceived as a transitionary passage to the subsequent section, it can be highlighted that these bars are supported by two relatively large numbers, 7 and 6, suggesting a significant amount of tension by containing a large amount of intervallic movement.
7 6
Example 7.12 Bars 29 to 32 (With the Intervallic Movement for Bars 31 and 32).
When making observations on the findings from the music at a middleground level to the data points, it is interesting to observe how the key note, B is sustained across bars 27 to 31. It shifts slightly to Bf at bar 31, followed by a lower neighbour movement before returning to the original key note in these bars, B. The initial structural note (B) is supported by an increase in data points, reinforcing the sense of heightened tension in the music. B occurs three times within the first two bars as it is part of a repeated melodic idea, much like a sequence. As each idea is repeated, it could be given more emphasis, correlating with the increase of data points, which aids in the gradual build-up of the climactic moment of the section. The overall movement (the background level of the Schenkerian analysis) from B to Bf (within bars 27 to 31) also supports this notion of a gradual build-up as there is an increase
135 in the intervallic movement, correlating with the increase in dynamics and expansion of register. However, the increase in the data points behaves differently to the notes as the movement from B to Bf is through a decrease by a semitone. It could be argued that when B moves to a Bf, one can hear that the movement contains some instability and feels incomplete.
Table 7.13 Data Points on Key Note @ in Bars 27 to 33. Bar 27 28 31 32 33 Key Note B B B Bf B Lower Neighbour Movement (A) A Individual Data Points 2 4 5 4 (6) 8 6 Overall Movement +2 +2
However, the lower neighbour movement in bars 31 to 33 (Bf-A-B) is supported by a different set of data. It can be observed that the movement from Bf to B is from 4 to 6 and the movement within the notes is parallel to the intervallic movement. The increase in data points could play a strong structural role as bar 33 marks the beginning of the climactic moment of the entire movement. This disputes the earlier statement that one would expect an increase in intervals from B to Bf as Bf on its own appears unstable and one would expect a decrease upon its return to B. However, it will not be the same in every case as other musical factors will have to be taken into consideration. In this instance, dynamics (a crescendo from bar 32 into 33) and repetition (of the short melodic figure in bar 31 and into 32) correlate to the increase in data points and in turn, intensifies the music and creates a structural emphasis at bar 33, the climax of the movement.
Example 7.13 Identifying the Melodic Ideas in Bars 31 and 32.
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The neighbour note, A, is presented on data point 8, a number much higher than the outer notes and one could arguably perceive this moment as the climactic point of this subphrase. It is worth highlighting that there are two possibilities for the neighbour note, A - one in bar 31 and the other in bar 32. One could argue that the first A in bar 31 could be used but this appears as part of a sequence and is situated on a weak beat (end of the subphrase). This A is essentially preparing for the next section and thus the second A would be the ideal candidate. Whilst it appears at the end of the phrase and is situated on a weak beat, much like the first, its appearance coincides with the repeat of the melodic fragment, strongly suggesting that its reiteration should be given more emphasis both in performance and analysis. It is also worth noticing that in the inner melody, the 3-note progression is supported by a series of data points that are much higher than the sustained key note. The ascending movement from D to Fs/Gf is correlated with the increased data points on the graph, moving from 6 to 7. Whilst it is evident from an overall perspective (from the background level Schenkerian chart) that the data points increase slightly, it is worth highlighting that the movement between D, E and Fs involved a significant movement: an increase and decrease on the graph. This is rather peculiar as this would suggest that on a deeper level, there is more harmonic tension within the notes. Whilst the pedal point (E) sustained throughout these few bars could evoke a sense of stability, this was not the case when examining the inner melody. What is then even more interesting is the sharp increase that coincides with the small chromatic movement (D to Df and E to Ef etc.) as this can almost be perceived as a preparation for the “key inner” note, Bf. The subsequent increase from the lower neighbour movement strongly suggests that the prior movement contributes greatly to the preparation of the climax in bar 33.
Table 7.14 Key Note and 3-prg and its Data Points in Bars 27 to 29. Bar 27 28 29 Key Note B Data Point 2 3-prg D E Fs Fs Fs Gf Data Points 6 6 7 8 6 9
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Example 7.14 Chromatic Movements in Bars 27 to 29.
The last note of the 3-note progression, Fs, also plays another role as the note is sustained across a number of bars and its final appearance is in its enharmonic form, Gf. Overall, the data points reveal an increase (+2) and correlate to the action within the music as structurally, these bars (29 and 30) act as the transitionary passage to the highest moment of this section (Bf at bar 31). This is further supported by the crescendo in these two bars as well as by the sequence of figures in both the treble and bass lines where the treble reiterates the idea Fs-Es-As three times and by a 3-note figure in the bass that descends by a semitone in its subsequent appearances. An even more interesting point is the slight decrease between the second and third Fs as there is a decrease from 9 to 6. It could perhaps be argued that there is another layer of understanding to this passage where the decrease could act as a form of preparation to the final note (Gf) in this sustained passage. Even though Fs and Gf are enharmonically the same, a visual perspective of Gf can appear to be further than Fs, and this could result in different data points. As such, one can observe the effectiveness of a Schenkerian approach, as the “shift” from Fs to Gf connects the transitionary passage (bars 29 and 30) to the next melodic idea (bar 31), highlighting the importance of the inner melody.
Table 7.15 Data Points on Fs and Gf in Bar 29. Bar 29 3-prg Fs Fs Fs Gf Data Points 7 8 6 9 Individual movement +1 -2 +3 Overall movement +2
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Example 7.15 Prolongation of Fs/Gf in Bars 29 to 31.
In bars 27 to 32, one can observe that there is a strong correlation between the music at the background level and the data points. More significant details and data are uncovered from the middleground level analysis, highlighting the importance of the “inner melody” in a Schenkerian analysis and thus influencing how one would approach playing the section – to draw out the inner voice. This in turn reaffirms the usefulness of a Schenkerian analysis as the smaller details are revealed, creating a deep level of insight into the music, details that might not be initially realised on the surface level.
Additions to the Urlinie (Bars 26 to 32) Upon identifying these “significant” moments, it was uncovered that three new additions can be made to the Urlinie in these few bars. It is interesting to note that in all three cases, Bf has been deduced to be the most appropriate for addition to the final analytical chart. Whilst other notes may be suitable, one needs to consider whether this note can be distinctly heard, why it was not considered upon initial listening and the various musical elements that led to the final decision. In the overall structure, by having three additional Bfs, this will further support and sustain the key note (@) especially in sections where it is not immediately apparent. In the first scenario, even though Bf has been chosen to be included in the Urlinie, there is in fact another possibility that could emerge from the pitch collection in bar 27: D. It can be argued that D could potentially act as a prolongation of the first note of the “inner” melody (3-note progression: D, E, Fs-Gf). F and G in this particular instance, would not fit the typical set of Schenkerian principles in establishing melodic features such as prolongations and progressions (e.g. 3-prg, 4-prg). From a closer listening and from applying the principles of Hindemith’s harmonic language, F and G can be perceived as melodic embellishments. As for the second case, much like the first, there is another possibility, E. This could support the second note of the 3-note progression in the inner melody. Fs and Gs
139 would not be suitable for inclusion as they do not adhere to the typical set of Schenkerian principles, and are not heard distinctly and they appear as melodic decorations in the bass line. In the third instance in bar 31, it could be argued that whilst Bf is the most suitable, C could be included in the graph as this would then create an upper neighbour movement against the key note Bf. However, as there is a lower neighbour movement in these two bars and the C is situated on the second half of the beat (a weaker beat), the A would take precedence over the C. Even though Bf is not in the outer voice (as it appears in the bass line) and cannot be immediately heard, it appears on the first half of beat 2 and can be seen to be driving towards C in the subsequent bar on the same beat.
Example 7.16 Addition of D to Bar 27.
Example 7.17 Bars 29 to 31.
Example 7.18 Addition of C to Bar 31.
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Upon further examination, the addition of these notes (all Bf) has made a profound impact on the contour of the music through their individual intervallic changes. It can be observed that the whenever B moves to Bf (bars 26 to 27 and bars 27 to 28), where the notes are lowered by a semitone, it is reflected on the graph by a significant increase of the data points, +9 and +7. Similarly, the movement of Bf to B, where it rises by a semitone, is supported by a large decrease of data points, -7 and -6.
Table 7.16 Additions to the Urlinie for Bars 26 to 32.
Bar 26 27 28 30 31 32 Initial Key Notes B B B Bf B Suggested Additions Bf Bf Bf Data Points 2 11 4 11 5 4 8 6 Individual Movement +9 -7 +7 -6 -1 +4 -2
However, as bars 27 to 28 are a sequence, the large intervallic movement in this case strongly reinforces the movement of B to Bf within the melody, encouraging listeners or performers to consider what notes are significant and should be drawn out more than others. Other factors have to be taken into consideration, particularly with rhythm where B and Bf are on crotchet beats and the other notes within the phrase are smaller in value (triplets and quavers). Furthermore, as the presence of Bf occurs at the end of the subphrase, from a performance perspective, this note will need to be “phrased” off, to be played with a gentler touch to mark the close of the melodic idea. The means by which a melodic figure (that is marked by a slur) may be “phrased” off can include a slight decrescendo, ritardando and possibly some slight accents to notes that are regarded as the highest point. But as the results from the data have suggested the importance of this note, this could indicate that the note should be given some emphasis to reinforce the connection from B to Bf. It is also worth noting that whilst the data points of the first appearance of B to Bf increases significantly (+9), thus adding to the element of “surprise”, at its repetition, the movement is not as big as the first occurrence (+7). This is particularly interesting as it is generally implied that the use of repetition involves more movement to heighten the tension of the music but it was not the case in this particular context.
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+9 -7 +7 -6 Example 7.19 Identifying the Significant Intervallic Movement in Bars 27 to 29.
It is also fascinating to note that the large decrease in the data points between bars 28 and 29 plays a particular structural role as it could almost be a hint to anticipate the subsequent transitionary passage. The significant decrease at bar 27, the transition to the repeat of the next phrase, reinforces the idea that in the overall structure, the repetition of the melodic idea is unified through smaller intervallic movement.
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7.5 Bars 33 to 37
Analytical Chart 7.17 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 23 to 51 (A Focus on Bars 33 to 37).
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8
Bf 7
D Cn A 6
C B
5
f Cn Ds B 4 A
Bn Number Number ofIntervals B B D E 3
Cs 2 Cs B
1 B
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
First Idea Second Idea Bar Numbers Analytical Chart 7.18 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 33 to 37).
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Analytical Chart 7.19 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 33 to 37.
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8
B 7 B A (B) 6
5 Fs
4 Bs Bs As B
Number of Intervalsof Number 3 Cs
2 Ds Ds B 1
0 33 34 35 36 Bar Numbers Analytical Chart 7.20 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 33 to 37.
