Augmented family: Difference between revisions

Trisected: review
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Trisected: + subgroup temperaments
 
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== Trisected ==
== Trisected ==
{{Main|Trisected}}
{{Main|Trisected}}
{{See also|Subgroup temperaments #Trisect}}
Trisected tempers out [[1029/1024]] and [[1029/1000]], so it is the intersection of augmented and [[slendric]]. It can be described as the {{nowrap| 15 & 36 }} temperament.
Trisected tempers out [[1029/1024]] and [[1029/1000]], so it is the intersection of augmented and [[slendric]]. It can be described as the {{nowrap| 15 & 36 }} temperament.


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=== 11-limit ===
=== 11-limit ===
This extension also tempers out [[4000/3993]], equating 3 intervals of [[11/10]] with [[4/3]].
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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=== 13-limit ===
=== 13-limit ===
This extension is natural since it equates the [[10/7]], which is 1/3 of [[3/1]] since 1029/1000 is tempered out, with [[13/9]], thus tempering out [[91/90]] and [[2197/2187]].
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13