# 187edo

 ← 186edo 187edo 188edo →
Prime factorization 11 × 17
Step size 6.41711¢
Fifth 109\187 (699.465¢)
Semitones (A1:m2) 15:16 (96.26¢ : 102.7¢)
Dual sharp fifth 110\187 (705.882¢) (→10\17)
Dual flat fifth 109\187 (699.465¢)
Dual major 2nd 32\187 (205.348¢)
Consistency limit 7
Distinct consistency limit 7

187 equal divisions of the octave (abbreviated 187edo or 187ed2), also called 187-tone equal temperament (187tet) or 187 equal temperament (187et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 187 equal parts of about 6.42 ¢ each. Each step represents a frequency ratio of 21/187, or the 187th root of 2.

This edo is a bit of a chimera. It has a fifth which is 2.9 cents flat and a classical major third 1.3 cents flat, but the 7, 11 and 13 are more accurate. The equal temperament tempers out 78732/78125 (sensipent comma) in the 5-limit and 225/224 in the 7-limit, providing the optimal patent val for sensei which tempers out both. In the 11-limit it tempers out 441/440, 1375/1372 and 4000/3993 and in the 13-limit 351/350, 625/624, 1188/1183, 1716/1715 and 2200/2197.

### Odd harmonics

Approximation of odd harmonics in 187edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -2.49 -1.29 +0.16 +1.44 +0.55 +0.11 +2.64 -2.28 -2.33 -2.33 +0.60
Relative (%) -38.8 -20.1 +2.5 +22.4 +8.6 +1.8 +41.1 -35.6 -36.2 -36.3 +9.4
Steps
(reduced)
296
(109)
434
(60)
525
(151)
593
(32)
647
(86)
692
(131)
731
(170)
764
(16)
794
(46)
821
(73)
846
(98)

### Subsets and supersets

Since 187 factors into 11 × 17, 187edo contains 11edo and 17edo as its subsets.