# 150edo

← 149edo | 150edo | 151edo → |

^{2}**150 equal divisions of the octave** (abbreviated **150edo** or **150ed2**), also called **150-tone equal temperament** (**150tet**) or **150 equal temperament** (**150et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 150 equal parts of exactly 8 ¢ each. Each step represents a frequency ratio of 2^{1/150}, or the 150th root of 2.

## Theory

150edo is contorted in the 5-limit, tempering out the same commas as 75edo, including 20000/19683 and 2109375/2097152. However, every 11th step of 150edo is equal to the 88cET nonoctave tuning, which is also represented as octacot through a regular temperament theory perspective. It provides a good tuning for octacot, for which 88 cents provides a generator.

The equal temperament tempers out 245/243, 2401/2400, and 4000/3969 in the 7-limit, 385/384, 896/891, and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 13-limit.

### Odd harmonics

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | +2.04 | -2.31 | -0.83 | -3.91 | +0.68 | -0.53 | -0.27 | -0.96 | -1.51 | +1.22 |

Relative (%) | +25.6 | -28.9 | -10.3 | -48.9 | +8.5 | -6.6 | -3.4 | -11.9 | -18.9 | +15.2 | |

Steps (reduced) |
238 (88) |
348 (48) |
421 (121) |
475 (25) |
519 (69) |
555 (105) |
586 (136) |
613 (13) |
637 (37) |
659 (59) |

### Subsets and supersets

Since 150 factors into 2 × 3 × 5^{2}, 150edo has subset edos 2, 3, 5, 6, 10, 15, 25, 30, 50, and 75.

## Regular temperament properties

### Rank-2 temperaments

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

1 | 11\150 | 88.00 | 21/20 | Octacot (150e) / october (150) |

1 | 29\150 | 232.00 | 8/7 | Quadrawell |

10 | 31\150 (1\150) |
248.00 (8.00) |
15/13 (176/175) |
Decoid (150e) |

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