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Discussion (Bars 33 to 37) The climactic moment in the entire movement is reflected rather peculiarly in the data points (from the background level analysis). The movement between the three main chords is by 3 and it can be strongly suggested that the climax can be driven and built up through smaller intervallic movements.
Example 7.20 Identifying the Key Chords in Bars 33 to 37.
Whilst the data from the background level might be described as an anomaly, it will be the middleground level analysis that will provide more details on the inner movement of the climax. On a middleground level analysis, one can observe some significant features: the sustained B and the unfoldings.
Table 7.17 Data Points and its Movements in Bars 33 to 36. Bar 33 34 36 Key Note B Data Point 6 3 7 7 1 Individual Movement -3 +4 0 -6
Firstly, it is interesting to note that the key note is supported by a wide range of numbers spanning from 6 to 1. The decrease to 3 in bar 34 coincides with the end of the descending figure and it could be argued that this allows the music to have a moment of release in the tension before increasing significantly again in bar 35. The sudden and significant decrease at bar 37, a large contrast to prior numbers, creates an element of surprise and almost depicts a release of tension in the climax. As data point 1 has not appeared elsewhere, this could play a structural role in suggesting the beginning of a new section. In general, the appearance of “larger” intervallic movement in these few bars supports the climactic moment.
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7 1 6 3 7 Example 7.21 Data Points to B in Bars 33 to 37.
However, unlike the previous bars (27 to 32), the key note plays an important role in supporting the inner melody as the data points in the key note are larger than the ones in the inner melody. In turn, this provides the key note with more emphasis and demonstrates how it stretches over a series of bars. It can be highlighted that the data point of the key note in bar 34 is exactly the same as the end of the first unfolding, and the third data point of the key note supports the increase of the second unfolding. This in turn reaffirms the strong relationship between the key note and the inner melody through the support of the data points. Several general observations can be made when comparing the data points to the notes of the unfoldings: 1. The sustained notes (Ds and Bs) in the first and third unfoldings retain the same number, the same amount of intervallic movement. This suggests that there is a sense of stability evoked by the repeated amount of intervallic movement and as these coincide with the same chord, it suggests continuity within the unfoldings. 2. All the data points from the three unfoldings mirror the movement in the music – e.g. an increase in data points when there is an ascending melody. For instance, in the first unfolding, the individual movements between As and Ds descends, like the melody.
Table 7.18 Key Note and Unfoldings Identified in Bars 33 to 36. Bar 33 34 36 Key Note B Data Point 6 3 7 7 1 Inner Melody As Ds - Ds Cs Fs Bs - Bs Unfolding Unfolding Unfolding Data Point 3 2 2 3 5 4 4
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However, in the third unfolding where the melody is descending, the data points depict an initial decrease from 5 to 3 before ascending to 6 and decreasing again to mark the end of the unfolding. This significantly contrasts with the data obtained from the first unfolding but it could be argued that as this is its second appearance (bearing a strong resemblance to the first), this would mean that there is more harmonic tension and perhaps the notes in this phrase will need to be emphasised to illustrate this. As for the second unfolding, in the broader scope, these notes could be perceived as the “link” between the first and third unfoldings as the data points have increased. This can be reflected in the music as the presence of this melodic figure ties the two separate ideas or unfoldings together, where the second idea is repeated a third lower than the first.
Table 7.19 Identifying the Individual Movements in the Unfoldings. Melodic Movement Descending Ascending Descending Inner Melody As Ds - Ds Cs Fs Bs - Bs Unfolding 1 Unfolding 2 Unfolding 3 Data Point 3 2 2 3 5 4 4 Individual Movement 7 5 4 3 5 6
Furthermore, upon a detailed examination of Gould and Richter’s recordings of these bars, essentially the climactic moment of the first movement, one can hear the differences in approach by the performers. It is useful to observe what the analysis reveals in these bars and to investigate some possible suggestions for interpretation in performance. In bars 33 to 37, a distinct difference in approach was taken by Gould and Richter. The climax is achieved in Richter’s interpretation through his approach to the rhythm and dynamics. For instance, he treats the quavers in the inner voice of bar 33 as a propellant, a series of notes moving in contrary motion acting as a driving force to the subsequent phrases (bars 34 to 35 and bars 35 to 36). It is particularly interesting to observe that the first appearance of the descending quaver figure is strongly emphasised and almost declamatory and on its reiteration, is slightly less emphasised, like an echo. Furthermore, Richter “phrased” off each of these through the use of a subtle crescendo and decrescendo within the slur. A sense of continuity and movement is established within these few bars due to Richter’s manipulation of rhythm and his careful and nuanced consideration of the melodic features. However, this was not the case in Gould’s interpretation. Overall, whilst one can hear that Richter is intensifying the phrase and creating a sense of the climactic moment by driving the music towards its highest point at bar 37,
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Gould’s interpretation focuses on establishing a clear distinction between each melodic idea (descending quaver passages) as well as defining the smaller arches within the broader structure. The overall structure is less distinct in Gould’s interpretation and at times, it is challenging to identify a clear directional impulse. Nevertheless, his approach to the smaller arcs are neatly shaped and “phrased” off appropriately without much recourse to the longer line. In terms of contrapuntal emphasis, he does give much more emphasis to the inner voices than Richter. It is also particularly interesting to observe Gould’s approach to the first beat of bar 33. This can arguably be perceived as the highest point and the beginning of the climax, but Gould approaches this like any other slur. As B in bar 33 is articulated by Hindemith as the last note of the phrase, Gould phrases this off by playing the note in a softer and gentler manner. However, in both recordings, the performers have created a sense of momentum within the inner voices by carefully shaping the phrases, with crescendos and decrescendos to reinforce a flowing approach. Gould’s approach to the reiteration of the melodic figure in bar 35 is different to Richter’s, as Gould’s emphasis is on shaping the individual phrases and the climactic and the intensified moment cannot be heard as such. This has resulted in the passage being treated much like any other passing figures. The examination of these recordings has in fact supported the findings of the analysis, in its initial stages from identifying the step progressions and performing the rhythmic reduction to examining how the data obtained from the Schenkerian/NRT charts reinforces the assessment of passages that are significant for the analyst and performer. Using the same example, this can be seen within the inner voices, the descending quaver passages. It is interesting to point out that Richter in particular emphasises Ds, the second half of last beat in bar 32 as this note plays a crucial role in building up the climactic moment of the section. Therefore, there is an emphasis on the descending triadic motion Fs-Ds-B as a way to introduce the subsequent melodic figure. Richter’s interpretation can also suggest that the step progression for this idea should include Ds, rather than simply stating the outline, Fs and B. Although this may challenge Hindemith’s melodic principles, it suggests that a performer’s interpretation can enrich an analyst’s view of the work. However, in Gould’s interpretation, he focuses on “phrasing” off, by tapering and decrescendos to B. This is particularly interesting as Gould regards the first beat of the bar, B, as part of the preceding phrase as opposed to being the first beat of the bar, which typically has more emphasis. In this instance, the step progression, as identified in the first layer of analysis, is closely reflected in Gould’s interpretation.
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Furthermore, when comparing the two recordings, the pedal note in the upper voice, B, is distinctly clearer in Richter’s interpretation as opposed to Gould’s where the emphasis is on bringing out the inner voices. This pedal note is also reflected in the Urlinie of the Schenkerian chart and thus reinforces its structural significance (prolonging the key note @) from an analytical perspective.
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7.6 Bars 37 to 51
Analytical Chart 7.21 NRT-Inspired VL Calculations with the Schenkerian Chart (Minim Subdivision) for Bars 23 to 51 (A Focus on Bars 37 to 51).
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8
Bf 7
D Cn A 6
C B
5
Cn Ds Bf 4 A
Bn Number Number ofIntervals B B D E 3
Cs 2 Cs B
1 B
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
First Idea Second Idea Bar Numbers Analytical Chart 7.22 Intervallic Movement Graphs with the Urlinie between Minim Beats for the First Movement (A Focus on Bars 37 to 51).
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Analytical Chart 7.23 NRT-Inspired VL Calculations with the Schenkerian Chart (Crotchet Subdivision) for Bars 37 to 51.
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10
D 9
D 8 B | B 7 C B Bf B G 6 Fs C Ef B B B | E | 5 A C Cs Ds A A
Number of Intervalsof Number 4
3
2 C (B) 1
0 Bar Numbers 37 38 39 41 42 45 46 49 50 Analytical Chart 7.24 Intervallic Movement Graphs with the Urlinie between Every Crotchet Beat in Bars 37 to 51.
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Discussion (Bars 37 to 51) Observations between the data obtained from the main chords alongside the Urlinie have revealed that there are significantly fewer increases in the final section of the movement, suggesting a sense of stability. It can also be seen that there is an overall decrease in the intervallic movement and fewer significant harmonic shifts to mark the end of the movement. However, a closer inspection of the chords on a more detailed level from the middleground analysis will reveal a deeper insight into the inner movement within the music. Much like the previous set of data, plotting the data points from every pitch collection against the Urlinie have provided a different insight into how one would approach the music. Firstly, the overall data from the prolonged key note B depicts an increase from bar 37 through to the end. This reinforces the idea that the harmonies are the key factor in increasing the tension towards the final moment of the movement. The appearance of such large intervals reinforces the idea that @ in Schenkerian terms contains the notion of instability and a heightened sense of tension. Furthermore, the key note moves to D, before finishing on E, reinforcing the movement from a tonic to dominant relationship across the entire movement. The data points in this final moment depict a decrease in intervallic movement (-4) and thus provide a clear suggestion that the music has reached a point of resolution. However, as the last data point can be perceived as a large intervallic movement, this could be particularly significant as it could ultimately foreshadow the next movement.
Table 7.20 Key Notes and its Data Points at a Minim Subdivision for Bars 37 to 51. Bar 37 46 48 51 Key Notes B B D E Data Point 5 3 2 3 Individual Movement -2 -1 +1 Overall Movement -2
In addition, there are numerous sets of unfoldings in this last section. The first set of unfoldings occurs twice between bars 37 to 39 from C to A and it is interesting to observe that even though these notes are repeated, much like a sequence, they are in fact supporting the Urlinie through the slight increase in intervallic movement and in turn, heightening the tension. This can be further reinforced by the appearances of C in bars 37 and 39 as its data points coincide with the data points of the key note. Although the data points suggest an increase, the notes are moving in a descending manner.
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Table 7.21 Key Notes and its Data Points at a Crotchet Subdivision for Bars 37 to 51. Bar 37 38 42 45 49 51 Key Notes B D E Data Points 1 5 5 6 7 9 5 Inner Movement +4 0 +1 +1 +2 -4 Overall Movement +6
4 - 5 4 - 5 Example 7.22 Data Points in Bars 37 to 39.
