All chords on 12 notes

Example

This:

  1. M7#5 = (4,4,3,1) = augmented major tetrachord = 4-19B

means that:

All the possible chords (up to chord inversions) are here! The ordering is arbitrary and the interval-stacking definition is "cyclic", for example (4,4,3,1) is the same thing as (4,3,1,4), (3,1,4,4) and (1,4,4,3).

The names of chords (such as dim7, aug, maj7#5 are quite arbitrary and loosely based on "jazz harmony".

Descriptions like "augmented major tetrachord = 4-19B" come from a classification included in the music21 Python library.

You can wonder about things like "Did you know that there are exactly 18 pentads that contain 10 different triads, and that this is the maximum number of triads that a pentad can contain?" Chords of special interest have a special background.

I can generate the same list for chords on 13 different notes (13 divisions of the octave), or any other n. What about n=2i+1? This is a simple model that just counts intervallic configurations of n different notes up to octave, in which chord inversions and modes are the same thing.What's the smallest n such that there is an all-interval trichord? Is there such an n? (In reference to the 4 all-interval tetrachords when n=12.)

1-note chords (1)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. (12,) = unison = 1-1 [up]

2-note chords (6)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. tt = (6,6) = Augmented Fourth = 2-6 [up]

    • mirror: tt
  2. 54 = (7,5) = Perfect Fifth = 2-5 [up]

    • mirror: 54
  3. b63 = (8,4) = Augmented Fifth = 2-4 [up]

  4. 6b3 = (9,3) = Major Sixth = 2-3 [up]

  5. b72 = (10,2) = Augmented Sixth = 2-2 [up]

  6. 7b2 = (11,1) = Major Seventh = 2-1 [up]

3-note chords (19)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. aug = (4,4,4) = augmented triad = 3-12 [up]

    • mirror: aug
    • intervals (1): b63
  2. min = (5,3,4) = enharmonic equivalent to minor triad = 3-11A [up]

  3. maj = (5,4,3) = major triad = 3-11B [up]

  4. 44 = (5,5,2) = quartal trichord = 3-9 [up]

    • mirror: 44
    • intervals (2): b72, 54
  5. dim = (6,3,3) = diminished triad = 3-10 [up]

  6. 13b7 = (6,2,4) = incomplete dominant-seventh chord = 3-8A [up]

  7. 13b5 = (6,4,2) = incomplete half-diminished seventh chord = 3-8B [up]

  8. 4tt = (6,1,5) = tritone-fourth = 3-5A [up]

  9. tt4 = (6,5,1) = tritone-fourth = 3-5B [up]

  10. 1b34 = (7,3,2) = incomplete dominant-seventh chord = 3-7B [up]

  11. 1b3b7 = (7,2,3) = incomplete minor-seventh chord = 3-7A [up]

  12. 134 = (7,4,1) = incomplete major-seventh chord = 3-4B [up]

  13. 137 = (7,1,4) = incomplete major-seventh chord = 3-4A [up]

  14. 22 = (8,2,2) = whole-tone trichord = 3-6 [up]

  15. 1b33 = (8,3,1) = major-minor trichord = 3-3B [up]

  16. 1b37 = (8,1,3) = major-minor trichord = 3-3A [up]

  17. 2m2 = (9,2,1) = minor trichord = 3-2B [up]

  18. m22 = (9,1,2) = phrygian trichord = 3-2A [up]

  19. m2m2 = (10,1,1) = chromatic trimirror = 3-1 [up]

4-note chords (43)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. dim7 = (3,3,3,3) = diminished seventh chord = 4-28 [up]

    • mirror: dim7
    • 3-note chords (1): dim
    • intervals (2): tt, 6b3
  2. m7 = (4,3,2,3) = minor seventh chord = 4-26 [up]

  3. m7b5 = (4,2,3,3) = half-diminished seventh chord = 4-27A [up]

  4. 7 = (4,3,3,2) = German augmented sixth chord = 4-27B [up]

  5. 7b5 = (4,2,4,2) = French augmented sixth chord = 4-25 [up]

  6. 7#5 = (4,4,2,2) = augmented seventh chord = 4-24 [up]

  7. M7#5 = (4,4,3,1) = augmented major tetrachord = 4-19B [up]

  8. mM7 = (4,4,1,3) = minor-augmented tetrachord = 4-19A [up]

