31ed6
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Prime factorization
31 (prime)
Step size
100.063¢
Octave
12\31ed6 (1200.76¢)
(convergent)
Twelfth
19\31ed6 (1901.2¢)
(convergent)
Consistency limit
10
Distinct consistency limit
5
| ← 30ed6 | 31ed6 | 32ed6 → |
(convergent)
(convergent)
Division of the sixth harmonic into 31 equal parts (31ED6) is very nearly identical to 12 EDO, but with the 6/1 rather than the 2/1 being just. The octave is about 0.7568 cents stretched and the step size is about 100.0631 cents.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.76 | -0.76 | +1.51 | +15.45 | +0.00 | +33.32 | +2.27 | -1.51 | +16.21 | -48.73 | +0.76 | -37.75 | +34.08 | +14.70 | +3.03 |
| Relative (%) | +0.8 | -0.8 | +1.5 | +15.4 | +0.0 | +33.3 | +2.3 | -1.5 | +16.2 | -48.7 | +0.8 | -37.7 | +34.1 | +14.7 | +3.0 | |
| Steps (reduced) |
12 (12) |
19 (19) |
24 (24) |
28 (28) |
31 (0) |
34 (3) |
36 (5) |
38 (7) |
40 (9) |
41 (10) |
43 (12) |
44 (13) |
46 (15) |
47 (16) |
48 (17) | |
Division of 6/1 into 31 equal parts
Note: 31 equal divisions of the hexatave is not a "real" xenharmonic tuning; it is a slightly stretched version (with an octave of 1200.8 cents) of the normal 12-tone scale, similar to 19ED3.