# 1817edo

← 1816edo | 1817edo | 1818edo → |

**1817 equal divisions of the octave** (abbreviated **1817edo** or **1817ed2**), also called **1817-tone equal temperament** (**1817tet**) or **1817 equal temperament** (**1817et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1817 equal parts of about 0.66 ¢ each. Each step represents a frequency ratio of 2^{1/1817}, or the 1817th root of 2.

1817edo distinctly consistent in the 17-odd-limit, and a fairly strong 17-limit system. Past that, adding the mapping for 29 is worth considering.

In the 5-limit, it is a strong tuning for tricot. It also tempers out are [128 13 -64⟩, the 323 & 1171 temperament, which divides the third harmonic into 64 equal parts, as well as [-89 -42 67⟩ and [-50 -71 70⟩. In the 7-limit, it tempers out 4375/4374 (the ragisma). In the 11-limit it tempers out 117649/117612, 2097152/2096325, and tunes rank-3 temperaments heimdall and bragi. In the 13-limit, it tempers out 4096/4095, 6656/6655, and in the 17-limit, 12376/12375 and 14400/14399.

In the 17-limit and the 2.3.5.7.11.13.17.37 subgroup (add-37 17-limit), the patent val tunes the gold temperament which divides the octave into 79 parts, though it is worth noting that the error on the 37th harmonic is quite large.

### Prime harmonics

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

Error | Absolute (¢) | +0.000 | +0.081 | +0.037 | +0.024 | +0.141 | +0.199 | +0.053 | -0.320 | -0.206 | +0.032 | +0.149 |

Relative (%) | +0.0 | +12.3 | +5.7 | +3.6 | +21.3 | +30.1 | +8.0 | -48.4 | -31.2 | +4.9 | +22.5 | |

Steps (reduced) |
1817 (0) |
2880 (1063) |
4219 (585) |
5101 (1467) |
6286 (835) |
6724 (1273) |
7427 (159) |
7718 (450) |
8219 (951) |
8827 (1559) |
9002 (1734) |

### Subsets and supersets

Since 1817 factors into 23 × 79, 1817edo contains 23edo and 79edo as subsets.