  9. M7 = (4,3,4,1) = major seventh chord = 4-20 [up]

  10. 7sus4 = (5,2,3,2) = quartal tetramirror = 4-23 [up]

  11. 69 = (5,3,2,2) = perfect-fourth minor tetrachord = 4-22B [up]

  12. add9 = (5,2,2,3) = major-second major tetrachord = 4-22A [up]

  13. mM7b5 = (5,1,3,3) = major-diminished tetrachord = 4-18A [up]

  14. min#4 = (5,3,3,1) = minor-diminished tetrachord = 4-18B [up]

  15. 135#9 = (5,3,1,3) = major-minor tetramirror = 4-17 [up]

  16. add#4 = (5,4,2,1) = all-interval tetrachord = 4-29B [up]

  17. add4 = (5,4,1,2) = perfect-fourth major tetrachord = 4-14B [up]

  18. 136b7 = (5,1,2,4) = all-interval tetrachord = 4-29A [up]

  19. M7b5 = (5,1,4,2) = minor-second quartal tetrachord = 4-16A [up]

  20. madd9 = (5,2,1,4) = major-second minor tetrachord = 4-14A [up]

  21. 134b7 = (5,2,4,1) = tritone quartal tetrachord = 4-16B [up]

  22. 44b2 = (5,5,1,1) = perfect fourth tetramirror = 4-6 [up]

  23. 4b24 = (5,1,5,1) = double tritone tetramirror = 4-9 [up]

  24. 9no5 = (6,2,2,2) = whole-tone tetramirror = 4-21 [up]

  25. 1b36b7 = (6,1,2,3) = minor-second diminished tetrachord = 4-13A [up]

  26. 7#9no5 = (6,2,3,1) = all-interval tetrachord = 4-15B [up]

  27. 1b367 = (6,2,1,3) = harmonic minor tetrachord = 4-12A [up]

  28. dimadd4 = (6,3,2,1) = perfect-fourth diminished tetrachord = 4-13B [up]

  29. 1b347 = (6,1,3,2) = all-interval tetrachord = 4-15A [up]

  30. dimadd3 = (6,3,1,2) = major-third diminished terachord = 4-12B [up]

  31. 7add7 = (6,1,1,4) = major third tetracluster = 4-5A [up]

  32. maj7add11 = (6,1,4,1) = double-fourth tetramirror = 4-8 [up]

  33. 134b5 = (6,4,1,1) = major third tetracluster = 4-5B [up]

  34. 156b7 = (7,2,1,2) = minor tetramirror = 4-10 [up]

  35. 15b6b7 = (7,1,2,2) = phrygian tetrachord = 4-11A [up]

  36. 1567 = (7,2,2,1) = lydian tetrachord = 4-11B [up]

  37. 15b67 = (7,1,3,1) = Arabian tetramirror = 4-7 [up]

  38. 1b224 = (7,1,1,3) = minor third tetracluster = 4-4A [up]

  39. 1b226 = (7,3,1,1) = minor third tetracluster = 4-4B [up]

  40. 2m2m2 = (8,2,1,1) = major-second tetracluster = 4-2B [up]

  41. m2m22 = (8,1,1,2) = major-second tetracluster = 4-2A [up]

  42. m22m2 = (8,1,2,1) = alternating tetramirror = 4-3 [up]

  43. m2m2m2 = (9,1,1,1) = chromatic tetramirror = 4-1 [up]

5-note chords (66)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. penta9 = (3,3,2,2,2) = dominant-ninth = 5-34 [up]

  2. penta = (3,2,3,2,2) = major pentatonic = 5-35 [up]

  3. (3,3,2,3,1) = Neapolitan pentachord = 5-32B [up]

  4. (3,3,3,2,1) = flat-ninth pentachord = 5-31B [up]

  5. (3,3,1,3,2) = Neapolitan pentachord = 5-32A [up]

  6. (3,3,3,1,2) = diminished minor-ninth chord = 5-31A [up]

  7. augpenta = (4,2,2,2,2) = whole-tone pentachord = 5-33 [up]

  8. (4,3,2,2,1) = minor-ninth chord = 5-27B [up]

  9. (4,1,3,2,2) = enigmatic pentachord = 5-30A [up]

  10. (4,1,2,2,3) = major-ninth chord = 5-27A [up]

  11. (4,2,3,1,2) = Javanese pentatonic = 5-28B [up]

