# 499edo

← 498edo | 499edo | 500edo → |

**499 equal divisions of the octave** (abbreviated **499edo** or **499ed2**), also called **499-tone equal temperament** (**499tet**) or **499 equal temperament** (**499et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 499 equal parts of about 2.4 ¢ each. Each step represents a frequency ratio of 2^{1/499}, or the 499th root of 2.

## Theory

499et tempers out 33554432/33480783, 359661568/358722675 and 2401/2400 in the 7-limit; 100663296/100656875, 2097152/2096325, 536870912/535869675, 151263/151250, 104857600/104825259, 131072/130977, 200704/200475, 17537553/17500000, 19712/19683, 1479016/1476225, 3025/3024, 41503/41472, 532400/531441 and 67110351/67108864 in the 11-limit.

### Prime harmonics

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

Error | Absolute (¢) | +0.00 | +0.25 | +0.86 | +0.31 | -0.62 | +1.16 | +0.86 | +0.68 | -0.62 | -0.32 | -0.35 |

Relative (%) | +0.0 | +10.4 | +35.8 | +13.0 | -25.6 | +48.1 | +35.6 | +28.4 | -25.7 | -13.3 | -14.4 | |

Steps (reduced) |
499 (0) |
791 (292) |
1159 (161) |
1401 (403) |
1726 (229) |
1847 (350) |
2040 (44) |
2120 (124) |
2257 (261) |
2424 (428) |
2472 (476) |

### Subsets and supersets

499edo is the 95th prime edo.

## Regular temperament properties

Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
---|---|---|---|---|---|

Absolute (¢) | Relative (%) | ||||

2.3 | [791 -499⟩ | ⟨499 791] | -0.0787 | 0.0787 | 3.27 |

2.3.5 | [32 -7 -9⟩, [1 36 -25⟩ | ⟨499 791 1159] | -0.1760 | 0.1519 | 6.32 |

2.3.5.7 | 2401/2400, 1959552/1953125, 26873856/26796875 | ⟨499 791 1159 1401] | -0.1598 | 0.1345 | 5.59 |

### Rank-2 temperaments

Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
---|---|---|---|---|

1 | 23\499 | 55.311 | 16875/16384 | Escapade |

1 | 126\499 | 303.006 | 25/21 | Quinmite |

1 | 146\499 | 351.102 | 49/40 | Newt |

1 | 178\499 | 428.056 | 2800/2187 | Osiris |

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct