81edo: Difference between revisions
Jump to navigation
Jump to search
m with default precision the picture gets clearer |
mNo edit summary |
||
| Line 1: | Line 1: | ||
{{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. | ||
| Line 12: | Line 22: | ||
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]] | ||
| Line 30: | Line 40: | ||
[[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]] | ||
Revision as of 00:35, 23 February 2022
| ← 80edo | 81edo | 82edo → |
81edo divides the octave into 81 steps of 14.815 cents each. It is notable as a tuning for 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 erato. The electronic music pioneer Daphne Oram was interested in 81edo.
As a step in the Golden meantone series of EDOs, 81 EDO marks the point at which the series ceases to display audible changes to meantone temperament, and is also the EDO with the lowest average and most evenly spread Just-error across the scale (though 31 EDO does have the best harmonic 7th).
Script error: No such module "primes_in_edo".
Comma list
- 5-limit commas: 81/80, [-48 1 20⟩
- 7-limit commas: 81/80, 126/125, [-24 1 0 8⟩
- 11-limit commas: 81/80, 126/125, 385/384, 12005/11979
- 13-limit commas: 81/80, 105/104, 144/143, 196/195, 6655/6591