  12. (4,1,2,3,2) = Kumoi pentachord = 5-29A [up]

  13. (4,2,1,3,2) = augmented-sixth pentachord = 5-28A [up]

  14. (4,2,3,2,1) = Kumoi pentachord = 5-29B [up]

  15. (4,3,2,1,2) = minor-diminished ninth chord = 5-25B [up]

  16. (4,2,2,3,1) = enigmatic pentachord = 5-30B [up]

  17. (4,2,1,2,3) = diminished-major ninth chord = 5-25A [up]

  18. (4,2,2,1,3) = diminished-augmented ninth chord = 5-26A [up]

  19. (4,3,1,2,2) = augmented-diminished ninth chord = 5-26B [up]

  20. (4,3,1,1,3) = center-cluster pentamirror = 5-37 [up]

  21. (4,1,3,3,1) = Persian pentamirror = 5-22 [up]

  22. (4,3,3,1,1) = diminished pentacluster = 5-38B [up]

  23. (4,1,1,3,3) = diminished pentacluster = 5-38A [up]

  24. (4,3,1,3,1) = Lebanese pentachord = 5-21B [up]

  25. (4,1,3,1,3) = major-augmented ninth chord = 5-21A [up]

  26. (4,4,1,1,2) = augmented pentacluster = 5-13A [up]

  27. (4,1,4,1,2) = Balinese Pelog pentatonic = 5-20A [up]

  28. (4,4,2,1,1) = augmented pentacluster = 5-13B [up]

  29. (4,4,1,2,1) = minor-major ninth chord = 5-17 [up]

  30. (4,2,4,1,1) = asssymetric pentamirror = 5-15 [up]

  31. monk5 = (4,2,1,4,1) = Hirajoshi pentatonic = 5-20B [up]

  32. (5,2,2,1,2) = major pentachord = 5-23B [up]

  33. (5,2,1,2,2) = dorian pentachord = 5-23A [up]

  34. (5,1,2,2,2) = phrygian pentachord = 5-24A [up]

  35. (5,2,2,2,1) = lydian pentachord = 5-24B [up]

  36. (5,1,2,1,3) = major-minor-diminished pentachord = 5-16A [up]

  37. (5,3,2,1,1) = minor-seventh pentacluster = 5-36B [up]

  38. (5,1,1,2,3) = major-seventh pentacluster = 5-36A [up]

  39. (5,2,1,1,3) = center-cluster pentachord = 5-11A [up]

  40. (5,2,1,3,1) = Roma (Gypsy) pentachord = 5-18B [up]

  41. (5,1,1,3,2) = double-seconds triple-fourth pentachord = 5-14A [up]

  42. (5,3,1,1,2) = center-cluster pentachord = 5-11B [up]

  43. (5,1,2,3,1) = Javanese pentachord = 5-19A [up]

  44. (5,2,3,1,1) = double-seconds triple-fourth pentachord = 5-14B [up]

  45. (5,3,1,2,1) = major-minor diminished pentachord = 5-16B [up]

  46. (5,1,3,2,1) = Balinese pentachord = 5-19B [up]

  47. (5,1,3,1,2) = Roma (Gypsy) pentachord = 5-18A [up]

  48. (5,4,1,1,1) = major-third pentacluster = 5-5B [up]

  49. (5,1,4,1,1) = double pentacluster = 5-7B [up]

  50. (5,1,1,4,1) = double pentacluster = 5-7A [up]

  51. (5,1,1,1,4) = major-third pentacluster = 5-5A [up]

  52. m222m2 = (6,1,2,2,1) = locrian pentachord = 5-12 [up]

  53. m22m22 = (6,1,2,1,2) = alternating pentachord = 5-10A [up]

  54. m2m222 = (6,1,1,2,2) = tritone-expanding pentachord = 5-9A [up]

  55. 2m22m2 = (6,2,1,2,1) = alternating pentachord = 5-10B [up]

  56. 2m2m22 = (6,2,1,1,2) = tritone-symmetric pentamirror = 5-8 [up]

  57. 22m2m2 = (6,2,2,1,1) = tritone-contracting pentachord = 5-9B [up]

  58. (6,3,1,1,1) = minor-third pentacluster = 5-4B [up]

  59. (6,1,1,1,3) = blues pentacluster = 5-4A [up]

