# 901edo

← 900edo | 901edo | 902edo → |

**901 equal divisions of the octave** (abbreviated **901edo** or **901ed2**), also called **901-tone equal temperament** (**901tet**) or **901 equal temperament** (**901et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 901 equal parts of about 1.33 ¢ each. Each step represents a frequency ratio of 2^{1/901}, or the 901st root of 2.

901edo is consistent to the 15-odd-limit. The equal temperament tempers out [-16 35 -17⟩ (minortone comma) and [-68 18 17⟩ (vavoom comma) in the 5-limit; 4375/4374, 2100875/2097152, and [7 -4 -16 13⟩ in the 7-limit; 41503/41472, 160083/160000, 234375/234256, and 806736/805255 in the 11-limit; 4225/4224, 4459/4455, 6656/6655, 34398/34375, and 50421/50336 in the 13-limit, supporting mitonic, vavoom, and egads.

### Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | +0.000 | -0.068 | -0.076 | -0.568 | +0.069 | -0.128 | +0.261 | -0.510 | +0.361 | -0.054 | +0.358 |

Relative (%) | +0.0 | -5.1 | -5.7 | -42.7 | +5.2 | -9.6 | +19.6 | -38.3 | +27.1 | -4.1 | +26.9 | |

Steps (reduced) |
901 (0) |
1428 (527) |
2092 (290) |
2529 (727) |
3117 (414) |
3334 (631) |
3683 (79) |
3827 (223) |
4076 (472) |
4377 (773) |
4464 (860) |

### Subsets and supersets

901 factors into 17 × 53. In light of containing 17edo and 53edo as subsets, it supports the chlorine temperament, which has period 17, and iodine temperament, which has period 53.

1802edo, which doubles 901edo, corrects the mapping for 7.