Fundamental intervals

Many important intervals in the 72 tone matrix, organized into 31 pitch classes (two are in italics because they lie outside the 41-tone Miracle scale).

This method could be used to determine ideal tuning of notes in a chord, if microtonal intervals are available (as in vocals, violin-type instruments and trombones).

0. perfect prime (unison), 1/1
2. semiaugmented prime, 64/63
4. augmented prime, 27/26
5. augmented prime, 21/20
7. minor second, 16/15
9. neutral second, 12/11
10. neutral second, 11/10
11. major second (less than whole tone), 10/9
12. major second (whole tone), 9/8
14. diminished third, 8/7
16. augmented second ("blues" third), 7/6
18. minor third (Pytagorean), 32/27
19. minor third, 6/5
21. neutral second, 11/9
23. major third, 5/4
25. diminished fourth, 14/11
26. diminished fourth, 9/7
28. semidiminished fourth, 21/16
30. perfect fourth, 4/3
32. semiaugmented fourth, 15/11
33. semiaugmented fourth, 11/8
35. augmented fourth (tritone I), 7/5
37. diminished fifth (tritone II), 10/7
39. semidiminished fifth, 16/11
40. semidiminished fifth, 22/15
42. perfect fifth, 3/2
44. semiaugmented fifth, 32/21
46. augmented fifth, 14/9
47. augmented fifth, 11/7
49. minor sixth, 8/5
51. neutral sixth, 18/11
53. major sixth, 5/3
54. major sixth (Pythagorean), 27/16
56. septimal major sixth, 12/7
58. septimal minor "blues" seventh, 7/4
60. minor seventh (Pythagorean), 16/9
61. minor seventh, 9/5
62. neutral seventh, 20/11
63. neutral seventh, 11/6
65. major seventh, 15/8
67. diminished octave, 40/21
68. diminished octave, 27/16
70. semidiminished octave, 63/32
72. perfect octave, 2/1