# 260edo

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Prime factorization
2
Step size
4.61538¢
Fifth
152\260 (701.538¢) (→38\65)
Semitones (A1:m2)
24:20 (110.8¢ : 92.31¢)
Consistency limit
9
Distinct consistency limit
9

← 259edo | 260edo | 261edo → |

^{2}× 5 × 13**260 equal divisions of the octave** (abbreviated **260edo** or **260ed2**), also called **260-tone equal temperament** (**260tet**) or **260 equal temperament** (**260et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 260 equal parts of about 4.62 ¢ each. Each step represents a frequency ratio of 2^{1/260}, or the 260th root of 2.

## Theory

260edo is enfactored in the 7-limit, with the same tuning as 65edo in the 5-limit, and the same as 130edo in the 7-limit. The mappings for harmonics 11 and 17 differ, but 260edo's are hardly an improvement over 130edo's. 29 is the first harmonic that is offered as a sizeable improvement over 130edo, tempering out 841/840, 16820/16807, and 47096/46875.

### Prime harmonics

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

Error | Absolute (¢) | +0.00 | -0.42 | +1.38 | +0.40 | -2.09 | -0.53 | +1.20 | -2.13 | -0.58 | -0.35 | -0.42 |

Relative (%) | +0.0 | -9.0 | +29.9 | +8.8 | -45.2 | -11.4 | +26.0 | -46.1 | -12.6 | -7.5 | -9.1 | |

Steps (reduced) |
260 (0) |
412 (152) |
604 (84) |
730 (210) |
899 (119) |
962 (182) |
1063 (23) |
1104 (64) |
1176 (136) |
1263 (223) |
1288 (248) |

## Scales

- Kartvelian Tetradecatonic: 18 18 18 18 18 18 19 19 19 19 19 19 19 19