186edo: Difference between revisions
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{{Infobox ET}} | |||
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[[ | 186edo is closely related to [[31edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. The equal temperament [[tempering out|tempers out]] 67108864/66430125 ([[misty comma]]) and 390625000/387420489 ([[quartonic comma]]) in the 5-limit, as well as 6115295232/6103515625 ([[vishnuzma]]); [[3136/3125]], [[5120/5103]] and 117649/116640 in the 7-limit. Using the patent val, it tempers out [[385/384]], 1331/1323, [[2200/2187]], and 3773/3750 in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1573/1568]] in the 13-limit. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|186}} | |||
=== Subsets and supersets === | |||
Since 186 factors into {{factorization|186}}, 186edo has subset edos {{EDOs| 2, 3, 6, 31, 62, and 93 }}. | |||
Latest revision as of 19:23, 20 February 2025
| ← 185edo | 186edo | 187edo → |
186 equal divisions of the octave (abbreviated 186edo or 186ed2), also called 186-tone equal temperament (186tet) or 186 equal temperament (186et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 186 equal parts of about 6.45 ¢ each. Each step represents a frequency ratio of 21/186, or the 186th root of 2.
186edo is closely related to 31edo, but the patent vals differ on the mapping for 3. The equal temperament tempers out 67108864/66430125 (misty comma) and 390625000/387420489 (quartonic comma) in the 5-limit, as well as 6115295232/6103515625 (vishnuzma); 3136/3125, 5120/5103 and 117649/116640 in the 7-limit. Using the patent val, it tempers out 385/384, 1331/1323, 2200/2187, and 3773/3750 in the 11-limit; 325/324, 352/351, 847/845, and 1573/1568 in the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +1.27 | +0.78 | -1.08 | -2.93 | -1.82 | -1.73 | -0.74 | -2.47 | +2.68 | -3.10 |
| Relative (%) | +0.0 | +19.7 | +12.1 | -16.8 | -45.4 | -28.2 | -26.8 | -11.5 | -38.3 | +41.6 | -48.1 | |
| Steps (reduced) |
186 (0) |
295 (109) |
432 (60) |
522 (150) |
643 (85) |
688 (130) |
760 (16) |
790 (46) |
841 (97) |
904 (160) |
921 (177) | |
Subsets and supersets
Since 186 factors into 2 × 3 × 31, 186edo has subset edos 2, 3, 6, 31, 62, and 93.