Several observations can be made with the other sets of unfoldings from bars 41 to 51. Firstly, it can be highlighted that only the second set of unfoldings, comprising an ascending movement, correlates with the increase in data points. The increase could be interpreted as the union between melody and harmony to reach the climax of the phrase and the end of the section. This in turn could suggest that the last four to five bars of the movement can be perceived as a “coda”. Secondly, there is a decrease in the intervallic movement in the last set of unfoldings despite the ascending melodic figure. It can be argued that there is a need for this last set to decrease in intervallic movement as a way to evoke the sense of finality of the movement, the final “phrase” with slightly smaller movement but containing a range of harmonic colours. As these unfoldings are essentially sequences that descend at each iteration, it is interesting to note that different results are produced. Furthermore, the inner movement within the unfoldings illustrates a mathematical pattern, where the movement increases by 2, a tone each time. This could potentially suggest how the tension is heightened through each unfolding and therefore, analysing the inner harmonic and intervallic movement alongside the Urlinie has revealed details that would not have been realised on a general surface level. The consistent increase could then be an indicator of an increase in tension where the appearance of each of these unfoldings should have more emphasis each time.
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Table 7.22 Unfoldings in Bars 41 to 51. Unfolding 1 Unfolding 2 Unfolding 3 Key Notes Bf - Ds Fs - B D - G Main Data Points 6 - 5 6 - 7 9 - 6 Inner Data Points 5 5 2 4 7 3 Amount of Movement 0 2 4
The results gathered through segregating the movement into smaller segments have suggested that there is a strong correlation between musical parameters (e.g. melodic contour) and the corresponding data points. It can be observed that by drawing observations from the graph on different structural levels, applying the concept of SPs and making larger connections between phrases, one’s initial perception of how the notes should be played is challenged. It suggests that certain notes should be given extra emphasis and that a particular group of notes that appear at first glance to be passing tones might actually play a larger role.
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Chapter 8
Application of the Analytical Method Part IV: Beyond Schenker and Further Observations
What other insights might the analytical results offer? This chapter will explore the possibility of going beyond Schenker and discuss further observations that might be made regarding the Piano Sonata. The first part contains the data gathered from the graphs and the second comprises observations derived from these findings. The following questions will be considered for discussion:
What are the most common BiPs and VL movement? How can this information assist in understanding the smaller ideas and larger sections? Does it play a role in revealing continuity or creating harmonic tension? How can the BiP and statistical data reveal additional insights into the phrases and melodic contours? Are there recurring patterns and/or consecutive use of certain BiPs for particular phrases? Do the performance recordings support the data and does the data support the interpretations in the recordings?
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Part 1 Data Collection
8.1.1 Statistics and Frequency of Voice-Leading Movement - Minim Subdivision
Analytical Table 8.1 Statistical Observations for Bars 1 to 51 (Minim Subdivision).
Total number of intervallic changes 47 Mean 160/49 = 3.26530612 Median 3 Mode 3
Analytical Table 8.2 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 1 to 11.
Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences 1 1 [001] 1 2 2 [002] 1 [011] 1 3 4 [012] 4 4 2 [0112] 1 [022] 1 5 2 [1112] 1 [113] 1 6 1 [123] 1
Analytical Table 8.3 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 11 to 21.
Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences
1 1 [001] 1 2 2 [002] 1 [011] 1 3 4 [012] 4 4 2 [0112] 1 [022] 1 5 2 [1112] 1 [113] 1 6 1 [123] 1
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Analytical Table 8.4 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 23 to 32. Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences
2 3 [011] 2 [002] 1 3 3 [012] 2 [111] 1 6 1 [123] 1 7 1 [133] 1
Analytical Table 8.5 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 33 to 39.
Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences
3 3 [012] 3 5 1 [113] 1 6 1 [222] 1
Analytical Table 8.6 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 40 to 51.
Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences 2 2 [011] 2 3 3 [012] 3 4 1 [112] 1
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Analytical Table 8.7 No. of Occurrences Within Each BiP and Intervallic Movement for the First Movement (Minim Subdivision). Amount of BiP No. of Occurrences movement between First Idea Second Idea Total each chord Bars 1 - 21 Bars 22 - 51 1 [001] 5 0 5 2 [002] 3 1 10 [011] 1 5 3 [012] 11 8 21 [111] 1 1 4 [0112] 1 0 5 [022] 2 0 [112] 1 1 5 [1112] 1 0 3 [113] 1 1 6 [123] 2 1 4 [222] 0 1 7 [133] 0 1 1
Analytical Table 8.8 VL Movement across the First Movement (Minim Subdivision).
VL Movement Bars 1-10 Bars 11-21 Bars 23-51 Total No. of between Each Chord Occurrences 0 19 11 15 45 1 16 15 23 54 2 12 10 15 37 3 1 2 4 7
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8.1.2 Statistics and Frequency of Voice-Leading Movement - Crotchet Subdivision
Analytical Table 8.9 Statistical Data for Bars 1 to 11 (Crotchet Subdivision).
Total number of intervallic changes 28 Mean 125/28 = 4.464285 Median 4 Mode 4
Analytical Table 8.10 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 1 to 11.
Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences 2 1 [002] 1 3 7 [0012] 3 [012] 4 4 9 [0013] 1 [0022] 2 [0112] 2 [013] 1 [022] 2 [112] 1 5 2 [0122] 2 [023] 1 [122] 2 6 3 [0123] 1 [0222] 2 7 1 [124] 1 8 2 [0233] 1 [2222] 1
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Analytical Table 8.11 Statistical Data for Bars 11 to 21 (Crotchet Subdivision).
Total number of intervallic changes 30 Mean 128/30 = 4.2666 Median 4 Mode 4
Analytical Table 8.12 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 11 to 21.
Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences 2 4 [0002] 1 [011] 2 [02] 1 3 5 [0012] 1 [012] 1 [111] 2 [12] 1 4 9 [0013] 1 [0022] 1 [0112] 4 [013] 1 [04] 1 [13] 1 5 7 [0005] 1 [0122] 1 [014] 1 [023] 2 [122] 2 6 2 [015] 1 [222] 1 7 2 [133] 2 8 1 [1223] 1
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Analytical Table 8.13 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 1 to 21 (Crotchet Subdivision).
Amount of BiP No. of Occurrences movement between each Bars Bars Total chord 1 - 10 11 - 21 2 [0002] 0 1 5 [002] 1 0 [011] 0 2 [02] 0 1 3 [0012] 3 1 12 [012] 4 1 [111] 0 2 [12] 0 1 4 [0013] 1 1 18 [0022] 2 1 [0112] 2 4 [013] 1 1 [022] 2 0 [04] 0 1 [112] 1 0 [13] 0 1 5 [0005] 0 1 12 [0122] 2 1 [014] 0 1 [023] 1 2 [122] 2 2 6 [0123] 1 0 5 [015] 0 1 [0222] 2 0 [222] 0 1 7 [124] 1 0 3 [133] 0 2 8 [0233] 1 0 3 [1223] 0 1 [2222] 1 0
Analytical Table 8.14 VL Movement in the First Idea for Bars 1 to 21 (Crotchet Subdivision).
VL Movement between Each Bars 1 - 10 Bars 11 - 21 Total No. of Occurrences Chord 0 30 27 57 1 21 32 53 2 41 24 65 3 6 10 16 4 1 2 3 5 0 1 1
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Analytical Table 8.15 Statistical Data for Bars 22 to 26 (Crotchet Subdivision).
Total number of intervallic changes 16 Mean 101/16 = 6.3125 Median 6 Mode 6
Analytical Table 8.16 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 22 to 26.
Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences 4 2 [004] 1 [022] 1 5 1 [122] 1 6 7 [024] 2 [033] 2 [123] 2 [222] 1 7 7 [016] 1 [025] 1 [133] 1 8 2 [044] 1 [134] 1 9 1 [225] 1
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Analytical Table 8.17 Statistical Data for Bars 26 to 32 (Crotchet Subdivision).
Total number of intervallic changes 24 Mean 156/24 = 6.5 Median 6 Mode 6
Analytical Table 8.18 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 26 to 32. Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences 2 2 [0011] 1 [002] 1 3 1 [0012] 1 4 3 [004] 1 [0012] 2 5 1 [0113] 1 6 6 [0114] 2 [0123] 1 [024] 2 [1122] 1 7 2 [0223] 1 [133] 1 8 3 [026] 1 [1133] 1 [1223] 1 9 4 [1134] 2 [1224] 1 [1233] 1 11 2 [0335] 1 [2234] 1
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Analytical Table 8.19 Statistical Data for Bars 33 to 36 (Crotchet Subdivision).
Total number of intervallic changes 20 Mean 88/20 = 4.4 Median 4 Mode 7
Analytical Table 8.20 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 33 to 36. Amount of movement Number of BiP Specific Number of between each chord Occurrences Occurrences 1 1 [001] 1 2 3 [0011] 3 3 3 [0012] 1 [0111] 1 [012] 1 4 4 [0022] 1 [1111] 3 5 3 [0023] 1 [0122] 1 [1112] 1 6 1 [222] 1 7 5 [0124] 1 [0223] 1 [1123] 1 [1222] 1 [124] 1
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Analytical Table 8.21 Statistical Data for Bars 37 to 51 (Crotchet Subdivision).
Total number of intervallic changes 20 Mean 102/20 = 5.1 Median 5 Mode 4
Analytical Table 8.22 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 37 to 51.
Amount of movement Number of BiP Specific Number between each chord Occurrences of Occurrences 2 1 [011] 1 3 1 [0012] 1 4 7 [00022] 2 [0112] 1 [022] 3 5 3 [00122] 2 [01112] 1 [1112] 1 6 5 [00123] 1 [0222] 1 [1113] 1 [1122] 1 [114] 1 7 2 [111112] 1 [1222] 1 9 1 [01233] 1
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Analytical Table 8.23 No. of Occurrences Within Each BiP and Intervallic Movement for Bars 22 to 51 (Crotchet Subdivision).
Amount of BiP No. of Occurrences movement between each Bars Bars Bars Bars Total chord 22 - 26 27 - 32 33 - 36 37 - 51 1 [001] 0 0 1 0 1 2 [0011] 0 1 3 0 6 [002] 0 1 0 0 [011] 0 0 0 1 3 [0012] 0 1 1 1 5 [0111] 0 0 1 0 [012] 0 0 1 0 4 [00022] 0 0 0 2 15 [0022] 0 0 1 0 [004] 1 1 0 0 [0112] 0 2 0 1 [022] 1 0 0 3 [1111] 0 0 3 0 5 [00122] 0 0 0 2 9 [0023] 0 0 1 0 [01112] 0 0 0 1 [0113] 0 1 0 0 [0122] 0 0 1 0 [1112] 0 0 1 1 [122] 1 0 0 0 6 [00123] 0 0 0 1 19 [0114] 0 2 0 0 [0123] 0 1 0 0 [0222] 0 0 0 1 [024] 2 2 0 0 [033] 2 0 0 0 [1113] 0 0 0 1 [1122] 0 1 0 1 [114] 0 0 0 1 [123] 2 0 0 0 [222] 1 0 1 0
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7 [0124] 0 0 1 0 12 [016] 1 0 0 0 [0223] 0 1 1 0 [025] 1 0 0 0 [111112] 0 0 0 1 [1123] 0 0 1 0 [1222] 0 0 1 1 [124] 0 0 1 0 [133] 1 1 0 0 8 [026] 0 1 0 0 5 [044] 1 0 0 0 [1133] 0 1 0 0 [1223] 0 1 0 0 [134] 1 0 0 0 9 [01233] 0 0 0 1 6 [1134] 0 2 0 0 [1224] 0 1 0 0 [1233] 0 1 0 0 [225] 1 0 0 0 11 [0335] 0 1 0 0 2 [2234] 0 1 0 0
Analytical Table 8.24 VL Movement (Crotchet Subdivision) in the Second Idea (Bars 22 to 51).
