Archytas family: Difference between revisions
Cleanup; edo lists reviewed |
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The '''archytas family''' of temperaments [[tempering out|tempers out]] [[64/63]], and thereby identifies the [[otonal]] [[tetrad]] with the [[dominant seventh chord]], which is familiar from [[12edo]] and also a feature of [[22edo]] and [[27edo]]. | |||
= Archytas = | |||
[[Comma]]: 64/63 | [[Comma]]: 64/63 | ||
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{{EDOs|legend=1| 5, 7, 10, 12, 22, 27, 49 }} | {{EDOs|legend=1| 5, 7, 10, 12, 22, 27, 49 }} | ||
Scales | == Scales == | ||
* [[archytas12]] | * [[archytas12]] | ||
* [[archytas12synch]] | * [[archytas12synch]] | ||
Music | == Music == | ||
Chris Vaisvil | Chris Vaisvil | ||
| Line 43: | Line 45: | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/Archytas12%20sync%20Study%203.mp3 Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/Archytas12%20sync%20Study%203.mp3 Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3] | ||
= Ares = | |||
[[Comma]]s: 64/63, 100/99 | [[Comma]]s: 64/63, 100/99 | ||
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Scales: [[ares12]] | Scales: [[ares12]] | ||
= Vulcan = | |||
Commas: 56/55, 64/63 | Commas: 56/55, 64/63 | ||
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[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Archytas]] | [[Category:Archytas]] | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 04:41, 6 January 2021
The archytas family of temperaments tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord, which is familiar from 12edo and also a feature of 22edo and 27edo.
Archytas
Comma: 64/63
7-limit minimax
[|1 0 0 0>, |2 1/3 0 -1/3>, |2 -2/3 1 -1/3>, |2 -2/3 0 2/3>]
Eigenmonzos: 2, 6/5, 7/5
9-limit minimax
[|1 0 0 0>, |3/2 1/2 0 -1/4>, |3/2 -1/2 1 -1/4>, |3 -1 0 1/2>]
Eigenmonzos: 2, 6/5, 9/7
Lattice basis: 3/2 length 1.0508 5/4 length 2.3219
Angle(3/2, 5/4) = 90 degrees
Map to lattice: [<0 1 0 -2|, <0 0 1 0|]
Map: [<1 0 0 6|, <0 1 0 -2|, <0 0 1 0|]
Generators: 2, 3, 5
EDOs: 5, 7, 10, 12, 22, 27, 49
Scales
Music
Chris Vaisvil
Joel Taylor
Ares
Commas: 64/63, 100/99
[|1 0 0 0 0>, |3/2 1/2 0 -1/4 0>, |2 0 0 -1/2 1/2>, |3 -1 0 1/2 0>, |3 -1 0 -1/2 1>]
Eigenmonzos: 2, 11/9, 9/7
Lattice basis: 3/2 0.9878 6/5 1.4312
Angle(3/2, 6/5) = 75.0475 degrees
Map to lattice: [<0 1 1 -2 0|, <0 0 -1 0 -2|]
Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|]
Generators: 2, 3, 5
EDOs: 12, 15, 22, 27e, 34d, 49
Badness: 0.000469
Scales: ares12
Vulcan
Commas: 56/55, 64/63
Map: [<1 0 0 6 9|, <0 1 0 -2 -2|, <0 0 1 0 -1|]
Generators: 2, 3, 5
Badness: 0.000577