187edo
| ← 186edo | 187edo | 188edo → |
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
| 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 (%) | -39 | -20 | +2 | +22 | +9 | +2 | +41 | -36 | -36 | -36 | +9 | |
| 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.