212edo: Difference between revisions
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212edo is distinctly [[consistent]] in the [[15-odd-limit]] with harmonics of 3 through 13 all tuned flat. 212 = 4 × 53, and it shares the 3rd, 5th, and 13th [[harmonic]]s with [[53edo]], but the mapping differs for 7 and 11. | 212edo is distinctly [[consistent]] in the [[15-odd-limit]] with harmonics of 3 through 13 all tuned flat. 212 = 4 × 53, and it shares the 3rd, 5th, and 13th [[harmonic]]s with [[53edo]], but the mapping differs for 7 and 11. | ||
The equal temperament tempers out the same commas ([[15625/15552]], [[32805/32768]], [[amity comma|1600000/1594323]], etc.) as 53edo in the [[5-limit]]. In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma]]), and 4802000/4782969 ([[canousma]]). In the [[11-limit]], [[385/384]], [[1375/1372]], [[6250/6237]], [[9801/9800]] and [[14641/14580]]; in the [[13-limit]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]] and [[10648/10647]]. | |||
It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[Kleismic rank three family #Rank-3 kleismic|rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit. | It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[Kleismic rank three family #Rank-3 kleismic|rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
A step of 212edo is exactly 50 [[türk sent]]s. | Since 212 factors into 2<sup>2</sup> × 53, 212edo has subset edos {{EDOs| 2, 4, 53, and 106 }}. As such, it can be used to tune the period-53 [[cartography]] temperament and the period-106 [[boiler]] temperment. | ||
A step of 212edo is exactly 50 [[türk sent]]s. | |||
== Regular temperament properties == | == Regular temperament properties == | ||