79ed12
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| ← 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.
Theory
79ed12 is closely related to 22edo, but with the 12th harmonic rather than the octave 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.0 | +4.0 | -4.0 | -9.1 | +2.0 | +7.4 | -6.0 | +7.9 | -11.1 | -12.7 | +0.0 |
| Relative (%) | -3.6 | +7.3 | -7.3 | -16.7 | +3.6 | +13.6 | -10.9 | +14.6 | -20.4 | -23.4 | +0.0 | |
| Steps (reduced) |
22 (22) |
35 (35) |
44 (44) |
51 (51) |
57 (57) |
62 (62) |
66 (66) |
70 (70) |
73 (73) |
76 (76) |
79 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +24.8 | +5.4 | -5.1 | -7.9 | -4.0 | +6.0 | +21.3 | -13.1 | +11.4 | -14.7 | +17.2 | -2.0 |
| Relative (%) | +45.5 | +9.9 | -9.4 | -14.6 | -7.3 | +10.9 | +39.1 | -24.0 | +20.9 | -27.0 | +31.7 | -3.6 | |
| Steps (reduced) |
82 (3) |
84 (5) |
86 (7) |
88 (9) |
90 (11) |
92 (13) |
94 (15) |
95 (16) |
97 (18) |
98 (19) |
100 (21) |
101 (22) | |
Subsets and supersets
79ed12 is the 22nd prime ed12, so it does not contain any nontrivial subset ed12's.