# 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 2^{1/15601}, or the 15601st root of 2. It is the denominator of the next convergent for log_{2}3 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 | +0.0 | -40.0 | +45.6 | +40.7 | +44.0 | +49.2 | +8.3 | -9.0 | -36.2 | -41.7 | |

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.