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COMPUTATIONAL ANALYSIS of QUARTER-TONE COMPOSITIONS by CHARLES IVES and IVAN WYSCHNEGRADSKY a Thesis Submitted to the College Of

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COMPUTATIONAL ANALYSIS of QUARTER-TONE COMPOSITIONS by CHARLES IVES and IVAN WYSCHNEGRADSKY a Thesis Submitted to the College Of COMPUTATIONAL ANALYSIS OF QUARTER-TONE COMPOSITIONS BY CHARLES IVES AND IVAN WYSCHNEGRADSKY A thesis submitted to the College of the Arts of Kent State University in partial fulfillment of the requirements for the degree of Master of Arts by Andrew M. Blake May 2020 Table of Contents Page List of Figures ................................................................................................................................. v List of Tables ................................................................................................................................. vi CHAPTER I .................................................................................................................................... 1 INTRODUCTION .......................................................................................................................... 1 The Quarter-Tone System ........................................................................................................... 1 Notation and Intervals ............................................................................................................. 2 Ives’ Some Quarter-Tone Impressions ........................................................................................ 4 Wyschnegradsky’s Manual of Quarter-Tone Harmony .......................................................... 6 Approaches to Analysis of Quarter-Tone Music ....................................................................... 10 The Place of Quarter-Tones in the Harmonic Series ................................................................. 11 Pitch-Class Set Theory in 24-EDO ........................................................................................ 14 Computational Analysis ........................................................................................................ 16 Further Review of Related Literature .................................................................................... 17 CHAPTER II ................................................................................................................................. 24 ANALYSES OF SELECTED EXCERPTS.................................................................................. 24 Ives’ Three Quarter-Tone Pieces ............................................................................................... 24 Three Quarter-Tone Pieces - I. Largo .................................................................................... 24 Three Quarter-Tone Pieces: III. Chorale ............................................................................... 30 Wyschnegradsky’s 24 Preludes ................................................................................................ 34 Prelude 1 in C ........................................................................................................................ 38 Prelude 4 in E ¼-sharp .......................................................................................................... 41 CHAPTER III ............................................................................................................................... 45 COMPUTATIONAL TOOLS FOR MICROTONAL ANALYSIS ............................................. 45 The Limitations of the Humdrum Toolkit ................................................................................. 45 Microtonal Hint ......................................................................................................................... 46 Microtonal Set-Theory Tools .................................................................................................... 49 CHAPTER IV ............................................................................................................................... 52 COMPUTATIONAL ANALYSES OF SELECTED EXCERPTS .............................................. 52 Compiling a Small Corpus ........................................................................................................ 52 Analyzing and Interpreting the Output of mhint ....................................................................... 53 Ives’ Three Quarter-Tone Pieces ............................................................................................... 54 Largo ...................................................................................................................................... 55 Chorale................................................................................................................................... 57 Wyschnegradsky’s 24 Preludes: Comparing Preludes I and IV. .............................................. 61 CHAPTER V ................................................................................................................................ 66 CONCLUSION AND FUTURE WORK ..................................................................................... 66 Conclusion ................................................................................................................................. 66 Future Avenues of Research ..................................................................................................... 67 References ..................................................................................................................................... 70 v List of Figures Figure 1. Spectrum of 24-EDO Accidentals. ................................................................................. 2 Figure 2. Ives' Primary, or "Fundamental Major" Chord. .............................................................. 5 Figure 3. Ives' Secondary, or "Fundamental Minor" Chord. ......................................................... 6 Figure 4. Quarter-tone Appoggiaturas (Wyschnegradsky 1932, 12). ............................................. 7 Figure 5. Wyschnegradsky's 13 Quarter-tone Altered Triads (Wyschnegradsky, 1932, 17). ....... 7 Figure 6. Quarter-Tone Modulations (Wyschnegradsky 1932, 20). .............................................. 8 Figure 7. Motivic Repetition in Wyschnegradsky's Prelude No. 1. ............................................. 10 Figure 8. Wyschnegradsky's "Diatonicized-Chromatic" Scale on C. .......................................... 11 Figure 9. Deviation of Interval Approximations in 12-EDO from the Harmonic Series. ........... 12 Figure 10. Deviation of Interval Approximations in 24-EDO from the Harmonic Series. ......... 13 Figure 11. Quarter-Tone Passing Motion and primary theme of Ives Largo (A). ....................... 26 Figure 12. Ives' Primary chord, punctuated by other quartal/quintal sonorities. ......................... 27 Figure 13. Underlying augmented triads in mm. 34-37 of Largo. ............................................... 28 Figure 14. "Tonic Prolongation" in mm. 1-4 of Ives' Chorale. .................................................... 31 Figure 15. Primary and secondary chords in transition section. .................................................. 32 Figure 16. "Parallel diatonic thirds" within an altered G Major scale. ........................................ 33 Figure 17. Triadic structures and a return to Ives' primary and secondary chords. ..................... 34 Figure 18. 3-step cycles in the C-DC scale. ................................................................................. 35 Figure 19. 3-step cycle "tonic tetrachord" of Wyschnegradsky's C-DC scale. ............................. 36 Figure 20. "Composing out" the tonic tetrachord in Prelude 1. ................................................... 40 Figure 21. The E 1/4-sharp DC scale on which Prelude 4 is based. ............................................ 41 Figure 22. Prelude 4, mm. 1-6 with E 1/4-sharp ostinato present. .............................................. 41 Figure 23. Prelude 4, mm. 1-6 with ostinato omitted. ................................................................. 42 Figure 24. Polyrhythm and syncopation in Prelude 4. ................................................................. 43 Figure 25. Imitation emphasizing thirds of various sizes in Prelude 4. ....................................... 44 Figure 26. Imitation in the coda of Prelude 4. ............................................................................. 44 Figure 27. Calculating a specific interval from generic interval and size in cents. ..................... 47 Figure 28. Wyschnegradsky's Prelude No. 4 (two piano score). ................................................. 48 Figure 29. Wyschnegradsky's Prelude No. 4 (condensed study score). ...................................... 48 Figure 30. Exponential growth in the number of hexachords in N-EDO systems (6-36). .......... 50 Figure 31. Exponential growth in the number of N/2-chords in N-EDO (6-36). ........................ 50 Figure 32. Frequencies of intervals in Ives' Largo. ...................................................................... 55 Figure 33. Differences in Interval Class content in sections of Largo. ........................................ 57 Figure 34. Intervallic content of Ives' Chorale. ........................................................................... 58 Figure 35. Frequencies of ICs 2.5, 3.5, and 5 in sections of Ives' Chorale. ................................. 60 Figure 36. Primary and secondary chords in the coda of Ives' Chorale. ...................................... 61 Figure 37. Intervallic content of Prelude 1. ................................................................................. 62 Figure 38. Pentachord
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