185edo: Difference between revisions
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{{Infobox ET}} | |||
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== Theory == | |||
The [[patent val]] of 185edo [[tempering out|tempers out]] [[126/125]], [[1029/1024]], [[6144/6125]] in the 7-limit, and [[243/242]] in the 11-limit, making it useful for various purposes. It is an excellent tuning for [[starling]], the [[7-limit]] [[planar temperament]] tempering out 126/125; [[valentine]], which also tempers out 1029/1024; and [[cuckoo]], tempering out 126/125 and 243/242. | |||
Using the 185c val, it tempers out [[225/224]] and 1029/1024 in the 7-limit, 243/242, [[385/384]], [[441/440]], and [[540/539]] in the 11-limit, providing a great alternative to [[72edo]] for [[miracle]]. With the 185cf val {{val| 185 293 '''429''' 519 640 '''684''' }}, it makes for an excellent tuning of 13-limit [[manna]]. Meanwhile the 185cff val {{val| 185 293 '''429''' 519 640 '''686''' }} is a first-class tuning of 13-limit [[miraculous]]. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|185}} | |||
=== Subsets and supersets === | |||
Since 185 factors into {{factorization|185}}, 185edo contains [[5edo]] and [[37edo]] as its subsets. | |||
== Scales == | == Scales == | ||
* [[nova]] | * [[nova]] | ||
* [[novadene]] | * [[novadene]] | ||
Latest revision as of 14:08, 20 February 2025
| ← 184edo | 185edo | 186edo → |
185 equal divisions of the octave (abbreviated 185edo or 185ed2), also called 185-tone equal temperament (185tet) or 185 equal temperament (185et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 185 equal parts of about 6.49 ¢ each. Each step represents a frequency ratio of 21/185, or the 185th root of 2.
Theory
The patent val of 185edo tempers out 126/125, 1029/1024, 6144/6125 in the 7-limit, and 243/242 in the 11-limit, making it useful for various purposes. It is an excellent tuning for starling, the 7-limit planar temperament tempering out 126/125; valentine, which also tempers out 1029/1024; and cuckoo, tempering out 126/125 and 243/242.
Using the 185c val, it tempers out 225/224 and 1029/1024 in the 7-limit, 243/242, 385/384, 441/440, and 540/539 in the 11-limit, providing a great alternative to 72edo for miracle. With the 185cf val ⟨185 293 429 519 640 684], it makes for an excellent tuning of 13-limit manna. Meanwhile the 185cff val ⟨185 293 429 519 640 686] is a first-class tuning of 13-limit miraculous.
Odd 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) | |
Subsets and supersets
Since 185 factors into 5 × 37, 185edo contains 5edo and 37edo as its subsets.