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Archytas family: Difference between revisions

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Archytas temperament [[tempering_out|tempers out]] [[64/63|64/63]], and thereby identifies the [[otonal|otonal]] [[tetrad|tetrad]] with the [[dominant_seventh_chord|dominant seventh chord]], which is familiar from [[12edo|12edo]] and also a feature of [[22edo|22edo]] and [[27edo|27edo]].
Archytas temperament [[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]].


[[Comma|Comma]]: 64/63
[[Comma]]: 64/63


7-limit minimax
7-limit minimax
Line 8: Line 8:
|2 -2/3 1 -1/3>, |2 -2/3 0 2/3>]
|2 -2/3 1 -1/3>, |2 -2/3 0 2/3>]


[[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 7/5
[[Eigenmonzo]]s: 2, 6/5, 7/5


9-limit minimax
9-limit minimax
Line 15: Line 15:
|3/2 -1/2 1 -1/4>, |3 -1 0 1/2>]
|3/2 -1/2 1 -1/4>, |3 -1 0 1/2>]


[[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 9/7
[[Eigenmonzo]]s: 2, 6/5, 9/7


Lattice basis: 3/2 length 1.0508 5/4 length 2.3219
Lattice basis: 3/2 length 1.0508 5/4 length 2.3219
Line 25: Line 25:
Map: [<1 0 0 6|, <0 1 0 -2|, <0 0 1 0|]
Map: [<1 0 0 6|, <0 1 0 -2|, <0 0 1 0|]


[[generator|Generators]]: 2, 3, 5
[[Generator]]s: 2, 3, 5


[[EDO|Edos]]: [[7edo|7]], [[10edo|10]], [[12edo|12]], [[15edo|15]], [[22edo|22]], [[27edo|27]], [[37edo|37]], [[49edo|49]], [[59edo|59]]
{{EDOs|legend=1| 5, 7, 10, 12, 22, 27, 49 }}


Scales: [[archytas12|archytas12]], [[archytas12synch|archytas12synch]]
Scales:  
* [[archytas12]]
* [[archytas12synch]]


Music: Chris Vaisvil
Music:  


[http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3 12 archytas hobbits with ale]
Chris Vaisvil
 
* [http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3 12 archytas hobbits with ale]


Joel Taylor
Joel Taylor


[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]
 
==11 limit children==


==Ares==
== Ares ==
[[Comma|Commas]]: 64/63, 100/99
[[Comma]]s: 64/63, 100/99


[[Minimax_tuning|Minimax tuning]]
[[Minimax tuning]]


[|1 0 0 0 0>, |3/2 1/2 0 -1/4 0>,  
[|1 0 0 0 0>, |3/2 1/2 0 -1/4 0>,  
Line 50: Line 52:
|3 -1 0 -1/2 1>]
|3 -1 0 -1/2 1>]


[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 9/7
[[Eigenmonzo]]s: 2, 11/9, 9/7


Lattice basis: 3/2 0.9878 6/5 1.4312
Lattice basis: 3/2 0.9878 6/5 1.4312
Line 60: Line 62:
Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|]
Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|]


[[generator|Generators]]: 2, 3, 5
[[Generator]]s: 2, 3, 5


[[EDO|Edos]]: [[12edo|12]], [[15edo|15]], [[22edo|22]], [[37edo|37]], [[49edo|49]]
{{EDOs|legend=1| 12, 15, 22, 27e, 34d, 49 }}


Badness: 0.000469
Badness: 0.000469


Scales: [[ares12|ares12]]
Scales: [[ares12]]


==Vulcan==
== Vulcan ==
Commas: 56/55, 64/63
Commas: 56/55, 64/63


Line 75: Line 77:
Generators: 2, 3, 5
Generators: 2, 3, 5


EDOs: 5, 10, 12, 15
{{EDOs|legend=1| 5, 10, 12, 15, 27e }}


Badness: 0.000577
Badness: 0.000577
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