149edo: Difference between revisions
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" Tags: Mobile edit Mobile web edit |
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== Theory == | == Theory == | ||
149edo is the smallest division which is [[consistency|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous|ominous]] in the 13- and 17-limit. | 149edo is the smallest division which is [[consistency|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous|ominous]] in the 13- and 17-limit. | ||
It is also usable in the [[23-limit]], only missing [[19/11]], [[21/11]], and their [[octave complement]]s in the [[23-odd-limit]]. In the [[27-odd-limit]], additional inconsistencies include [[25/21]], [[25/22]], [[27/20]], [[27/25]], [[27/19]], and their octave complements. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
149edo is the 35th [[prime edo]]. | 149edo is the 35th [[prime edo]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||