15601edo
| ← 15600edo | 15601edo | 15602edo → |
(convergent)
15601 equal divisions of the octave (abbreviated 15601edo or 15601ed2), also called 15601-tone equal temperament (15601tet) or 15601 equal temperament (15601et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 15601 equal parts of about 0.0769 ¢ each. Each step represents a frequency ratio of 21/15601, or the 15601st root of 2. It is the denominator of the next convergent for log23 past 665, before 31867, and has a fifth which is 0.000002 cents stretched.
This system is at its best behavior in the 2.3.19.23 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.0000 | +0.0000 | -0.0308 | +0.0351 | +0.0313 | +0.0338 | +0.0379 | +0.0064 | -0.0069 | -0.0278 | -0.0320 |
| relative (%) | +0 | +0 | -40 | +46 | +41 | +44 | +49 | +8 | -9 | -36 | -42 | |
| Steps (reduced) |
15601 (0) |
24727 (9126) |
36224 (5022) |
43798 (12596) |
53971 (7168) |
57731 (10928) |
63769 (1365) |
66272 (3868) |
70572 (8168) |
75789 (13385) |
77290 (14886) | |
Subsets and supersets
15601edo is the 1819th prime edo.
31202edo, which doubles 15601edo, provides a good correction to harmonics 5, 7, 11, 13 and 17. 78005edo, which slices each step of 15601edo in five, is notable for an exceptional approximation quality of the 5-limit.