# 2901edo

← 2900edo | 2901edo | 2902edo → |

**2901 equal divisions of the octave** (abbreviated **2901edo** or **2901ed2**), also called **2901-tone equal temperament** (**2901tet**) or **2901 equal temperament** (**2901et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2901 equal parts of about 0.414 ¢ each. Each step represents a frequency ratio of 2^{1/2901}, or the 2901st root of 2.

## Theory

2901edo is consistent in the 17-odd-limit and is otherwise an excellent 31-limit system, with only the pair {19/17, 34/19} being mapped inconsistently in the 31-odd-limit. It provides a good tuning for the jacobin temperament in the 13-limit, the rank-5 temperament tempering out 6656/6655. Alongside jacobin, it tunes the tridecimal quartismic temperament, which also tempers out 123201/123200. It also tunes the monzismic temperament.

### Prime harmonics

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

Error | absolute (¢) | +0.000 | +0.010 | +0.036 | -0.057 | +0.078 | +0.010 | +0.112 | -0.098 | +0.061 | -0.001 | -0.051 |

relative (%) | +0 | +2 | +9 | -14 | +19 | +2 | +27 | -24 | +15 | -0 | -12 | |

Steps (reduced) |
2901 (0) |
4598 (1697) |
6736 (934) |
8144 (2342) |
10036 (1333) |
10735 (2032) |
11858 (254) |
12323 (719) |
13123 (1519) |
14093 (2489) |
14372 (2768) |

### Subsets and supersets

Since 2901 factors into 3 × 967, 2901edo contains 3edo and 967edo as subsets.

## Music

*Demo*(2024)