  60. (6,1,1,3,1) = Asian pentacluster = 5-6A [up]

  61. (6,1,3,1,1) = Asian pentacluster = 5-6B [up]

  62. m2m22m2 = (7,1,1,2,1) = minor-second major pentachord = 5-3A [up]

  63. 2m2m2m2 = (7,2,1,1,1) = major-second pentacluster = 5-2B [up]

  64. m22m2m2 = (7,1,2,1,1) = Spanish pentacluster = 5-3B [up]

  65. m2m2m22 = (7,1,1,1,2) = major-second pentacluster = 5-2A [up]

  66. m2m2m2m2 = (8,1,1,1,1) = chromatic pentamirror = 5-1 [up]

6-note chords (80)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. augscale = (2,2,2,2,2,2) = whole tone scale = 6-35 [up]

  2. (3,2,2,2,2,1) = augmented-eleventh = 6-34B [up]

  3. (3,2,1,2,2,2) = dorian hexachord = 6-33A [up]

  4. (3,2,2,1,2,2) = C all combinatorial (P6, I3, RI9) = 6-32 [up]

  5. (3,2,2,2,1,2) = dominant-eleventh = 6-33B [up]

  6. (3,1,2,2,2,2) = Scriabin's Mystic-chord = 6-34A [up]

  7. (3,3,2,2,1,1) = forte class 6-46B = 6-46B [up]

  8. (3,2,3,1,2,1) = combinatorial RI (RI4) = 6-49 [up]

  9. (3,3,2,1,2,1) = combinatorial I (I1) = 6-27B [up]

  10. (3,2,3,1,1,2) = forte class 6-47A = 6-47A [up]

  11. (3,1,2,3,1,2) = Messiaen's truncated mode 2 = 6-30A [up]

  12. (3,2,3,2,1,1) = blues scale = 6-47B [up]

  13. (3,3,1,2,2,1) = double-phrygian heachord = 6-28 [up]

  14. MttM = (3,2,1,3,2,1) = Stravinsky's Petrouchka-chord = 6-30B [up]

  15. (3,2,2,1,3,1) = combinatorial I (I11) = 6-31B [up]

  16. (3,2,1,2,3,1) = combinatorial RI (RI1) = 6-50 [up]

  17. (3,2,1,3,1,2) = combinatorial RI (RI9) = 6-29 [up]

  18. (3,2,2,3,1,1) = combinatorial RI (RI2) = 6-48 [up]

  19. (3,3,2,1,1,2) = combinatorial RI (RI6) = 6-45 [up]

  20. (3,1,3,1,2,2) = combinatorial I (I7) = 6-31A [up]

  21. (3,3,1,1,2,2) = forte class 6-46A = 6-46A [up]

  22. (3,3,1,2,1,2) = combinatorial I (I11) = 6-27A [up]

  23. (3,3,1,3,1,1) = quasi raga Bauli = 6-44B [up]

  24. (3,1,3,1,3,1) = E all combinatorial (P2, P6, P10, I3, I7, R4, R8, RI1, RI5, RI9) = 6-20 [up]

  25. (3,3,1,1,3,1) = Schoenberg Anagram hexachord = 6-44A [up]

  26. (3,3,3,1,1,1) = combinatorial RI (RI3) = 6-42 [up]

  27. (4,1,2,2,2,1) = phrygian hexamirror = 6-26 [up]

  28. (4,2,1,2,2,1) = minor hexachord = 6-25B [up]

  29. (4,2,2,2,1,1) = combinatorial I (I5) = 6-22B [up]

  30. (4,2,1,2,1,2) = combinatorial RI (RI8) = 6-23 [up]

  31. (4,2,2,1,2,1) = melodic-minor hexachord = 6-24B [up]

  32. (4,1,2,2,1,2) = locrian hexachord = 6-25A [up]

  33. (4,2,1,1,2,2) = combinatorial I (I1) = 6-21A [up]

  34. (4,2,2,1,1,2) = combinatorial I (I3) = 6-21B [up]

  35. (4,1,1,2,2,2) = combinatorial I (I11) = 6-22A [up]

  36. (4,1,2,1,2,2) = forte class 6-24A = 6-24A [up]

  37. (4,2,1,1,3,1) = combinatorial I (I1) = 6-16B [up]

  38. (4,1,1,1,3,2) = forte class 6-41A = 6-41A [up]

