81edo: Difference between revisions
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{{Infobox ET | |||
| Prime factorization = 3<sup>4</sup> | |||
| Step size = 14.815¢ | |||
| Fifth = 47\81 = 696.30¢ | |||
| Major 2nd = 13\81 = 192.59¢ | |||
| Semitones = 5:8 (74.1¢:118.5¢) | |||
| Consistency = 7 | |||
}} | |||
[[File:81 EDO structure-accidentals-notation-colour notation.png|thumb| | [[File:81 EDO structure-accidentals-notation-colour notation.png|thumb| | ||
By [[Tom Winspear]], utilizing the Accidents shown below. Left: Chain of 4ths/5ths , Right: Chromatic view. Black font represents the '6 accidentals deep' notation that covers the chromatic scale with enharmonics only across EF & BC. White text displays deep enharmonics in the ambiguous infrared & ultraviolet area of the colour notation. | By [[Tom Winspear]], utilizing the Accidents shown below. Left: Chain of 4ths/5ths , Right: Chromatic view. Black font represents the '6 accidentals deep' notation that covers the chromatic scale with enharmonics only across EF & BC. White text displays deep enharmonics in the ambiguous infrared & ultraviolet area of the colour notation. | ||
]] | ]] | ||
'''81edo''' divides the octave into 81 steps of 14.815 [[cent]]s each. It is notable as a tuning for [[meantone family|meantone]] and related temperaments and is the [[optimal patent val]] for a number of them. In particular it is the optimal patent val for 5-limit meantone, 7-limit meantone, 11-limit meanpop, 13-limit meanpop, and the rank three temperament [[Didymus rank three family|erato]]. The electronic music pioneer [https://web.archive.org/web/20120211182601/http://daphneoram.org/2012/01/13/letter-from-yehudi-menuhin/ Daphne Oram] was interested in 81edo. | '''81edo''' divides the octave into 81 steps of 14.815 [[cent]]s each. It is notable as a tuning for [[meantone family|meantone]] and related temperaments and is the [[optimal patent val]] for a number of them. In particular it is the optimal patent val for 5-limit meantone, 7-limit meantone, 11-limit meanpop, 13-limit meanpop, and the rank three temperament [[Didymus rank three family|erato]]. The electronic music pioneer [https://web.archive.org/web/20120211182601/http://daphneoram.org/2012/01/13/letter-from-yehudi-menuhin/ Daphne Oram] was interested in 81edo. | ||
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The chromatic scale can be notated utilizing only six accidentals in either direction - the rest are for enharmonics. | The chromatic scale can be notated utilizing only six accidentals in either direction - the rest are for enharmonics. | ||
]] | ]] | ||
{{primes in edo|81}} | {{primes in edo|81}} | ||
* 5-limit commas: 81/80, |-48 1 20 | == Comma list == | ||
* 7-limit commas: 81/80, 126/125, |-24 1 0 8 | * 5-limit commas: 81/80, {{monzo|-48 1 20}} | ||
* 7-limit commas: 81/80, 126/125, {{monzo|-24 1 0 8}} | |||
* 11-limit commas: 81/80, 126/125, 385/384, 12005/11979 | * 11-limit commas: 81/80, 126/125, 385/384, 12005/11979 | ||
* 13-limit commas: 81/80, 105/104, 144/143, 196/195, 6655/6591 | * 13-limit commas: 81/80, 105/104, 144/143, 196/195, 6655/6591 | ||
== Scales == | == Scales == | ||
* [[Leantone6]] | |||
* [[ | * [[Leantone7]] | ||
* [[ | * [[Leantone13]] | ||
* [[ | |||
[[Category:Theory]] | [[Category:Theory]] | ||
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[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Erato]] | [[Category:Erato]] | ||
[[Category:Golden meantone]] | |||
[[Category:Leantone]] | |||
[[Category:Meantone]] | [[Category:Meantone]] | ||
[[Category:Meanpop]] | [[Category:Meanpop]] | ||