319edo: Difference between revisions
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== Theory == | == Theory == | ||
319edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway its steps. The full 11-limit [[patent val]] is nonetheless a reasonable interpretation since the lower harmonics all tend sharp. Using this val, it [[tempering out|tempers out]] [[6144/6125]], [[10976/10935]], and {{monzo| 9 -10 9 -5 }} in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 15488/15435, 59290/59049, and [[65536/65219]] in the 11-limit. It [[support]]s [[mystery]] in the 5-limit and [[protolangwidge]]. | 319edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway its steps. Nonetheless, it provides the optimal patent val for 5-limit [[mystery]] temperament, which tempers out the [[29-comma]], despite poor 5-limit harmonic approximation. | ||
The full 11-limit [[patent val]] is nonetheless a reasonable interpretation since the lower harmonics all tend sharp. Using this val, it [[tempering out|tempers out]] [[6144/6125]], [[10976/10935]], and {{monzo| 9 -10 9 -5 }} in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 15488/15435, 59290/59049, and [[65536/65219]] in the 11-limit. It [[support]]s [[mystery]] in the 5-limit and [[protolangwidge]]. | |||
If we instead adopt the 2.9.… [[subgroup]] interpretation, then 2.9.15.21 is a good subgroup to start with. | If we instead adopt the 2.9.… [[subgroup]] interpretation, then 2.9.15.21 is a good subgroup to start with. | ||