  39. (4,3,1,1,2,1) = combinatorial P (P6) = 6-14B [up]

  40. (4,1,1,1,2,3) = forte class 6-40A = 6-40A [up]

  41. (4,2,1,3,1,1) = complement of all-tri-chord hexachord (inverted form) = 6-43B [up]

  42. (4,1,3,2,1,1) = all tri-chord hexachord (inverted form) = 6-17B [up]

  43. (4,1,3,1,2,1) = forte class 6-19B = 6-19B [up]

  44. (4,1,3,1,1,2) = combinatorial I (I3) = 6-16A [up]

  45. (4,1,2,3,1,1) = combinatorial I (I5) = 6-18B [up]

  46. (4,3,1,1,1,2) = forte class 6-39B = 6-39B [up]

  47. (4,2,1,1,1,3) = forte class 6-39A = 6-39A [up]

  48. (4,3,1,2,1,1) = combinatorial I (I5) = 6-15B [up]

  49. (4,1,1,3,2,1) = combinatorial I (I11) = 6-18A [up]

  50. (4,1,1,3,1,2) = complement of all tri-chord hexachord = 6-43A [up]

  51. (4,2,3,1,1,1) = forte class 6-41B = 6-41B [up]

  52. (4,1,1,2,1,3) = combinatorial I (I11) = 6-15A [up]

  53. (4,3,2,1,1,1) = forte class 6-40B = 6-40B [up]

  54. (4,1,1,2,3,1) = all tri-chord hexachord = 6-17A [up]

  55. (4,1,2,1,3,1) = forte class 6-19A = 6-19A [up]

  56. (4,1,2,1,1,3) = combinatorial P (P6) = 6-14A [up]

  57. (4,4,1,1,1,1) = combinatorial RI (RI4) = 6-37 [up]

  58. (4,1,1,4,1,1) = B all combinatorial (P3, P9, I5, R6, R12, R8) = 6-7 [up]

  59. (4,1,4,1,1,1) = combinatorial RI (RI3) = 6-38 [up]

  60. (5,1,1,2,1,2) = forte class 6-11A = 6-11A [up]

  61. (5,1,1,2,2,1) = forte class 6-12A = 6-12A [up]

  62. (5,1,2,1,1,2) = forte class 6-10A = 6-10A [up]

  63. (5,2,2,1,1,1) = combinatorial I (I3) = 6-9B [up]

  64. (5,2,1,1,2,1) = forte class 6-10B = 6-10B [up]

  65. (5,2,1,1,1,2) = D all combinatorial (P6, I1, RI7) = 6-8 [up]

  66. (5,2,1,2,1,1) = forte class 6-11B = 6-11B [up]

  67. (5,1,2,2,1,1) = forte class 6-12B = 6-12B [up]

  68. (5,1,2,1,2,1) = alternating hexamirror = 6-13 [up]

  69. (5,1,1,1,2,2) = combinatorial I (I11) = 6-9A [up]

  70. (5,1,3,1,1,1) = combinatorial I (I3) = 6-5B [up]

  71. (5,1,1,3,1,1) = double cluster hexamirror = 6-6 [up]

  72. (5,1,1,1,3,1) = combinatorial I (I11) = 6-5A [up]

  73. (5,3,1,1,1,1) = forte class 6-36B = 6-36B [up]

  74. (5,1,1,1,1,3) = forte class 6-36A = 6-36A [up]

  75. (6,1,1,1,2,1) = forte class 6-3A = 6-3A [up]

  76. (6,1,1,1,1,2) = combinatorial I (I11) = 6-2A [up]

  77. (6,2,1,1,1,1) = combinatorial I (I1) = 6-2B [up]

  78. (6,1,2,1,1,1) = forte class 6-3B = 6-3B [up]

  79. (6,1,1,2,1,1) = combinatorial RI (RI6) = 6-4 [up]

  80. (7,1,1,1,1,1) = A all combinatorial (P6, I11, RI5, RI11) = 6-1 [up]

7-note chords (66)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. melminor = (2,2,2,2,1,2,1) = melodic minor ascending scale = 7-34 [up]

  2. (2,2,2,2,2,1,1) = Neapolitan-major mode = 7-33 [up]

  3. diatonic = (2,2,2,1,2,2,1) = major scale = 7-35 [up]

  4. (3,1,2,2,2,1,1) = forte class 7-30B = 7-30B [up]

