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For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY SCHOOL OF MUSIC TOWARD A METHODOLOGY FOR THE ANALYSIS OF FUGUE: AN EXAMINATION OF SELECTED BACH ORGAN WORKS By SCOTT ROBERTS A Dissertation submitted to the School of Music in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Spring Semester, 2004 Copyright © 2004 Scott Roberts All Rights Reserved The members of the Committee approve the dissertation of Scott Roberts defended on March 29, 2004. _____________________________ James Mathes Professor Directing Dissertation _____________________________ Michael Corzine Outside Committee Member _____________________________ Evan Jones Committee Member _____________________________ Peter Spencer Committee Member Approved: _______________________________________________________________ Jon Piersol, Dean, School of Music The Office of Graduate Studies has verified and approved the above named committee members ii TABLE OF CONTENTS List of Tables ........................................................................................................................... iv List of Figures.......................................................................................................................... v Abstract.................................................................................................................................... vii 1. INTRODUCTION ............................................................................................................. 1 2. HISTORICAL WRITINGS ON FUGUE.......................................................................... 9 3. METHOD .......................................................................................................................... 30 4. EXPANSION AS A NOTABLE PROPERTY: A STUDY OF BACH’S FUGUE IN G MINOR, BWV 578 ............................................................................................................ 47 5. PALINDROME AS A NOTABLE PROPERTY: A STUDY OF BACH’S FUGUE IN E MINOR, BWV 533 ............................................................................................................ 64 6. UNEXPECTED CHANGE IN THE PREVAILING RHYTHMIC MOTION AS A NOTABLE PROPERTY: A STUDY OF BACH’S FUGUE IN C MAJOR, BWV 545... 78 7. COMBINING FORCES AS A NOTABLE PROPERTY: A STUDY OF BACH’S FUGUE IN C MAJOR, BWV 547 ................................................................................................... 93 CONCLUSION........................................................................................................................ 104 APPENDIX.............................................................................................................................. 106 BIBLIOGRAPHY.................................................................................................................... 110 BIOGRAPHICAL SKETCH ................................................................................................... 117 iii LIST OF TABLES 1. Statistics for fugues in the Well-Tempered Clavier........................................................... 3 2. Statistics for Bach’s organ fugues ..................................................................................... 4 3. Structure of Fugue in C minor from Book I of Well-tempered Clavier ............................ 38 4. Structure of Fugue in G minor, BWV 578 ........................................................................ 47 5. Traditional formal sections in BWV 578........................................................................... 55 6. Material used for integrants in BWV 578.......................................................................... 58 7. Quarter-note pitches in subject/answer entries and how they fit within the harmony....... 69 8. Palindrome and reflection of interval ratios in the structure of BWV 533........................ 76 9. Proportions in Fugue in C major, BWV 545..................................................................... 88 10. Exposition Blocks (integrants) and digressions in BWV 547 ........................................... 96 iv LIST OF FIGURES 1. Tree structure in Lerdahl and Jackendoff’s A Generative Theory of Tonal Music ........... 19 2. Lerdahl and Jackendoff’s analysis of the opening of Mozart’s Sonata in A major, K. 331 20 3. Forte and Gilbert’s analysis of the opening of Mozart’s Sonata in A major, K. 331........ 21 4. Subject of Toccata, BWV 915 (Example 1 of Harrison’s article)..................................... 27 5. Identification of Traditional Fugue Elements in Fugue in C minor, from Book I of the Well- tempered Clavier by J. S. Bach ......................................................................................... 33 6. Descending line 6 ^ -5 ^ -4 ^ -3 ^ .................................................................................................... 35 7. Ascent from 5 ^ to ^1 (measures 5-6)..................................................................................... 35 8. Rhythmic Cells in the Subject ........................................................................................... 36 9. Ascent from 5 ^ to ^1 (measures 17-18)................................................................................ 42 10. Set Containing Three Eighth Notes and an Eighth Rest.................................................... 42 11. Rhythmic Sets in the Episodes .......................................................................................... 43 12. Resolution of the notable properties ................................................................................. 45 13. BWV 578 – Annotated Score ............................................................................................ 48 14. Period V from BWV 578................................................................................................... 56 15. Use of various notable properties in the digressions ......................................................... 60 16. BWV 533 – Annotated Score ............................................................................................ 66 17. BWV 533 – Subject and Answer....................................................................................... 69 18. BWV 533 – Graph of Subject............................................................................................ 70 19. Ascent past 6 ^ disallowed................................................................................................... 71 20. Ascent from 3 ^ to 3 ^ ............................................................................................................. 72 v 21. 6 ^ as incomplete neighbor to 5 ^ ............................................................................................ 72 22. Second descent from 6 ^ to ^2 ............................................................................................... 73 23. Final attempt to ascend past 6 ^ ............................................................................................ 74 24. First digression .................................................................................................................. 76 25. BWV 545 – annotated score.............................................................................................. 79 26. Subject of Fugue in C major, BWV 545 ........................................................................... 83 27. Stepwise ascents in Fugue in G minor, BWV 578 ............................................................ 85 28. ‘Gap’ between 4 ^ and 5 ^ in BWV 545 ................................................................................. 86 29. Complete ascent from ^1 to ^1 in BWV 545 ....................................................................... 86 30. Progression to eighth-note rhythmic motion at the beginning of BWV 545..................... 87 31. Obscured entries in measures 28 and 35............................................................................ 90 32. Obscured entries in measures 52 and 79............................................................................ 91 33. Partially obscured entries in measures 84 and 89.............................................................. 92 34. Opening of Fugue in C major, BWV 547 ......................................................................... 94 35. Inversions of the subject and answer in transitions ........................................................... 98 36. Inversions as countersubjects in Exposition Blocks.......................................................... 99 37. Use of augmentation and inversion in subject entries ....................................................... 100 38. Overlapping of entries in Exposition Block 11 ................................................................. 101 ^ 39. Use of n4 in Exposition Block 11 ...................................................................................... 102 vi ABSTRACT A major difficulty in the study of fugue is the diversity found among fugues. Nineteenth- century formal structures do not apply adequately to fugue beyond a general three-part structure: exposition, departure from tonic, return to tonic. A recent article by Daniel