Augmented family: Difference between revisions
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The '''augmented family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the diesis a.k.a. augmented comma, [[128/125]], the amount by which three [[5/4]] major thirds fall short of an [[ | The '''augmented family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the diesis a.k.a. augmented comma, [[128/125]], the amount by which three [[5/4]] major thirds fall short of an [[octave]], and so identifies the major third with the 1/3-octave. Hence it has the same 400-cent 5/4-approximations as [[12edo]]. | ||
== Augmented == | == Augmented == | ||
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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 | ||