  5. (3,1,2,1,1,2,2) = forte class 7-26A = 7-26A [up]

  6. (3,2,1,2,1,2,1) = diminished scale = 7-31B [up]

  7. harmminor = (3,1,2,1,2,2,1) = harmonic minor scale = 7-32A [up]

  8. (3,1,1,2,1,2,2) = forte class 7-27A = 7-27A [up]

  9. (3,2,1,1,2,2,1) = forte class 7-28B = 7-28B [up]

  10. (3,2,2,1,1,1,2) = tritone major heptachord = 7-23B [up]

  11. (3,2,1,1,2,1,2) = forte class 7-25A = 7-25A [up]

  12. (3,2,1,2,1,1,2) = forte class 7-25B = 7-25B [up]

  13. (3,2,2,1,1,2,1) = forte class 7-26B = 7-26B [up]

  14. harmmajor = (3,1,2,2,1,2,1) = harmonic major scale = 7-32B [up]

  15. (3,1,1,1,2,2,2) = forte class 7-24A = 7-24A [up]

  16. (3,2,1,2,2,1,1) = forte class 7-29B = 7-29B [up]

  17. (3,2,2,2,1,1,1) = mystic heptaachord = 7-24B [up]

  18. (3,2,2,1,2,1,1) = modified blues = 7-27B [up]

  19. (3,1,2,2,1,1,2) = forte class 7-28A = 7-28A [up]

  20. (3,1,1,2,2,2,1) = Neapolitan-minor mode = 7-30A [up]

  21. (3,1,2,1,2,1,2) = alternating heptachord = 7-31A [up]

  22. (3,1,1,2,2,1,2) = forte class 7-29A = 7-29A [up]

  23. (3,2,1,1,1,2,2) = forte class 7-23A = 7-23A [up]

  24. (3,1,3,1,1,2,1) = forte class 7-21A = 7-21A [up]

  25. (3,3,1,1,1,2,1) = Debussy's heptatonic = 7-16A [up]

  26. (3,1,2,1,3,1,1) = double harmonic scale = 7-22 [up]

  27. (3,1,3,1,2,1,1) = Gypsy (Roma) hexatonic = 7-21B [up]

  28. (3,2,1,1,1,3,1) = forte class 7-18B = 7-18B [up]

  29. (3,1,1,3,1,1,2) = chromatic phrygian inverse = 7-20A [up]

  30. (3,3,2,1,1,1,1) = forte class 7-10B = 7-10B [up]

  31. (3,1,3,1,1,1,2) = forte class 7-18A = 7-18A [up]

  32. (3,3,1,2,1,1,1) = forte class 7-16B = 7-16B [up]

  33. (3,3,1,1,1,1,2) = forte class 7-10A = 7-10A [up]

  34. (3,2,1,3,1,1,1) = forte class 7-19B = 7-19B [up]

  35. (3,3,1,1,2,1,1) = forte class 7-17 = 7-17 [up]

  36. (3,2,1,1,3,1,1) = Greek chromatic = 7-20B [up]

  37. (3,1,2,3,1,1,1) = forte class 7-19A = 7-19A [up]

  38. (3,2,3,1,1,1,1) = forte class 7-12 = 7-12 [up]

  39. (4,1,1,1,2,2,1) = forte class 7-14A = 7-14A [up]

  40. (4,1,2,1,2,1,1) = forte class 7-38B = 7-38B [up]

  41. (4,2,2,1,1,1,1) = forte class 7-9B = 7-9B [up]

  42. (4,1,2,1,1,1,2) = forte class 7-11A = 7-11A [up]

  43. (4,2,1,1,2,1,1) = forte class 7-13B = 7-13B [up]

  44. (4,1,1,2,2,1,1) = forte class 7-15 = 7-15 [up]

  45. (4,1,2,1,1,2,1) = forte class 7-37 = 7-37 [up]

  46. (4,2,1,2,1,1,1) = forte class 7-36B = 7-36B [up]

  47. (4,1,1,2,1,1,2) = forte class 7-13A = 7-13A [up]

  48. (4,1,1,1,1,2,2) = forte class 7-9A = 7-9A [up]

  49. (4,1,2,2,1,1,1) = forte class 7-14B = 7-14B [up]

  50. (4,1,1,1,2,1,2) = forte class 7-36A = 7-36A [up]

