# 2513edo

← 2512edo | 2513edo | 2514edo → |

**2513 equal divisions of the octave** (abbreviated **2513edo** or **2513ed2**), also called **2513-tone equal temperament** (**2513tet**) or **2513 equal temperament** (**2513et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2513 equal parts of about 0.478 ¢ each. Each step represents a frequency ratio of 2^{1/2513}, or the 2513th root of 2.

2513edo is a very strong 5-limit system, with a lower 5-limit relative error than any edo until we reach the cosmically excellent 4296edo. 2513 = 7 × 359, and it shares its harmonic 3 with 359edo. A basis for its 5-limit commas consists of senior, [-17 62 -35⟩, and fortune, [-107 47 14⟩; it also tempers out pirate, [-90 -15 49⟩. It is uniquely consistent through to the 11-odd-limit, and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit.

### Prime harmonics

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

Error | Absolute (¢) | +0.0000 | -0.0051 | -0.0025 | +0.0559 | +0.2141 | -0.0979 | +0.0983 | -0.0200 | +0.1379 | -0.0507 | +0.0500 |

Relative (%) | +0.0 | -1.1 | -0.5 | +11.7 | +44.8 | -20.5 | +20.6 | -4.2 | +28.9 | -10.6 | +10.5 | |

Steps (reduced) |
2513 (0) |
3983 (1470) |
5835 (809) |
7055 (2029) |
8694 (1155) |
9299 (1760) |
10272 (220) |
10675 (623) |
11368 (1316) |
12208 (2156) |
12450 (2398) |