# 443edo

← 442edo | 443edo | 444edo → |

**443 equal divisions of the octave** (abbreviated **443edo**), or **443-tone equal temperament** (**443tet**), **443 equal temperament** (**443et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 443 equal parts of about 2.71 ¢ each. Each step of 443edo represents a frequency ratio of 2^{1/443}, or the 443rd root of 2.

## Theory

443edo is inconsistent to the 5-odd-limit and the error of harmonic 5 is quite large. To start with, the patent val ⟨443 702 **1029** **1244** **1533**] as well as the 443cde val ⟨443 702 **1028** **1243** **1532**] are worth considering.

Using the patent val, the equal temperament tempers out 6144/6125, 32805/32768, and 67108864/66976875 in the 7-limit; 540/539, 5632/5625, 8019/8000, and 131072/130977 in the 11-limit. It supports hemischis, the 130 & 313 temperament.

### Prime harmonics

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

Error | absolute (¢) | +0.00 | -0.37 | +1.05 | +0.93 | +1.28 | -0.80 | +0.69 | +0.46 | +0.17 | -0.23 | +0.79 |

relative (%) | +0 | -14 | +39 | +34 | +47 | -29 | +25 | +17 | +6 | -9 | +29 | |

Steps (reduced) |
443 (0) |
702 (259) |
1029 (143) |
1244 (358) |
1533 (204) |
1639 (310) |
1811 (39) |
1882 (110) |
2004 (232) |
2152 (380) |
2195 (423) |

### Subsets and supersets

443edo is the 86th prime edo. 886edo, which doubles it, gives a good correction until the 11-limit.

## Regular temperament properties

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

Absolute (¢) | Relative (%) | ||||

2.3 | [-702 443⟩ | [⟨443 702]] | 0.1183 | 0.1183 | 4.37 |

### Rank-2 temperaments

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

1 | 92\443 | 249.21 | 15/13 | Hemischis (443) |

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