1331/1323: Difference between revisions
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'''1331/1323''', the '''aphrowe comma''', is an [[11-limit]], and 3.7.11 subgroup, comma | '''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]]. | |||
Revision as of 05:27, 11 October 2024
| Interval information |
trilo-aruru comma
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)2 × (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 macrodiatonic scale generated by 11/7 against the tritave.