# 1776edo

← 1775edo | 1776edo | 1777edo → |

^{4}× 3 × 37**1776 equal divisions of the octave** (abbreviated **1776edo**), or **1776-tone equal temperament** (**1776tet**), **1776 equal temperament** (**1776et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1776 equal parts of about 0.676 ¢ each. Each step of 1776edo represents a frequency ratio of 2^{1/1776}, or the 1776th root of 2.

1776edo is consistent in the 15-odd-limit, and has good representation of it, with errors less than 26%. In the 2.5.7.11.13 subgroup, it is enfactored with the same mapping as 888edo, and corrects the latter's mapping for harmonic 3. A comma basis for the 13-limit is {4096/4095, 9801/9800, 67392/67375, 250047/250000, 531674/531441}.

In the 5-limit, it supports the squarschmidt temperament, tempering out the [61 4 -29⟩ comma, and it also tempers out [55 -64 -20⟩, [6, 68, -49⟩, [116, -60, -9⟩.

### Prime harmonics

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

Error | absolute (¢) | +0.000 | +0.072 | +0.173 | +0.093 | +0.033 | +0.013 | -0.226 | -0.216 | +0.104 | +0.153 | +0.235 |

relative (%) | +0 | +11 | +26 | +14 | +5 | +2 | -33 | -32 | +15 | +23 | +35 | |

Steps (reduced) |
1776 (0) |
2815 (1039) |
4124 (572) |
4986 (1434) |
6144 (816) |
6572 (1244) |
7259 (155) |
7544 (440) |
8034 (930) |
8628 (1524) |
8799 (1695) |

### Subsets and supersets

Since 1776 factors as 2^{4} × 3 × 37, it has subset edos 1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 48, 74, 111, 148, 222, 296, 444, 592, 888.