VL Movement Bars Bars Bars Bars Total No. of between Each Chord 22 – 26 27 - 32 33 - 36 37 - 51 Occurrences 0 10 19 20 22 73 1 6 26 33 28 93 2 14 19 19 29 81 3 9 15 3 4 31 4 6 9 2 1 18 5 2 1 0 0 3 6 1 1 0 0 2
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Analytical Table 8.25 VL Movement across the First Movement (Bars 1 to 51) (Crotchet Subdivision). First Idea Second Idea (A) (B) VL Movement Bars Bars Total Bars Bars Bars Bars Total Total between Each 1 - 10 11 - 21 No. 22 - 26 27 - 32 33 - 36 37 - 51 No. Number of Chord Appearances 0 30 27 57 10 19 20 22 73 130 1 21 32 53 6 26 33 28 93 146 2 41 24 65 14 19 19 29 81 146 3 6 10 16 9 15 3 4 31 47 4 1 2 3 6 9 2 1 18 21 5 0 1 1 2 1 0 0 3 4 6 0 0 0 1 1 0 0 2 2 Observations (from graph):
Analytical Table 8.26 Statistical Data for Bars 1 to 21 (Crotchet Subdivision).
Bars 1 - 10 Bars 11 – 21 Total Total number of intervallic 28 30 58 changes Mean 125/28 = 128/30 = 253/58 = 4.464285 4.2666 4.3620 Median 4 4 4 Mode 4 4 4
Analytical Table 8.27 Statistical Data for Bars 22 to 51 (Crotchet Subdivision). Bars 22 - 26 Bars 27 - 32 Bars 33 - Bars 37 - Total 36 51 Total number of 16 24 20 20 80 intervallic changes Mean 101/16 = 156/24 = 6.5 88/20 = 4.4 102/20 = 447/80 = 6.3125 5.1 5.5875 Median 6 6 4 5 6 Mode 6 6 7 4 6
Analytical Table 8.28 Statistical Data for Bars 1 to 51 (Crotchet Subdivision). Bars Bars Bars Bars Bars Bars Total 1 - 10 11 - 21 22 - 26 27 - 32 33 - 36 37 - 51 Total number 28 30 16 24 20 20 138 of intervallic changes Mean 125/28 = 128/30 101/16 = 156/24 = 88/20 102/20 700/138 = 4.464285 = 4.2666 6.3125 6.5 = 4.4 = 5.1 5.07246377 Median 4 4 6 6 4 5 5 Mode 4 4 6 6 7 4 4 172
Analytical Table 8.29 No. of Occurrences within Each BiP and Intervallic Movement for the First Movement (Crotchet Subdivision).
Amount of BiP No. of Occurrences movement between Bars Bars Bars Bars Bars Bars Total each chord 1 - 10 11 – 21 22 - 26 27 - 32 33 - 36 37 - 51 1 [001] 0 0 0 0 1 0 1 2 [0002] 0 1 0 0 0 0 11 [0011] 0 0 0 1 3 0 [002] 1 0 0 1 0 0 [011] 0 2 0 0 0 1 [02] 0 1 0 0 0 0 3 [0012] 3 1 0 1 1 1 17 [0111] 0 0 0 0 1 0 [012] 4 1 0 0 1 0 [111] 0 2 0 0 0 0 [12] 0 1 0 0 0 0 4 [00022] 0 0 0 0 0 2 33 [0013] 1 1 0 0 0 0 [0022] 2 1 0 0 1 0 [004] 0 0 1 1 0 0 [0112] 2 4 0 2 0 1 [013] 1 1 0 0 0 0 [022] 2 0 1 0 0 3 [04] 0 1 0 0 0 0 [1111] 0 0 0 0 3 0 [112] 1 0 0 0 0 0 [13] 0 1 0 0 0 0 5 [0005] 0 1 0 0 0 0 21 [00122] 0 0 0 0 0 2 [0023] 0 0 0 0 1 0 [01112] 0 0 0 0 0 1 [0113] 0 0 0 1 0 0 [0122] 2 1 0 0 1 0 [014] 0 1 0 0 0 0 [023] 1 2 0 0 0 0 [1112] 0 0 0 0 1 1 [122] 2 2 1 0 0 0
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6 [00123] 0 0 0 0 0 1 24 [0114] 0 0 0 2 0 0 [0123] 1 0 0 1 0 0 [015] 0 1 0 0 0 0 [0222] 2 0 0 0 0 1 [024] 0 0 2 2 0 0 [033] 0 0 2 0 0 0 [1113] 0 0 0 0 0 1 [1122] 0 0 0 1 0 1 [114] 0 0 0 0 0 1 [123] 0 0 2 0 0 0 [222] 0 1 1 0 1 0 7 [0124] 0 0 0 0 1 0 15 [016] 0 0 1 0 0 0 [0223] 0 0 0 1 1 0 [025] 0 0 1 0 0 0 [111112] 0 0 0 0 0 1 [1123] 0 0 0 0 1 0 [1222] 0 0 0 0 1 1 [124] 1 0 0 0 1 0 [133] 0 2 1 1 0 0 8 [0233] 1 0 0 0 0 0 8 [026] 0 0 0 1 0 0 [044] 0 0 1 0 0 0 [1133] 0 0 0 1 0 0 [1223] 0 1 0 1 0 0 [134] 0 0 1 0 0 0 [2222] 1 0 0 0 0 0 9 [01233] 0 0 0 0 0 1 6 [1134] 0 0 0 2 0 0 [1224] 0 0 0 1 0 0 [1233] 0 0 0 1 0 0 [225] 0 0 1 0 0 0 11 [0335] 0 0 0 1 0 0 2 [2234] 0 0 0 1 0 0
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Part 2 Discussion
8.2.1 Data Obtained from Minim Subdivision Voice-leading Movement It can be observed from Table 8.1 (VL Movement across the First Movement (Minim Subdivision (Bars 1 to 21)) that smaller intervallic changes between chords are the most common in the first movement. In this movement, a small intervallic change can be described as the use of VL numbers such as 0 or 1.
Table 8.1 Most to Least Common VL Movements from a Minim Subdivision (Bars 1 to 21). Most Common Least Common 1 0 2 3
By having smaller numbers such as 0 or 1, movements that can also be described as a common tone and a semitone means that most transformations between chords are created through small movements. It is particularly interesting to observe that the individual movement by one semitone has the most frequent number of appearances. This reinforces the notion that the intensity of the music (e.g. the climactic moment) can increase or decrease by simply transposing a phrase by a semitone from a note within a chord to the next. It is worthwhile highlighting that the movement by 3 semitones is least preferred as this translates into as a minor 3rd, and this shift will be quite significant if used consecutively without utilising smaller movements such as 0 or 1 within the BiP.
Intervallic Movement between Each Chord and its Basic Interval Pattern (BiP) Based on the above data, it can be observed that the most frequent amount of intervallic movement between chords is 3 and larger movements such as 6 and 7 tend to be used less frequently. The frequent appearance of 3 can be examined upon closer inspection of the specific BiP. In the first movement, there are two BiPs for the movement of 3, [012] and [111]. [012] appears more often than [111] and one can suggest several reasons as to its frequent appearance.
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Table 8.2 Most to Least Preferred BiP Intervallic Movement from a Minim Subdivision.
Most Preferred Least Preferred 3 2 4 1 6 5 7
When breaking down [012], the following details can be observed:
Table 8.3 Characteristics of BiP [012].
[012] 0 “Common Tone” – retaining the same note across the two chords 1 “Semitone” – the smallest amount of movement between the two chords 2 “Tone” or “Two Semitones” – the “largest” movement between the two chords, the fundamental note that determines the new chord.
In the opening idea, the appearance of [012] appears consecutively across bars 2 to 4 and it can be seen that the total number of appearances of 3 (total of [012]) is the largest in the context of the opening bars (bars 1 to 4). The presence of this particular combination in conjunction with other musical elements such as register and melodic contour, supports its significant role in creating momentum to drive the music to the end of its first statement. It can be further stated that the consecutive use of [012] creates a sense of coherence and unifies the first two subphrases, bars 1 to 2 and bars 3 to 4. In this particular instance, [012] has a structural role in supporting the music to reach the climax of its phrase. The notion that the peak of the phrase can be established by “smaller” intervallic movements (in this case, the BiP of [012]) challenges the common assumption that a larger intervallic movement is required to build the tension within the music. In turn, this could then have some influence on one’s perception of the phrase structure and in performance practice, where more emphasis could be given to the notes that move by 1 and 2 semitones, highlighting the change of colour within each chord.
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2 1 3 3 3 1
Example 8.1 Intervallic Movement Between Each Chord at a Minim Level in Bars 1 to 4.
It can also be observed in bar 7 that [012] is used twice in a row, correlating with the descending passage in the music. At this particular point, the music is developing and it could be perceived that this specific phrase is reaching the climax of the section. From a structural point of view, it can be seen that bar 10 marks the end of the statement of the first idea and the music in bars 7 and 8 reinforces the climactic peak of the section. Again, this example highlights how the intensity of the music can be driven by minimal intervallic movement. Likewise, in bars 17 to 19, as these bars can be heard as an anticipation of the climactic moment of the phrase in bar 20, this is reinforced by the consecutive use of [012] and therefore suggests its structural significance (that it plays a role in heightening the tension of the phrase).
3 3 3
Example 8.2 Intervallic Movement of 3 in Bars 7 to 8.
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3 3
Example 8.3 Intervallic Movement of 3 in Bars 17 to 19.
A slight variation of the use of [012] can be found in the opening bars of the second idea, bars 23 to 25. It is worth noting there is a consecutive use of 3 semitones in these bars containing the chords E minor, Cs minor and D minor, and utilising the BiP [012] as well as [111]. The movement of 3 semitones and its significance differs from the first idea (in contributing to the musical tension) as its role in this context contributes to establishing a sense of stability at the beginning of the second idea. Whilst it can be argued that a sense of tension can be heard as bar 23 marks the beginning of a new section, the occurrence of 3 semitones along with its specific BiP at bar 23 could also reinforce its structural role in establishing stability in the new idea. Furthermore, as this particular fragment is later repeated an octave higher in bars 27 to 29, it can be observed that the amount of intervallic movement is not identical to bars 23 to 25. However, the close numeric relationship in the total number of intervallic movement between the first and second phrases reaffirms the close relationship between the two phrases.
