1331/1323: Difference between revisions

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'''1331/1323''', the '''aphrowe comma''', is an [[11-limit]], and 3.7.11 subgroup, comma ~~that is~~ the ~~difference between a stack~~ of two intervals of [[11/7]] and [[27/11]]. Tempering it out in the 3.7.11 subgroup provides [[~~mintaka~~]] temperament, which is one of the simplest temperaments in this subgroup with decent accuracy, and creates a [[5L 2s (3/1-equivalent)|5L 2s]] macrodiatonic scale generated by 11/7 against the [[3/1|tritave]].

'''1331/1323''', the '''aphrowe comma''', is an [[11-limit]], and 3.7.11 subgroup, comma of approximately 10.4 cents. Tempering this out splits the interval of [[7/1]] into three major sevenths of [[21/11]], or [[8/7]] into three minor seconds of [[22/21]] (and therefore [[12/11]] into two of these intervals), the latter equivalence giving rise to this comma's [[S-expression]] as (S22 = [[484/483]])<sup>2</sup> × (S23 = [[529/528]]). From a no-twos point of view, it can also be seen as splitting [[27/7]] into three minor sixths of [[11/7]] (and thus equating [[27/11]] to two of them).

== Temperaments ==

Tempering it out in the 3.7.11 subgroup provides [[Mintaka]] temperament, which is one of the simplest temperaments in this subgroup with decent accuracy, and creates a [[5L 2s (3/1-equivalent)|5L 2s]] macrodiatonic scale generated by 11/7 against the [[3/1|tritave]].

[[Category:Commas with unknown etymology]]

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-'''1331/1323''', the '''aphrowe comma''', is an [[11-limit]], and 3.7.11 subgroup, comma that is the difference between a stack of two intervals of [[11/7]] and [[27/11]]. Tempering it out in the 3.7.11 subgroup provides [[mintaka]] temperament, which is one of the simplest temperaments in this subgroup with decent accuracy, and creates a [[5L 2s (3/1-equivalent)|5L 2s]] macrodiatonic scale generated by 11/7 against the [[3/1|tritave]].
+'''1331/1323''', the '''aphrowe comma''', is an [[11-limit]], and 3.7.11 subgroup, comma of approximately 10.4 cents. Tempering this out splits the interval of [[7/1]] into three major sevenths of [[21/11]], or [[8/7]] into three minor seconds of [[22/21]] (and therefore [[12/11]] into two of these intervals), the latter equivalence giving rise to this comma's [[S-expression]] as (S22 = [[484/483]])<sup>2</sup> × (S23 = [[529/528]]). From a no-twos point of view, it can also be seen as splitting [[27/7]] into three minor sixths of [[11/7]] (and thus equating [[27/11]] to two of them).
+== Temperaments ==
+Tempering it out in the 3.7.11 subgroup provides [[Mintaka]] temperament, which is one of the simplest temperaments in this subgroup with decent accuracy, and creates a [[5L 2s (3/1-equivalent)|5L 2s]] macrodiatonic scale generated by 11/7 against the [[3/1|tritave]].
+[[Category:Commas with unknown etymology]]