Contents

Chapters in this book

1. Frontmatter I
2. Contents VII
3. Preface to the Second Edition XI
4. Part I: Exposition
5. 1. Introduction 1
6. 2. Inversionally Complementary Cycles 7
7. 3. Symmetrical Chords and Progressions 12
8. 4. Dyadic Sums and Differences 18
9. 5. The Cyclic Set of Interval 7 20
10. 6. Cognate Sets 22
11. 7. Verticalization in Twelve-Tone Music 25
12. 8. Cyclic Chords and Axis-Note Dyads 27
13. 9. Difference Tables 31
14. 10. Composing with Twelve-Tone Modes 33
15. 11. The Odd and Even Modes 45
16. 12. Sum Tables 47
17. 13. Tonic and Resultant Set Forms 49
18. 14. Sum Tetrachords 53
19. 15. The Cyclic Set of Interval 1 57
20. 16. Larger Implications of Tonic Set Forms 61
21. 17. The Interval-1 and Interval-7 Sets Combined 67
22. 18. Derived Sets 71
23. 19. The Remaining Cyclic Sets 75
24. 20. Alban Berg's Master Array of the Interval Cycles 80
25. 21. Sum and Difference Scales 84
26. 22. The Master Modes 86
27. 23. The Master Keys 99
28. 24. Composing with Sum Tetrachords 111
29. 25. Modulation Through Tonic Chords 120
30. 26. Imitative Counterpoint 128
31. 27. Large-Scale Progression 132
32. 28. The Three Tonalities 138
33. 29. Triadic Arrays 146
34. 30. Conclusion 157
35. Part II: Developments and Recapitulations
36. 31. Symmetrical Progressions Through Non-Symmetrical Chords: A Postscript to Chapter 3 171
37. 32. Voice-Leading Implications of Sum Tetrachords 177
38. 33. Transpositional and Symmetrical Equivalence: Aggregate Sums and the Three Tonalities 183
39. 34. The Synoptic Array: A Postscript to Chapters 22 and 23 192
40. 35. Modulation Through Substitution: A Postscript to Chapter 25 198
41. 36. Modulation Through Reinterpretation 206
42. 37. Imitative Counterpoint II: A Postscript to Chapter 26 224
43. 38. Consonant and Dissonant Figuration 229
44. 39. Background and Foreground Sums and Cycles 235
45. 40. The Unanswered Questions 241
46. 41. Tonality 248
47. Appendix: Dyadic Cyclic Sets 253
48. Index to Names and Compositions 255
49. Index to Basic Definitions 256