Table 8.4 A Comparison of the Intervallic Movement Between Bars 23 to 25 and Bars 27 to 29.
Bar/s 23-25 26 (Transition) 27-29 Amount of movement 3 3 2 6 2 3 2 Total number of movement 8 7
Similarly, it is particularly interesting to observe the consecutive use of [012] in bars 33 to 36 on the assumed chords B major, E major, A major and C major. From a structural perspective, the occurrence of this BiP appears at a moment in the music where it can
178 arguably be described a climactic point of the movement. That the intensity and drive of this particular moment in the music can be formed by a combination of “small” intervallic successions within individual notes in a chord is extremely effective and therefore, it can even be argued that one should not assume that the “momentum” needs to be associated with large intervallic changes from one chord to the next. Other factors such as the use of sequences and faster rhythms (quavers) also contribute to this.
3 3 3 (Note: Bar 37 – missing note, C, bass, omitted) Example 8.4 Intervallic Movement of 3 in Bars 33 to 37.
[012] can also be seen across bars 44 to 48 but this plays a different role to its other appearances in the movement. At this point where it can almost be described as a coda, there is a sharp change in the dynamics with the support of fewer layers of harmony. The role of [012] in this context could resemble a transition, from supporting the climactic point into the more “subdued” conclusion of the movement. Upon a close examination, one can hear a significant amount of harmonic movement and “chords” that do not fit the implied tonality of A major, yet this is created by “small” intervallic movement. The appearance of this BiP also correlates with the series of repeated arpeggiated motives (bars 40, 44 and 48). The slight variation of dynamics where the second statement (the repetition of this idea at a third lower) is to be played mezzo forte whilst the first and third pairs are to be played piano, suggests that this motive is to be given more emphasis, the pinnacle of the last section of the piece.
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3 3 Example 8.5 Intervallic Movement of 3 in Bars 44 to 48.
Example 8.6 First Appearance of the Arpeggiated Figure (Bar 40).
Example 8.7 Second and Third Appearances of the Arpeggiated Figure (Bars 44 and 48).
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8.2.2 Data Obtained from Crotchet Subdivision Voice-leading movement In the first idea (bars 1 to 21), a close examination and calculation of the VL movement from a crotchet subdivision has revealed that the movement of 2 is most frequently used. This contrasts with the data obtained from the principal chords of the first movement where 1 is most preferred. However, in the context of the first idea, it is evident when comparing the two tables for most preferred to least preferred VL movement, there is a strong preference for smaller VL changes and “larger” movements such as 3, 4 and 5 are least preferred.
Table 8.5 Most to Least Common VL Movements from a Crotchet Subdivision (Bars 1 to 21). Most Preferred Least Preferred 2 0 1 3 4 5
Table 8.6 Most to Least Common VL Movements from a Minim Subdivision (Bars 1 to 21). Most Preferred Least Preferred 1 0 2 3
It can be observed that 1 is the most frequently used interval in the second idea (bars 22 – 51) and in turn strongly suggests that the harmonies in the development section move by 1 semitone. Unlike the first idea where 0 is the next most frequently used, the use of 2 (the movement by a tone or 2 semitones) is the second most frequently used in the second idea. This correlates with the ideas (as stated earlier) that harmonic tension can be created through smaller movement and the movement by 2 semitones plays a role in changing the harmonic colour of the subsequent chord.
Table 8.7 Most to Least Common VL Movements from a Crotchet Subdivision (Bars 22 to 51). Most Preferred Least Preferred 1 2 0 3 4 5 6
Several observations can be made when the data obtained from the two ideas (bars 1 to 21 and bars 22 to 51) are placed alongside each other. On the whole, it can be seen that the VL movements of 1 and 2 semitones are most preferred across the movement. 0 is also used
181 frequently in both ideas as this will mean that a common tone will be retained across the two chords. Evidently, larger VL movements are less preferred and if used, they are always applied in conjunction with a smaller VL movement such as 0, 1 and/or 2 to support this significant harmonic change. This further supports the notion that smaller VL changes play a significant role in supporting the increase in intensity as well as creating harmonic interest within the phrases. On a broader scope, it is interesting to compare how “larger” VL movement are used between chords in the first and second idea. “Larger” VL movement in the context of the first movement can be described as a number larger than 3 as this generally suggests fewer common tones and stepwise movements. As such, it can be observed that the use of larger VL movements such as 4, 5 and 6 are used much more frequently in the second idea than the first idea. Whilst these are applied in conjunction with smaller VL movement such as 0,1,2, the appearance of larger VL movements can contain some structural significance when considering their context. Delving into significantly different key areas and the appearance of larger VL movements in the second idea correlates with the idea that the contrasting development section of a sonata will contain more harmonic movement. However, it is worthwhile highlighting that the most frequently used VL movement in the first idea differs greatly to the second idea. 2 is most frequently used in the first idea whilst 1 is the most frequently used in the second idea. It can be argued that 1 is used in the second idea as a way to support larger VL movements. However, the frequent use of 2 in the context of the first idea can be perceived to be a slightly larger VL movement and its appearance alongside smaller numbers play a significant role in supporting the harmonic tension and creating a sense of continuity in the harmonies from the beginning of the movement.
Intervallic Movement between Each Chord and its Basic Interval Pattern (BiP) From a crotchet subdivision, the most frequent intervallic movement in the opening idea (bars 1 to 21) is 4, one semitone higher than the result obtained from analysing the minim chords. However, if segregated further into its two main phrases, 3 is the most frequently used intervallic movement in bars 1 to 10 and 4 in bars 11 to 21. In bars 1 to 10, the frequent use of 3 bears a strong resemblance to the data from the minim subdivision where 3 is the most frequently used intervallic movement across the entire movement.
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The frequent appearance of the 4 in bars 11 to 21 could then be of structural significance as the opening theme is restated with further developments and extensions. It can be observed that the increase from 3 to 4 correlates with more harmonic changes. The most frequently used BiP with 4 semitones, [0112], is used twice in a row between bars 19 and 20 and the other BiPs, [0022] occur prior to [0112]. Hence the BiP in this passage appears as [0022], [0112] and [0112].
[0022] [0112] [0112] Example 8.8 Intervallic Movement of 4 and its Corresponding BiPs in Bars 19 and 20.
Even though the BiP slightly differs from [0112], [0112] and [0022] both add up to 4. The fact that 4 is used consecutively at the climactic moment of the phrase further reinforces the idea that harmonic intensity can be established through a combination of smaller VL movement. These three BiPs all share 0, indicating that a shift between each chord contains a common tone and using this alongside the use of 1 and 2 aids in creating momentum in the music. Table 8.8 Characteristics of BiP [0112] and [0022]. BiP [0112] Movement BiP [0022] 0 No changes 0 1 Decreases by 1 0 1 Increases by 1 2 2 No changes 2
From the data in the second idea (bars 22 to 51), it is evident that the movement by 6 semitones is the most frequently used. However, segmenting the music further into its key phrases and climactic moments produced different results.
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Table 8.9 Phrase Subdivision of the 2nd Idea and its Corresponding Intervallic Movement and BiPs. Bars 22-26 Bars 27-32 Bars 33-36 Bars 37-51 Amount of Intervallic 6 6 7 4 Movement No. of Occurrences 7 6 5 7 Frequently used BiP and [024] 2 [0114] 2 [0124] 1 [022] 3 Number of Occurrences [033] 2 [024] 2 [0223] 1 [123] 2 [1123] 1 [1222] 1 [124] 1
Table 8.10 Statistical Overview of Bars 22 to 51 in its Respective Phrase Divisions.
Bars 22 - 26 Bars 27 - 32 Bars 33 - 36 Bars 37 - 51 Mean 101/16 = 6.3125 156/24 = 6.5 88/20 = 4.4 102/20 = 5.1 Median 6 6 4 5 Mode 6 6 7 4
As illustrated in the discussion of the analytic charts and the above tables, it is interesting to observe that there are different results in bars 22 to 32 and bars 33 to 51. The mean, median and mode from bars 22 to 32 is 6 but the other two subdivisions, bars 33 to 36 and bars 37 to 51 suggest a very different set of data. It can perhaps be stated that bars 22 to 32 is a separate section and is supported by larger intervallic movement. When comparing this to the first idea, these bars coincide with the new materials thus suggesting that there is more harmonic interest. Overall, it can be observed that the mean, median, and mode for the respective sections tend to have the same number but this was not the case for bars 33 to 36 and bars 37 to 51. In bars 33 to 36, the most frequently used number is 7 whilst 4 is the mean and median for these bars. The appearance of 7 in bars 34 and 36 coincides with the ascending 3-note figure in the treble and the broken chord in the bass. Whilst the first instance at bar 34 appears on the last crotchet beat of the bar and continues into bar 35, the second appearance at bar 36 begins half a beat earlier. Despite the slight variation in its appearances, it is evident that the intervallic movement of 7 coincides with the 3-note figure, which supports the transitionary passages between phrases and sections. This also indicates that in this particular context, a larger intervallic movement (7) plays a structural role as the intervallic movement that follows the large movement is always significantly smaller, reinforcing the idea that this could correlate to a release in the tension of the music.
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However, despite 7 being the mode for these few bars, 4 is the mean and median. This could suggest that even though this passage has more instances of 7, the overall average of intervallic movement of 4 could bear a strong resemblance to the first idea, illustrating a resemblance to the very beginning of the movement.
7 7 7 7
Example 8.9 Intervallic Movement of 7 in Bars 33 to 37.
In bars 37 to 51, 4 is the mode whilst 5 is the mean and median, two different numbers in the last section of the movement. It would be worthwhile to observe where the use of 4 (mode) occurs and if it has any structural significance, like the frequent use of 7 in bars 33 to 36. The use of 4 mostly appears between bars 37 to 39 and it is worth noting that the consistent use of 4 coincides with the end of the climactic section and the order of BiP is the same each time, reaffirming the idea that the two passages are very much similar, both through their surface notes and the intervallic movement.
4 4 5 4 4 5 4
Example 8.10 Intervallic Movement in Bars 37 to 39.
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Table 8.11 VL Movement, BiP, and Intervallic Movement in Bars 38 and 39. Bar 37 38 39 VL movement between 2-0-2 2-0-2-0-0 1-0-2-0-2 0-2-2 2-0-2-0-0 1-0-2-0-2 2-0-2 each chord BiP 022 00022 00122 022 00022 00122 022 Total Amount of Intervallic 4 4 5 4 4 5 4 Movement between each chord
On the whole, it can be observed that the general amount of intervallic movement between chords for the second idea is 6, encompassing a range of BiPs. Two sets of BiPs can be highlighted, [024] and [0114]: [024] is used four times across bars 22 to 26 and [0114] is used twice in bars 27 to 32. The two instances of [0114] occur between bars 31 and 32 and it can be seen that [0114] appears twice within a short span of time. The first occurs at the end of a phrase whilst the other occurs at the start of the next phrase. [0114] in this particular scenario can be described as a bridge to connect the two phrases. On a larger level, this movement occurs at the end of the transitionary passage, right before the climax, under A, the neighbour note highlighted in the Urlinie.
