79ed12
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Prime factorization
79 (prime)
Step size
54.4551¢
Octave
22\79ed12 (1198.01¢)
Twelfth
35\79ed12 (1905.93¢)
Consistency limit
11
Distinct consistency limit
8
| ← 78ed12 | 79ed12 | 80ed12 → |
79 equal divisions of the 12th harmonic (abbreviated 79ed12) is a nonoctave tuning system that divides the interval of 12/1 into 79 equal parts of about 54.5 ¢ each. Each step represents a frequency ratio of 121/79, or the 79th root of 12.
79ED12 is very nearly identical to 22 EDO, but with the 12/1 rather than the 2/1 being just, resulting in octaves being compressed by about 1.99 ¢. The local zeta peak around 22 is located at 22.025147, which has a step size of 54.483 ¢ and an octave of 1198.63 ¢ (which is compressed by 1.37 ¢), making 79ed12 very close to optimal for 22edo.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.99 | +3.97 | -3.97 | -9.10 | +1.99 | +7.39 | -5.96 | +7.95 | -11.09 | -12.73 | +0.00 | +24.79 | +5.40 | -5.13 | -7.95 |
| Relative (%) | -3.6 | +7.3 | -7.3 | -16.7 | +3.6 | +13.6 | -10.9 | +14.6 | -20.4 | -23.4 | +0.0 | +45.5 | +9.9 | -9.4 | -14.6 | |
| Steps (reduced) |
22 (22) |
35 (35) |
44 (44) |
51 (51) |
57 (57) |
62 (62) |
66 (66) |
70 (70) |
73 (73) |
76 (76) |
79 (0) |
82 (3) |
84 (5) |
86 (7) |
88 (9) | |