  51. (4,1,1,2,1,2,1) = forte class 7-38A = 7-38A [up]

  52. (4,2,1,1,1,1,2) = forte class 7-8 = 7-8 [up]

  53. (4,2,1,1,1,2,1) = forte class 7-11B = 7-11B [up]

  54. (4,3,1,1,1,1,1) = forte class 7-3B = 7-3B [up]

  55. (4,1,1,3,1,1,1) = forte class 7-7B = 7-7B [up]

  56. (4,1,3,1,1,1,1) = forte class 7-6B = 7-6B [up]

  57. (4,1,1,1,1,1,3) = forte class 7-3A = 7-3A [up]

  58. (4,1,1,1,1,3,1) = forte class 7-6A = 7-6A [up]

  59. (4,1,1,1,3,1,1) = forte class 7-7A = 7-7A [up]

  60. (5,1,1,1,1,2,1) = forte class 7-4A = 7-4A [up]

  61. (5,2,1,1,1,1,1) = forte class 7-2B = 7-2B [up]

  62. (5,1,1,2,1,1,1) = forte class 7-5B = 7-5B [up]

  63. (5,1,1,1,2,1,1) = forte class 7-5A = 7-5A [up]

  64. (5,1,2,1,1,1,1) = forte class 7-4B = 7-4B [up]

  65. (5,1,1,1,1,1,2) = forte class 7-2A = 7-2A [up]

  66. (6,1,1,1,1,1,1) = chromatic heptamirror = 7-1 [up]

8-note chords (43)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. (2,2,2,1,1,1,2,1) = forte class 8-22A = 8-22A [up]

  2. (2,1,2,1,2,1,2,1) = octatonic scale = 8-28 [up]

  3. bebopdominant = (2,2,1,2,2,1,1,1) = Greek = 8-23 [up]

  4. (2,2,2,1,1,2,1,1) = forte class 8-24 = 8-24 [up]

  5. bebopmajor = (2,2,1,2,1,1,2,1) = blues = 8-26 [up]

  6. (2,2,1,2,1,2,1,1) = forte class 8-27B = 8-27B [up]

  7. (2,2,2,1,2,1,1,1) = Spanish octatonic scale = 8-22B [up]

  8. (2,2,2,2,1,1,1,1) = forte class 8-21 = 8-21 [up]

  9. (2,2,1,1,2,1,2,1) = forte class 8-27A = 8-27A [up]

  10. (2,2,1,1,2,2,1,1) = Messiaen's mode 6 = 8-25 [up]

  11. (3,1,1,1,1,2,2,1) = forte class 8-15A = 8-15A [up]

  12. (3,2,1,2,1,1,1,1) = forte class 8-13B = 8-13B [up]

  13. (3,1,1,1,2,1,2,1) = forte class 8-18A = 8-18A [up]

  14. (3,1,1,2,1,1,1,2) = forte class 8-14A = 8-14A [up]

  15. (3,1,1,2,1,1,2,1) = forte class 8-19A = 8-19A [up]

  16. (3,2,1,1,1,2,1,1) = forte class 8-14B = 8-14B [up]

  17. (3,2,2,1,1,1,1,1) = blues octatonic = 8-11B [up]

  18. (3,1,1,2,2,1,1,1) = enigmatic octachord = 8-16B [up]

  19. (3,1,2,1,2,1,1,1) = forte class 8-18B = 8-18B [up]

  20. (3,2,1,1,1,1,1,2) = forte class 8-10 = 8-10 [up]

  21. (3,2,1,1,2,1,1,1) = forte class 8-29B = 8-29B [up]

  22. (3,1,1,1,2,2,1,1) = forte class 8-16A = 8-16A [up]

  23. (3,1,1,1,1,1,2,2) = forte class 8-11A = 8-11A [up]

  24. (3,1,2,1,1,1,1,2) = forte class 8-12A = 8-12A [up]

  25. (3,1,2,1,1,1,2,1) = forte class 8-17 = 8-17 [up]

  26. (3,1,1,1,2,1,1,2) = forte class 8-29A = 8-29A [up]

  27. (3,1,2,2,1,1,1,1) = forte class 8-15B = 8-15B [up]

  28. (3,1,1,2,1,2,1,1) = forte class 8-20 = 8-20 [up]

  29. (3,2,1,1,1,1,2,1) = forte class 8-12B = 8-12B [up]