026 0114 1133 0114
Example 8.11 BiP in Bars 31 and 32.
The appearance of [024], much like [0114] appears at the start of bars 27 and 28 and it can be observed that the use of this particular BiP coincides with the rhythmic pattern as bar 28 can be seen to be a step higher than bar 27. It can be observed that within the movement from the first chord (G-B-D) in bar 27 to the first chord of bar 28 (Gs-B-Ds), B is the common tone between the two. Thus, by raising the surrounding notes, D and G by a
186 semitone, this has been particularly effective in creating different tonal colours. Therefore, the appearance of the same melodic figure alongside the same combination of numbers ([024]) has resulted in a series of unexpected harmonies.
024 0335 0112 0112 024 2234 0113 0011 5 Example 8.12 BiP in Bars 27 and 28.
Examining bars 33 to 37 for a set of BiP that is used more frequently has yielded different results to the earlier bars. Even though the most frequently used amount of movement is 7, the BiPs that recur more than once are [0011] and [1111]. It is particularly interesting to observe that [0011] and [1111] both occur consecutively, three times in a row. [0011] occurs in bar 34, the end of the first statement of the climactic moment, linking to the 3-note motive and appears much like a transition to bar 35. Interestingly, [1111] appears in bar 36, much like bar 34, where it occurs at the end of the descending 5-note figure and reinforces the transition to the next section. It is even more worthwhile to observe the comparison of the sum of the intervallic movement with the particular BiPs in these bars as it increases from 2 to 4. These details could be significant in how one performs the phrase as the increase in intervallic movement could correlate to the heightened tension within the music. This can suggest some fluctuation of the tempo, perhaps an accelerando and an increase in dynamics. As mentioned earlier, as the first appearance of the respective BiP occurs at the end of the phrase, this could prompt the performer to examine these phrases on a broader scale. Based on the data and other musical elements such as the use of repetition and an increase in dynamics, the second appearance is much more significant and should be given extra emphasis.
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Example 8.13 Segmentation of Bars 33 to 36.
Table 8.12 BiP and Observations on the Overall Movement in Bars 33 to 36. 33 34 35 36 012 1222 0122 0022 0011 0011 0011 0111 0124 124 0023 0012 1112 222 1111 1111 1111 1123 0223 001
2 +2 4
The numerical data obtained from the Schenkerian combined with NRT-inspired analysis supports the findings from the examination of the recordings, particularly with Richter’s interpretation (refer to Analytical Chart 7.19, page 145). The mode obtained from the crotchet subdivision indicates that compared to its preceding phrases there is a larger number of intervallic movement at the climax thus suggesting that bars 33 to 37 are of particular musical interest and perhaps should be given more attention. However, the median is of a smaller number, 4, compared to its preceding phrases (6). This suggests that the climactic moment of the section can be established through a smaller intervallic movement. It is also interesting to observe the intervallic movement of 7 between the 3-note figures, the transitional passages in bars 34 to 35 and bars 36 to 37 as this suggests more emphasis. When comparing this observation to the recordings, it appears that Richter responds to these features to a much greater extent than Gould. Not only does Richter imbue these three sets of notes with more emphasis, he also manipulates the tempo and gets louder, propelling the music towards the next phrasal closure. Gould on the other hand, “phrases” off by using a decrescendo to approach the last chord within the phrase marking. Richter’s approach thus suggests that the larger intervallic movement correlates to the idea that more emphasis might be given to the respective notes. Here, the analytical data and performance match each other closely, whereas Gould’s interpretation is more idiosyncratic. The data collection from the minim level analysis for these bars also suggests that the music is intensifying through its harmonic movement and driving it to the climax.
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From a BiP perspective, there is also a recurring appearance of the pattern [012] in these few bars. This pattern can suggest that the climactic moment of the music is driven by smaller voice-leading movement and it is other musical elements that add to the intensity of the moment. Furthermore, it is particularly interesting to observe that the way in which the respective performers “phrase” off the individual melodic ideas in the inner voices correlate with the obtained analytical data from a crotchet level analysis. For instance, when the first melodic figure (bars 33 to 34) descends in register and dynamics, there is a decrease in the data points between pitch collections and this can be heard in both recordings. And on its repetition (bars 35 to 36), both performers “phrased” off but there is a slight increase in the data points. This suggests that there is a need for the music to increase in intensity, with louder dynamics and slightly faster tempi to direct the music more effectively to the next melodic idea. With bars 37 to the end, there is one common BiP [022] and its sum, 4, reaffirms the amount of intervallic movement across the entire movement. This in turn could be of structural significance, as a relationship can be perceived between the last section (bars 37 to 51) and the first section (bars 11 to 21), where 4 is the most frequently used number. [022] appears within a short span of time, once at bar 37, the start of bar 38, and the beginning of bar 39. It can also be observed that these BiPs coincide with the same notes each time and the recurrence of this reinforces the idea that emphasis should be given to the notes (in bars 37 to 39), as it establishes the sense of a “constant” idea and creates a sense of stability.
4 4 5 4 4 5 4
022 022 022
Example 8.14 BiP and Intervallic Movement in Bars 37 to 39.
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Further observations can be made from an overall scope of the BiP collection from the first to the second idea. (e.g. what number resonates more in one idea than the next?)
Table 8.13 Intervallic Movement and its Number of Occurrences from a Crotchet Subdivision in the First Idea (Bars 1 to 21).
1st Idea Most Preferred Least Preferred Intervallic Movement 4 3,5 2,6 7,8 No. of occurrences 18 12 5 3
Table 8.14 Intervallic Movement and its Number of Occurrences from a Crotchet Subdivision in the First Idea (Bars 22 to 51).
2nd Idea Most Preferred Least Preferred Intervallic Movement 6 4 7 5 2,9 3, 8 11 1 No. of occurrences 19 15 12 9 6 5 2 1
From the above tables (illustrating the number of occurrences of the particular BiPs from most preferred to least preferred across the two distinct sections), it can be seen that the use of 6 in the second idea and 4 in the first are relatively close in value, illustrating potential symmetry between the two sections. It is particularly interesting to note that there are more “larger” intervallic movements in the second idea. The use of 7 and 9 are used much more frequently than smaller numbers, which in turn reaffirms the general use of larger intervallic movement to create momentum and harmonic interest. This significantly contrasts with the first idea where the use of large intervallic movements like 7 and 8 are least preferred and there are smaller intervals. Again, this could be significant from a structural viewpoint as one would expect some stability to be established at the beginning of the movement. It is interesting to note that all the BiPs used in the first idea can be found in the second idea and thus suggests that the second idea is almost like an expansion of the first idea. Naturally, the BiPs in the second idea will contain more variety and combinations which then correlate with the idea that a piece with two contrasting ideas should contain the following: the first idea would state the themes of the work and the second would contain more harmonic variety.
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Table 8.15 Intervallic Movement and its Number of Occurrences from a Crotchet Subdivision in the First Movement. Most Preferred Least Preferred 4 6 5 3 7 2 8 9 11 1
On the whole, the following observations on the BiP have established that 4 is the most common type of intervallic movement and the next two frequently used numbers, 6 and 5, can be considered to be “larger” movements. This is interesting as it would then suggest that larger intervallic movements coincide with the development and appearance of new materials.
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Chapter 9
Towards a New Model of Analysis for Neo-Classical Music
This project has been carried out with the objective to create a useful hybrid analytical method, for music that contains vestiges of tonality with post-tonal harmonic features (typical of Neo-Classical music). Some concluding thoughts are here offered on how a hybrid analytical approach to Neo-Classical music might be applied in other case studies. The great challenge of analysing Hindemith’s music lies mainly in its variety of tonal procedures. We are further flummoxed by the absence of a total theory that incorporates the differing and contrasting layers of neo-tonality, symmetrical phrasing, and harmonic fluctuation of the kind Hindemith describes in his writings. But it is even more challenging to have a method that attempts to make insightful observations without overlooking important features, such as melody and harmony. Through the study of Paul Hindemith’s Piano Sonata No. 1, we ascertain that the Schenkerian method is still applicable as the background harmonic structure is somewhat tonal. However, as the foreground harmonies are post-tonal, other analytical approaches are more useful to better understand these structural aspects. One such approach is NRT. Therefore, by integrating the analytical strengths of the Schenkerian and Neo- Riemannian methods, we can better understand post-tonal foreground harmonies and tonal harmonic structures in a piece such as this. Whilst it is impossible to have one methodology to explain all musical features, a synthesis of certain aspects of the selected methods has helped construct a more thoughtful and strategic approach to Neo-Classical music. Whilst Schenker’s principles of identifying certain melodic features (such as prolongation) and the fundamental structure are useful in illustrating the expansion of the harmonies, unconventional intervals will emerge from the Urlinie and Bassbrechung, and it is challenging to analyse the harmonies via traditional Roman numerals. As Hindemith’s music contains strong vestiges of tonality, Schenker’s principle of linear progression and Hindemith’s own melodic principles have yielded very similar results. However, if strict Schenkerian principles are practised, much of the distinct pitch activity might be overlooked or marginalised and it would be beneficial to extend his principles to better reflect the movement within the music. Tonal coherence can therefore be established through motivic connections between the music of different key areas as well as the unfolding of the tonic triad. As NRT rejects monotonality but rather focuses on the transformation from one chord to the next, and that all tonal regions and chord spaces are
192 given an equal status, this approach has been of benefit in elucidating these post-tonal foreground harmonies. It can also be challenging to construct an analytical approach, free of a schematic process and not simply justify chromatic events as an elaboration of or “distortion” from a diatonic structure. Due to the variety of tonal procedures, there appears to be a need for a theoretical model that can explain all the similarities amongst works that are commonly described as “Neo-Classical”. It may well be the case that what binds these works is their tonal background structure combined with post-tonal foreground harmonies. Through the analysis of Hindemith’s First Piano Sonata, it can be observed that despite the use of extended harmonies in the foreground details, what unifies each individual movement and the entire sonata is its tonal background structure. Whilst this study has demonstrated one way in which there can be a reconciliation between tonal and extended harmonies through the calculation of voice-leading movements, one way to further enrich this hybrid method for future research might be accomplished through the use of a modified Tonnetz. As a tool (previously mentioned) that is typically used in NRT, the Tonnetz is a conceptual lattice diagram that represents major and minor chords and key areas (see Figure 9.1).1 Although this has proven useful for late Romantic music such as Wagner and Brahms, it fails to account for all the diverse chords used in Hindemith’s Piano Sonata No. 1. In order to account for these chords, the Tonnetz will need to be modified. Even though it is known that NRT typically assumes enharmonic equivalence, integer notation (where the twelve tones will be represented as integers) will be employed instead of pitch names, as it will later prove to be a convenient way to calculate the distance between each voice in a chord or pitch collection (See Table 9.1).2 The Tonnetz is then re- drawn using integer notation where the lines in the Tonnetz connect the integers by a minor third (/), major third (\) and a perfect fifth (-) (See Figure 9.2).
