187edo: Difference between revisions
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This edo is a bit of a chimera. It has a [[3/2|fifth]] which is 2.9 | This edo is a bit of a chimera. It has a [[3/2|fifth]] which is 2.9{{c}} flat and a [[5/4|classical major third]] 1.3 cents flat, but the [[7/1|7]], [[11/1|11]] and [[13/1|13]] are more accurate. The equal temperament [[tempering out|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 === | === Odd harmonics === | ||
Latest revision as of 14:09, 20 February 2025
| ← 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 ¢ 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 (%) | -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.
Music
- Pillow(33) (187edo lullaby) by JUMBLE (Dec 2024, uses MOS 22L 11s)