  30. (3,1,1,1,1,2,1,2) = blues octatonic = 8-13A [up]

  31. (3,1,2,1,1,2,1,1) = forte class 8-19B = 8-19B [up]

  32. (3,1,1,1,3,1,1,1) = Messiaen's mode 4 = 8-9 [up]

  33. (3,1,1,3,1,1,1,1) = forte class 8-8 = 8-8 [up]

  34. (3,1,3,1,1,1,1,1) = forte class 8-7 = 8-7 [up]

  35. (3,3,1,1,1,1,1,1) = forte class 8-3 = 8-3 [up]

  36. (4,1,2,1,1,1,1,1) = forte class 8-4B = 8-4B [up]

  37. (4,1,1,1,2,1,1,1) = forte class 8-6 = 8-6 [up]

  38. (4,1,1,2,1,1,1,1) = forte class 8-5B = 8-5B [up]

  39. (4,2,1,1,1,1,1,1) = forte class 8-2B = 8-2B [up]

  40. (4,1,1,1,1,1,1,2) = forte class 8-2A = 8-2A [up]

  41. (4,1,1,1,1,2,1,1) = forte class 8-5A = 8-5A [up]

  42. (4,1,1,1,1,1,2,1) = forte class 8-4A = 8-4A [up]

  43. (5,1,1,1,1,1,1,1) = chromatic octamirror = 8-1 [up]

9-note chords (19)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. (2,1,2,1,2,1,1,1,1) = forte class 9-10 = 9-10 [up]

  2. (2,1,1,2,1,1,2,1,1) = Messiaen's mode 3 = 9-12 [up]

  3. (2,2,1,2,1,1,1,1,1) = forte class 9-7B = 9-7B [up]

  4. (2,2,1,1,2,1,1,1,1) = forte class 9-8B = 9-8B [up]

  5. (2,2,2,1,1,1,1,1,1) = forte class 9-6 = 9-6 [up]

  6. (2,2,1,1,1,2,1,1,1) = forte class 9-9 = 9-9 [up]

  7. (2,1,2,1,1,1,2,1,1) = forte class 9-11A = 9-11A [up]

  8. (2,2,1,1,1,1,1,2,1) = nonatonic blues = 9-7A [up]

  9. (2,2,1,1,1,1,2,1,1) = forte class 9-8A = 9-8A [up]

  10. (2,1,2,1,1,2,1,1,1) = diminishing nonachord = 9-11B [up]

  11. (3,1,1,1,1,1,1,1,2) = forte class 9-2A = 9-2A [up]

  12. (3,1,1,1,2,1,1,1,1) = forte class 9-5B = 9-5B [up]

  13. (3,1,1,2,1,1,1,1,1) = forte class 9-4B = 9-4B [up]

  14. (3,1,1,1,1,2,1,1,1) = forte class 9-5A = 9-5A [up]

  15. (3,1,1,1,1,1,2,1,1) = forte class 9-4A = 9-4A [up]

  16. (3,1,2,1,1,1,1,1,1) = forte class 9-3B = 9-3B [up]

  17. (3,2,1,1,1,1,1,1,1) = forte class 9-2B = 9-2B [up]

  18. (3,1,1,1,1,1,1,2,1) = forte class 9-3A = 9-3A [up]

  19. (4,1,1,1,1,1,1,1,1) = chromatic nonamirror = 9-1 [up]

10-note chords (6)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. (2,1,1,1,1,2,1,1,1,1) = Messiaen's mode 7 = 10-6 [up]

  2. (2,1,1,1,2,1,1,1,1,1) = major-minor mixed = 10-5 [up]

  3. (2,2,1,1,1,1,1,1,1,1) = forte class 10-2 = 10-2 [up]

  4. (2,1,2,1,1,1,1,1,1,1) = forte class 10-3 = 10-3 [up]

  5. (2,1,1,2,1,1,1,1,1,1) = forte class 10-4 = 10-4 [up]

  6. (3,1,1,1,1,1,1,1,1,1) = chromatic decamirror = 10-1 [up]

11-note chords (1)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. (2,1,1,1,1,1,1,1,1,1,1) = chromatic undecamirror = 11-1 [up]

12-note chords (1)

Go to n-chords, for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

  1. (1,1,1,1,1,1,1,1,1,1,1,1) = aggregate = 12-1 [up]