1 Edward Gollin, “From Matrix to Map,” 271-293. 2 Flor Aceff-Sánchez et al., “Musical Background,” in An Introduction to Group Theory, (Ventus Publishing, 2013), under “Chapter 4,” http://bookboon.com/en/an-introduction-to-group-theory-ebook. 193
Figure 9.1 Representation of Major and Minor Triads on the Tonnetz.
Pitch Class Tonal Counterparts 0 C Bs Dff 1 Cs Df BS 2 D Cx Eff 3 Ds Ef Fff 4 E DS Ff 5 F Es Gff 6 Fs Gf ES 7 G FS Aff 8 Gs Af 9 A GS Bff X As Bf Cff Y B AS Cf Table 9.1 Pitch Class and Tonal Names.
Figure 9.2 Tonnetz using Integers.
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However, if the connecting lines are taken away and the integers placed as a grid, it yields a far more useful result as non-major or minor chords can comfortably be sketched on the Tonnetz through more “abstract” shapes as opposed to the triangle used in the traditional Tonnetz. It then becomes more apparent how these tertian harmonies can be transformed from one to the next and the transformation to and from the “triads” via the combination of common tones and minimal voice-leading movement is revealed. Thus, there is no need to reduce the pitches into major or minor triads and any non-major or minor triads are allowed to become autonomous (see Figure 9.3). Each note within the chord will play an equal role in describing the transformation from one to the next.
Figure 9.3 An Alternate Tonnetz.
Upon sketching the pitch collections on the Tonnetz, it can be observed that these sets of pitches occur in close proximity to each other on the Tonnetz and a relationship might be established more meaningfully based on their spatial distance. As illustrated in Figure 9.4, sketching the minim pitch collections for the first five bars suggest that the progression in the harmonies can be described through its movement, where it moves diagonally across the Tonnetz. Figure 9.5 depicts the crotchet pitch collections for bars 1 and 2 and it can clearly be seen that despite the appearance of more obscure shapes (as the pitch collections are not simply major or minor chords), these seemingly unrelated pitches are much closer in proximity than might initially seem the case. Evidently, although the Tonnetz does not involve other significant musical elements such as melody and phrase structure, this modified
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NRT representation of the chords aids in accounting for all types of chords, clearly illustrating the close proximity between “unrelated” chords. This demonstrates the unexplored potential of the Tonnetz which might be investigated in future studies; perhaps this tool can be used as a substitute for traditional musical charts, where the Tonnetz could replace the archetypal Roman numeral analysis.
Figure 9.4. Illustration of Pitch Collections form a Minim Subdivision in Bars 1 to 5.
Figure 9.5. Illustration of Pitch Collections form a Crotchet Subdivision in Bars 1 and 2.
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Although this study has produced successful results, it is acknowledged that the method can be improved for future use. Perhaps this could be done with the use of notational software and programs that help in collecting the data and creating charts and graphs. Future studies can also perhaps include a comparative analysis of several Neo-Classical works and possibly other early twentieth-century works as well. As this particular method combines both harmonic and melodic analysis in conjunction with recordings of the work, performers might find this approach useful in uncovering the functional processes and motivic ideas and in exploring the relationships these have with articulation, dynamics, and expression. In the future, it is hoped that this analytical approach might become a tool that will be useful not only for analysts, but for performers as well.
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Bibliography
Works Cited Introduction Background and Paul Hindemith Fierro, Charles. “Hindemith: The Three Sonatas.” Charles Fierro, last modified 14 June, 2012, http://charlesfierro.blogspot.com.au/2012/06/hindemith-three-piano-sonatas- by.html. Hindemith, Paul. A Composer’s World. Cambridge: Harvard University Press, 1952. ———. The Craft of Musical Composition. London: Schott, 1941. Kemp, Ian. Hindemith. London: Oxford University Press, 2002. Machlis, Joseph. Introduction to Contemporary Music. New York: W.W. Norton, 1979. Messing, Scott. Neoclassicism in Music: From the Genesis of the Concept Through the Schoenberg/Stravinsky Polemic. Rochester: University of Rochester Press, 1988. Neumeyer, David. The Music of Paul Hindemith. New Haven: Yale University Press, 1986. Richter, Eckhart. “Paul Hindemith as Director of the Yale Collegium Musicum.” College Music Symposium 18.1 (1978): 20-44. Skelton, Geoffrey. Paul Hindemith: The Man Behind the Music: A Biography. London: Gollancz, 1975. Teachout, Terry. “The Last German Master.” Commentary 113.1 (2002): 47-51. Taruskin, Richard. “Review: Back to Whom? Neoclassicism as Ideology.” 19th-Century Music 16.3 (1993): 286-302.
Existing Studies Bedell, Melody Joy, “The Craft of Musical Composition Applied to Hindemith’s Clarinet Concerto.” MMus., University of Tennessee, 1985. Bruhn, Siglind. “Symmetry and Dissymmetry in Paul Hindemith’s Ludus Tonalis.” Symmetry: Culture and Science 7.2 (1996): 116-32. Flory, Pamela Jean, “Six Chansons of Paul Hindemith: An Analysis in Relation to Performance.” Hons., Butler University, 1970. Harner, Nevin L, “Hindemith: Third Piano Sonata. An Analysis.” M.A., University of Rochester, 1962. Kim, Sun Hee, “An Analytical Study: Applying Hindemith’s Tonal Theory to Niels Viggo Bentzon’s Third Piano Sonata, Op. 44.” D.M.A., University of North Texas, 2009.
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Mak, Yung Cheung, “Formal Functions of Metrical Dissonance in the Music of Paul Hindemith.” M.A., University of British Columbia, 1999. Ortmann, Otto. “An Analysis of Paul Hindemith’s ‘Unterweisung im Tonsatz’.” Bulletin of the American Musicological Society 4 (1940): 26-8. Trombetta, Domenico L., “Early Music Influences in Paul Hindemith’s Compositions for the Viola.” D.M.A., James Madison University, 2014. Uppercue, Kevin, “Modified Contrapuntal Conventions: Stability and Instability in the Neotonal Music of Hindemith.” MMus., University of North Carolina, 2013. Wildman, Simon R. “A Comparative Analysis of Paul Hindemith’s Sonata for Bassoon (1938) and Sonata for Tuba (1955).” D.M.A., University of Georgia, 2014.
Schenker and NRT Schenkerian Method Asada, Chizuko, “Schenkerian Analysis of Sonata no. 9, Op. 68 by Alexander Scriabin.” MMus., California State University, 1997. Cook, Nicholas. “Analysing Performance and Performing Analysis.” In Rethinking Music, edited by Nicholas Cook and Mark Everist, 239-61. Oxford: Oxford University Press, 1997. Everett, Walter. “Grief in ‘Winterreise’: A Schenkerian Perspective.” Music Analysis 9.2 (1990): 157-75. Plum, Karl-Otto and Drabkin, William. “Towards a Methodology for Schenkerian Analysis.” Music Analysis 7.2 (1988): 143-64. Swinkin, Jeffrey. “Schenkerian Analysis, Metaphor, and Performance.” College Music Symposium 47 (2007): 76-99. Schmalfeldt, Janet. “On the Relation of Analysis to Performance: Beethoven’s Bagatelles Op. 126, Nos. 2 and 5.” Journal of Music Theory 29.1 (1985): 1-31. White, John D. Comprehensive Musical Analysis. New Jersey: Scarecrow Press, 1994.
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Neo-Riemannian Theory Broman, Per F. “Reger and Riemann: Some Analytical and Pedagogical Prospects.” Svensk Tidskrift för Musikforskning [The Journal of the Swedish Musicological Society] 84 (2002): 13–25. Cohn, Richard. “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late- Romantic Triadic Progressions.” Music Analysis 15.1 (1996): 9-40. Douthett Jack and Peter Steinbach. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal of Music Theory 42.2 (1998): 241-63. Gollin Edward. “From Matrix to Map: Tonbestimmung, the Tonnetz, and Riemann’s Combinatorial Conception of Interval.” In The Oxford Handbook of Neo-Riemannian Music Theories, edited by Edward Gollin and Alexander Rehding, 271-93. New York: Oxford University Press, 2011. Lewin, David. Generalized Musical Intervals and Transformations. New York: Oxford University Press, 2007. Mason, Laura Felicity, “Essential Neo-Riemannian Theory for Today’s Musician.” MMus., University of Tennessee, 2013. Ramirez, Miguel. “Chromatic‐Third Relations in the Music of Bruckner: A Neo‐Riemannian Perspective.” Music Analysis 32.2 (2013): 155-209. Tymoczko, Dmitri. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. New York: Oxford University Press, 2011.
Integration of NRT and Schenker Baker, Steven Scott, “Neo-Riemannian Transformations and Prolongational Structures in Wagner's “Parsifal”.” Ph.D., Florida State University, 2003. Gollin, Edward, and Alexander Rehding. The Oxford Handbook of Neo-Riemannian Music Theories. New York: Oxford UP, 2011. Lewin, David. “Transformational Techniques in Atonal and Other Music Theories.” Perspectives of New Music 21.1/2 (1982): 312-71. Pieslak, Jonathan Robert, “Conflicting Analytical Approaches to Late Nineteenth- and Early Twentieth-Century Tonal Music: A Meta-Theoretical Study.” Ph.D., University of Michigan, 2003. Plotkin, Richard James, “Transforming Transformational Analysis: Applications of Filtered Point-Symmetry.” Ph.D., University of Chicago, 2010.
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Rifkin, Deborah. “A Theory of Motives for Prokofiev’s Music.” Music Theory Spectrum 26.2 (2004): 265-90. Rings, Steven. “Perspectives on Tonality and Transformations in Schubert’s Impromptu in E- flat, D. 899, No. 2.” Journal of Schenkerian Studies 2 (2007): 33. Rusch, René. “Schenkerian Theory, Neo-Riemannian Theory and Late Schubert.” Journal of the Society for Musicology in Ireland 8 (2012-13): 3-20. Sayrs, Elizabeth Paige, “Approaches to Wolf: Schenker, Transformation, Function.” Ph.D., Ohio State University, 1997.
