No-fives subgroup temperaments: Difference between revisions
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Hemif tempers out the [[parahemif comma]], equating a [[Pythagorean apotome]] with a stack of two septimal third-tones of [[28/27]], and splits the fifth in two. In this temperament, the interval class of [[7/1|7]] is found at +13 steps, as a semi-augmented sixth (C–A{{demisharp2}}). It also equates the large septimal diesis of [[49/48]] with the [[Pythagorean comma]]. This means the fifth should be tuned sharp and the septimal third-tone should be flattened to a somewhat large quartertone which can be used as the undecimal quartertone of [[33/32]], leading to a natural 11-limit extension where [[243/242]] and [[896/891]] are tempered out. | Hemif tempers out the [[parahemif comma]], equating a [[Pythagorean apotome]] with a stack of two septimal third-tones of [[28/27]], and splits the fifth in two. In this temperament, the interval class of [[7/1|7]] is found at +13 steps, as a semi-augmented sixth (C–A{{demisharp2}}). It also equates the large septimal diesis of [[49/48]] with the [[Pythagorean comma]]. This means the fifth should be tuned sharp and the septimal third-tone should be flattened to a somewhat large quartertone which can be used as the undecimal quartertone of [[33/32]], leading to a natural 11-limit extension where [[243/242]] and [[896/891]] are tempered out. | ||
Hemif is the common [[restriction]] of [[hemififths]] (41 & 58) and [[salsa]] (24 & 41), | Hemif is the common [[restriction]] of [[breedsmic temperaments #Hemififths|hemififths]] (41 & 58) and [[schismatic family #Salsa|salsa]] (24 & 41), as well as the low-accuracy [[meantone family #Mohamaq|mohamaq]] (7d & 24). It is the add-7 [[extension]] of [[rastmic clan #Namo|namo]]. [[Weak extension]]s of hemif include [[diaschismic family #Sruti|sruti]] (24 & 58) and [[tetracot family #Bunya|bunya]] (41 & 75). | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||