187edo

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← 186edo187edo188edo →
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.