# 1817edo

 ← 1816edo 1817edo 1818edo →
Prime factorization 23 × 79
Step size 0.660429¢
Fifth 1063\1817 (702.036¢)
Semitones (A1:m2) 173:136 (114.3¢ : 89.82¢)
Consistency limit 17
Distinct consistency limit 17

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 21/1817, 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

Approximation of prime harmonics in 1817edo
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.