12655edo
| ← 12654edo | 12655edo | 12656edo → |
12655 equal divisions of the octave (abbreviated 12655edo or 12655ed2), also called 12655-tone equal temperament (12655tet) or 12655 equal temperament (12655et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 12655 equal parts of about 0.0948 ¢ each. Each step represents a frequency ratio of 21/12655, or the 12655th root of 2.
Theory
12655edo is notable for having a very accurate 5th harmonic. It is also notable for having an accurate 1/4-comma meantone fifth, being only about 0.00000097 cents sharp. 12655edo approximates the 2.5.7 subgroup very well, and is okay as a 7-limit system. Notably, 12655edo tempers out the exodia comma, supporting the exodia temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0284 | -0.0000 | -0.0073 | -0.0102 | -0.0061 | +0.0150 | +0.0453 | +0.0307 | +0.0238 | -0.0336 |
| Relative (%) | +0.0 | +30.0 | -0.0 | -7.7 | -10.7 | -6.5 | +15.8 | +47.7 | +32.3 | +25.1 | -35.4 | |
| Steps (reduced) |
12655 (0) |
20058 (7403) |
29384 (4074) |
35527 (10217) |
43779 (5814) |
46829 (8864) |
51727 (1107) |
53758 (3138) |
57246 (6626) |
61478 (10858) |
62695 (12075) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0349 | +0.0170 | -0.0361 | -0.0305 | +0.0158 | +0.0144 | -0.0456 | -0.0340 | -0.0047 | -0.0218 | -0.0327 |
| Relative (%) | +36.8 | +17.9 | -38.0 | -32.2 | +16.7 | +15.2 | -48.1 | -35.9 | -5.0 | -23.0 | -34.5 | |
| Steps (reduced) |
65926 (2651) |
67800 (4525) |
68669 (5394) |
70293 (7018) |
72487 (9212) |
74445 (11170) |
75053 (11778) |
76766 (836) |
77825 (1895) |
78332 (2402) |
79774 (3844) | |
Subsets and supersets
Since 12655 factorizes into 5 × 2531, 72569edo has subset edos 5 and 2531.