159edo: Difference between revisions
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More 23-limit commas that are tempered out... |
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* In the 19-limit, it is known to temper out 343/342 and 361/360, but since it is inconsistent in the 19-limit, there are other potential mappings available that temper out different commas. | * In the 19-limit, it is known to temper out 343/342 and 361/360, but since it is inconsistent in the 19-limit, there are other potential mappings available that temper out different commas. | ||
* In the 23-limit | * In the 23-limit, with the 19-limit skipped, this system is known to temper out 392/391, 460/459, 507/506, 529/528, 897/896, | ||
Notably, 159edo provides the [[optimal patent val]] for 11-limit guiron, 13-limit tritikleismic, the 13-limit rank-3 temperament [[Gamelismic family #Portending|portending]], as well as the 17-limit rank-6 temperament tempering out 273/272. In addition to this, it also supports both forms of the yarman temperament, with a generator of 2\159 which can be taken as an approximate 105/104. Both have a [[MOS]] of 79 or 80 notes to the octave, and have their optimal patent vals supplied by 159edo in 7-limit, 11-limit, 13-limit, 17-limit and even 19-limit forms. | Notably, 159edo provides the [[optimal patent val]] for 11-limit guiron, 13-limit tritikleismic, the 13-limit rank-3 temperament [[Gamelismic family #Portending|portending]], as well as the 17-limit rank-6 temperament tempering out 273/272. In addition to this, it also supports both forms of the yarman temperament, with a generator of 2\159 which can be taken as an approximate 105/104. Both have a [[MOS]] of 79 or 80 notes to the octave, and have their optimal patent vals supplied by 159edo in 7-limit, 11-limit, 13-limit, 17-limit and even 19-limit forms. | ||