Synthesis of Schenker and NRT Aceff-Sánchez, Flor et al. “Musical Background.” In An Introduction to Group Theory. London: Bookboon, 2013. http://bookboon.com/en/an-introduction-to-group-theory- ebook. Callender, Clifton. “Voice-leading Parsimony in the Music of Alexander Scriabin.” Journal of Music Theory 42.2 (1998): 219-33. Douthett, Jack and Peter Steinbach. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal of Music Theory 42.2 (1998): 241-63. Hook, Julian. “Uniform Triadic Transformations.” Journal of Music Theory 46.1/2 (2002): 57-126. Kim, Yeajin, “Smooth Voice-Leading Systems for Atonal Music.” Ph.D., Ohio State University, 2013. Lerdahl, Fred and Carol L. Krumhansl. “Modeling Tonal Tension.” Music Perception 24.4 (2007): 329-66. Roeder John Barlow, “Voice Leading as Transformation.” In Musical Transformation and Musical Intuition: Essays in Honor of David Lewin, edited by Raphael Atlas and Michael Cherlin, 41-58. Dedham: Ovenbird Press, 1994. Straus, Joseph N. “Total Voice Leading.” Music Theory Online 20.2 (2014): 1-9. ———. “Uniformity, Balance, and Smoothness in Atonal Voice Leading.” Music Theory Spectrum 25.2 (2003): 305-52. Tymoczko, Dmitri. “Set-Class Similarity, Voice Leading, and the Fourier Transform.” Journal of Music Theory 52.2 (2008): 251-72.
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Analysis and Performance Barolsky, Daniel and Edward Klorman. “Performance and Analysis Today: New Horizons.” Music Theory Online 22.2 (2016): 1-4. Berry, Wallace. Musical Structure and Performance. New Haven: Yale University Press, 1989. Brendel, Alfred. Alfred Brendel on Music. London: JR Books, 2001. Cone, Edward T. Musical Form and Musical Performance. New York: W.W. Norton, 1968. Dunsby, Jonathan. “Guest Editorial: Performance and Analysis of Music.” Music Analysis 8/1-2 (1989): 5-20. Fisk, Charles. “Analysis, and Musical Imagining. I. Schumann’s Arabesque.” College Music Symposium 36 (1996): 59-72. Howell, Tim. “Analysis and Performance: The Search for a Middleground.” In Companion to Contemporary Musical Thought, edited by John Paynter, Tim Howell, Richard Orton and Peter Seymour, 692-714. New York: Pendragon, 1992. Kroll, Mark. “Reviews: “The Keyboard Sonatas of Domenico Scarlatti and Eighteenth- Century Musical Style.” Notes 61.1 (2004): 145-7. Le Guinn, Elisabeth. Boccherini’s Body: An Essay in Carnal Musicology. Berkeley: University of California Press, 2006. Lester, Joel. “Performance and Analysis: Interaction and Interpretation.” In The Practice of Performance: Studies in Musical Intepretation, edited by John Rink, 197-216. Cambridge: Cambridge University Press, 1995. Lewin, David. “Music Theory, Phenomenology, and Modes of Perception.” Music Perception: An Interdisciplinary Journal 3.4 (1986): 327-92. Narmour, Eugene. “On the Relationship of Analytical Theory to Performance and Interpretation.” In Explorations in Music, the Arts, and Ideas: Essays in Honor of Leonard B. Meyer, edited by Leonard B. Meyer, Ruth A. Solie and Eugene Narmour, 317-41. Stuyvesant: Pendragon Press, 1988. ———. The Analysis and Cognition of Melodic Complexity: The Implication-Realization Model. Chicago: University of Chicago Press, 1992. Rink, John. “Analysis and (or?) Performance.” In Musical Performance: A Guide to Understanding, edited by John Rink, 35-58. New York: Cambridge University Press, 2002. Rink, John. “Review of Berry.” Music Analysis 9/3 (1990): 319-39.
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Rothstein, William. “Analysis and the Act of Performance.” In The Practice of Performance: Studies in Musical Intepretation, edited by John Rink, 217-40. Cambridge: Cambridge University Press, 1995. ———. Phrase Rhythm in Tonal Music. New York: Schirmer Books, 1989. Samson, Jim. “Analysis in Context.” In Rethinking Music, edited by Nicholas Cook and Mark Everist, 35-54. Oxford: Oxford University Press, 1997. Schachter, Carl. “Rhythm and Linear Analysis: Durational Reduction.” In The Music Forum Vol. 5, edited by Felix Salzer, 197-232. New York: Columbia University Press, 1980. Sutcliffe, Dean W. The Keyboard Sonatas of Domenico Scarlatti and Eighteenth-Century Musical Style. Cambridge: Cambridge University Press, 2003. Tovey, Donald Francis. A Companion to Beethoven’s Pianoforte Sonatas. London: Associated Board of the Royal Schools of Music, 1931. Winn James A. “Review: “Boccherini’s Body: An Essay in Carnal Musicology.” Studies in Romanticism 45.4 (2006): 643-9. Yih, Annie. “Connecting Analysis and Performance: A Case Study for Developing An Effective Approach.” Gamut 6.1 (2013): 277-308.
Sound Recordings and Musical Score Paul Hindemith. Piano Sonatas Nos. 1-3 (Gould). Sony Classical 074645267029, 1992. Compact disc. Paul Hindemith. Richter: Live in Kiev Volume 5 & 6. TNC Recordings H1465-66, 2002. Compact disc. P. Hindemith, Sonaten für Klavier. Mainz: Schott, 1964.
Preliminary Schenkerian Analysis MacDonald, Malcolm. “Piano Sonata No. 1.” Hyperion. Last modified 2013. http://www.hyperion-records.co.uk/dw.asp?dc=W14764_67977
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Other Works Consulted Schenkerian Method Baker, James M. “Voice Leading in Post-Tonal Music: Suggestions for Extending Schenker's Theory.” Music Analysis 9.2 (1990): 177-200. Beach, David. “A Schenkerian Analysis.” In Readings in Schenker Analysis and Other Approaches, edited by Maury Yeston, 204-216. New Haven: Yale University Press, 1977. Bent, Ian. “Heinrich Schenker, Chopin and Domenico Scarlatti.” Music Analysis 5.2/3 (1986): 131-49. Blasius, Leslie D. Schenker’s Argument and the Claims of Music Theory. Cambridge: Cambridge University Press, 1996. Brown, Matthew. Exploring Tonality. Rochester: University of Rochester Press, 2005. Cohn, Richard. “Schenker’s Theory, Schenkerian Theory: Pure Unity of Constructive Conflict?” Indiana Theory Review 13 (1992): 1-19. Dodson, Alan. “Performance, Grouping and Schenkerian Alternative Readings in Some Passages from Beehoven’s ‘Lebwohl’ Sonata.” Music Analysis 27 (2008): 107-134. Dunsby, Jonathan. “Schenkerian Theory in Great Britain: Developments and Responses.” In Schenker Studies, edited by Heidi Siegel, 182-192. Cambridge: Cambridge University Press, 1990. Forte, Allen. “Schenker’s Conception of Musical Structure.” In Readings in Schenker Analysis and Other Approaches, edited by Maury Yeston, 3-38. New Haven: Yale University Press, 1977. Forte, Allen and Steven E. Gilbert. Introduction to Schenkerian Analysis. New York: W.W. Norton, 1982. Franck, Peter. “Reaching –Over and its Interaction with Invertible Counterpoint at the Tenth.” Theory and Practice 36 (2011): 1-33. Givan, Benjamin. “Swing Improvisation: A Schenkerian Perspective.” Theory and Practice 35 (2010): 25-56. Goldenberg, Yosef. “Schenkerian Voice-Leading and Neo-Riemannian Operations: Analytical Integration without Theoretical Reconciliation.” Journal of Schenkerian Studies (2007): 65-87. Goldenberg, Yosef. “The Interruption-Fill and Corollary Procedures.” Society for Music Theory 18.4 (2012). http://mtosmt.org/issues/mto.12.18.4/mto.12.18.4.goldenberg.html.
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Hatten, Robert S. “Performance Expressive Closure in Structurally Open Contexts: Chopin’s Prelude in A minor and the Last Two Dances of Schumann’s Davidsbündlertänze.” Society for Music Theory 20.4 (2014). http://www.mtosmt.org/issues/mto.14.20.4/mto.14.20.4.hatten.html. Heyer, David J. “Applying Schenkerian Theory to Mainstream Jazz: A Justification for an Orthodox Approach.” Society for Music Theory 18.3 (2012). http://www.mtosmt.org/issues/mto.12.18.3/mto.12.18.3.heyer.html. Marsel, Arthur. “Voice leading as Drama in Wozzeck.” In Schenker Studies 2, edited by Carl Schachter and Heidi Siegel, 160-91. Cambridge: Cambridge University Press, 1990. McCreless, Patrick. “Schenker and Chromatic Tonicisation: A Reappraisal.” In Schenker Studies, edited by Heidi Siegel, 125-145. Cambridge: Cambridge University Press, 1990. McFarland, Mark. “Schenker and the Tonal Jazz Repertory: A Response to Martin.” Society for Music Theory 18.3 (2012). http://www.mtosmt.org/issues/mto.12.18.3/mto.12.18.3.mcfarland.html. Neumeyer, David. A Guide to Schenkerian Analysis. New Jersey: Prentice-Hall, 1992. ———. “The Ascending ‘Urlinie’.” Journal of Music Theory 31.2 (1987): 275-303. Novack, Saul. “Foreground, Middleground and Background: Their Significance in the History of Tonality.” In Schenker Studies, edited by Heidi Siegel, 60-71. Cambridge: Cambridge University Press, 1990. Palmer, Robert. “An Original Analytic Technique.” In Readings in Schenker Analysis and Other Approaches, edited by Maury Yeston, 217-26. New Haven: Yale University Press, 1977. Preda-Ulita, Anca. “Adaptations of the Schenkerian Analysis to Post-Tonal Music.” Transylvania University of Brasor Series VIII: Performing Arts 6.55 (2013): 85-91. Rothgeb, John. “Schenkerian Theory and Manuscript Studies: Modes of Interaction.” In Schenker Studies, edited by Heidi Siegel, 4-14. Cambridge: Cambridge University Press, 1990. Rothstein, William. “The Americanization of Heinrich Schenker.” In Schenker Studies, edited by Heidi Siegel, 193-203. Cambridge: Cambridge University Press, 1990. Samarotto, Frank. “Strange Dimensions: Regularity and Irregularity in Deep Levels of Rhythmic Reduction.” In Schenker Studies 2, edited by Carl Schachter and Heidi Siegel, 222-39. Cambridge: Cambridge University Press, 1990.
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Appendix
Appendix A1. Hindemith, Piano Sonata No. 1, bars 1 to 24.
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Appendix A1.1. Hindemith, Piano Sonata No. 1, bars 25 to 51.
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Minerva Access is the Institutional Repository of The University of Melbourne
Author/s: Teo, Yvonne
Title: A synthesis of Schenkerian and Neo-Riemannian theories: the first movement of Paul Hindemith’s Piano Sonata No. 1 as a case study
Date: 2017
Persistent Link: http://hdl.handle.net/11343/191811
File Description: A synthesis of Schenkerian and Neo-Riemannian theories: the first movement of Paul Hindemith’s Piano Sonata No. 1 as a case study
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