96edo: Difference between revisions
m →Rank-2 temperaments: Added spog |
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== Theory == | == Theory == | ||
As a [[5-limit]] system, 96edo can be characterized by the fact that it tempers out both the [[Pythagorean comma]], 531441/524288, [[Würschmidt's comma]], 393216/390625, the [[unicorn comma]], 1594323/1562500, and the kwazy comma, {{monzo| -53 10 16 }}. It therefore has the same familiar 700-cent fifth as [[12edo]], and has a best major third of 387.5 cents, a bit over a cent sharp. There is therefore nothing to complain of with its representation of the 5-limit and it can be recommended as an approach to the [[würschmidt family]] of temperaments. It also tempers out the unicorn comma, and serves a way of tuning temperaments in the [[unicorn family]]. It supports [[Substitute harmonic#Sitcom|sitcom]] temperament. | As a [[5-limit]] system, 96edo can be characterized by the fact that it tempers out both the [[Pythagorean comma]], 531441/524288, [[Würschmidt's comma]], 393216/390625, the [[unicorn comma]], 1594323/1562500, and the [[kwazy comma]], {{monzo| -53 10 16 }}. It therefore has the same familiar 700-cent fifth as [[12edo]], and has a best major third of 387.5 cents, a bit over a cent sharp. There is therefore nothing to complain of with its representation of the 5-limit and it can be recommended as an approach to the [[würschmidt family]] of temperaments. It also tempers out the unicorn comma, and serves a way of tuning temperaments in the [[unicorn family]]. It supports [[Substitute harmonic#Sitcom|sitcom]] temperament. | ||
In the [[7-limit]], 96 has two possible mappings for [[7/4]], a sharp one of 975 cents from the [[patent val]], and a flat one of 962.5 cents from 96d. Using the sharp mapping, 96 tempers out [[225/224]] and [[support]]s 7-limit [[würschmidt]] temperament, and using the flat mapping it tempers out [[126/125]] and supports [[worschmidt]] temperament. We can also dispense with 7 altogether, and use it as a no-sevens system, where it tempers out [[243/242]] in the 11-limit and [[676/675]] in the 13-limit. If we include 7, then the sharp mapping tempers out [[99/98]] and [[176/175]] in the 11-limit, and [[169/168]] in the 13-limit, and this provides the optimal patent val for the [[Marvel temperaments #Interpental|interpental temperament]]. With the flat 7 it tempers out [[385/384]] in the 11-limit and [[196/195]] and [[364/363]] in the 13-limit, and serves for the various temperaments of the unicorn family. | In the [[7-limit]], 96 has two possible mappings for [[7/4]], a sharp one of 975 cents from the [[patent val]], and a flat one of 962.5 cents from 96d. Using the sharp mapping, 96 tempers out [[225/224]] and [[support]]s 7-limit [[würschmidt]] temperament, and using the flat mapping it tempers out [[126/125]] and supports [[worschmidt]] temperament. We can also dispense with 7 altogether, and use it as a no-sevens system, where it tempers out [[243/242]] in the 11-limit and [[676/675]] in the 13-limit. If we include 7, then the sharp mapping tempers out [[99/98]] and [[176/175]] in the 11-limit, and [[169/168]] in the 13-limit, and this provides the optimal patent val for the [[Marvel temperaments #Interpental|interpental temperament]]. With the flat 7 it tempers out [[385/384]] in the 11-limit and [[196/195]] and [[364/363]] in the 13-limit, and serves for the various temperaments of the unicorn family. | ||
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| 1 | | 1 | ||
| 5\96 | | 5\96 | ||
| [[Unicorn]] | | [[Unicorn]] / [[camahueto]] (96d) | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 69: | Line 69: | ||
| 1 | | 1 | ||
| 29\96 | | 29\96 | ||
| [[ | | [[Submajor]] / [[interpental]] (96) | ||
|- | |- | ||
| 1 | | 1 | ||
| 31\96 | | 31\96 | ||
| [[Würschmidt]] | | [[Würschmidt]] (96) / [[worschmidt]] (96d) | ||
|- | |- | ||
| 2 | | 2 | ||
| 13\96 | | 13\96 | ||
| [[Kwazy]] / [[ | | [[Kwazy]] / [[bisupermajor]] (96d) | ||
|- | |- | ||
| 2 | | 2 | ||
| 25\96 | | 25\96 | ||
| [[Vines]] | | [[Vines]] (96d) | ||
|- | |- | ||
| 12 | | 12 | ||
| 1\96 | | 1\96 | ||
| [[Compton]] | | [[Compton]] (96d)<br>[[Substitute harmonic#Sitcom|Sitcom]] | ||
|- | |- | ||
| 24 | | 24 | ||
| 1\96 | | 1\96 | ||
| [[Hours]] | | [[Hours]] (96) | ||
|} | |} | ||
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; [[Tony Salinas]] | ; [[Tony Salinas]] | ||
* [[:File:01_-_Autumn_1.mp3|''Autumn'' for conic bellophone and mixed quintet]] | * [[:File:01_-_Autumn_1.mp3|''Autumn'' for conic bellophone and mixed quintet]] (2007) | ||
; [[Randy Wells]] | ; [[Randy Wells]] | ||
* [https://www.youtube.com/watch?v=XuS8VxDnJm4 ''Butterfly Skin''] (2021) | * [https://www.youtube.com/watch?v=XuS8VxDnJm4 ''Butterfly Skin''] (2021) | ||