185edo: Difference between revisions
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'''185edo''' is the [[EDO|equal division of the octave]] into 185 parts of 6.4865 [[cent]]s each. It [[tempering out|tempers out]] the [[comma]]s 126/125, 1029/1024, 6144/6125 and 243/242, making it useful for various purposes. It is an excellent tuning for [[Starling family|starling temperament]], the [[7-limit]] [[Planar Temperament|planar temperament]] tempering out 126/125; [[Starling family#Valentine temperament|valentine temperament]], which also tempers out 1029/1024; and the rank three 89&154&185 temperament tempering out 126/125 and 243/242. With 185cff, the val <185 293 429 519 640 686|, it makes for a first-class tuning of the 13-limit [[Gamelismic clan#Miracle-Miraculous|miraculous temperament]]. | '''185edo''' is the [[EDO|equal division of the octave]] into 185 parts of 6.4865 [[cent]]s each. It [[tempering out|tempers out]] the [[comma]]s 126/125, 1029/1024, 6144/6125 and 243/242, making it useful for various purposes. It is an excellent tuning for [[Starling family|starling temperament]], the [[7-limit]] [[Planar Temperament|planar temperament]] tempering out 126/125; [[Starling family#Valentine temperament|valentine temperament]], which also tempers out 1029/1024; and the rank three 89&154&185 temperament tempering out 126/125 and 243/242. With 185cff, the val <185 293 429 519 640 686|, it makes for a first-class tuning of the 13-limit [[Gamelismic clan#Miracle-Miraculous|miraculous temperament]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|185}} | |||
== Scales == | == Scales == | ||
Revision as of 21:16, 18 December 2022
| ← 184edo | 185edo | 186edo → |
185edo is the equal division of the octave into 185 parts of 6.4865 cents each. It tempers out the commas 126/125, 1029/1024, 6144/6125 and 243/242, making it useful for various purposes. It is an excellent tuning for starling temperament, the 7-limit planar temperament tempering out 126/125; valentine temperament, which also tempers out 1029/1024; and the rank three 89&154&185 temperament tempering out 126/125 and 243/242. With 185cff, the val <185 293 429 519 640 686|, it makes for a first-class tuning of the 13-limit miraculous temperament.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.41 | +2.88 | -2.34 | -2.83 | +0.03 | +2.72 | +1.46 | -1.17 | +0.87 | +2.73 | +0.91 |
| Relative (%) | -21.8 | +44.3 | -36.1 | -43.6 | +0.5 | +41.9 | +22.5 | -18.1 | +13.3 | +42.1 | +14.1 | |
| Steps (reduced) |
293 (108) |
430 (60) |
519 (149) |
586 (31) |
640 (85) |
685 (130) |
723 (168) |
756 (16) |
786 (46) |
813 (73) |
837 (97) | |