310edo: Difference between revisions
m Move from stub to todo:expand - it’s right on the border but I think there’s enough to build upon that the type of editor who enjoys working on todo:expand stuff will prefer it over the type who enjoys working on stubs |
Added more theory |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | |||
It inherits its 2.5.7 subgroup from 31edo. It is usable in the 2.5.7.13(.15).17.19 subgroup, being consistent in the tonality diamond of {1, 5, 7, 13, 15, 17, 19}. Note that adding harmonic 15 to the subgroup would be the same as adding harmonic 3, but many ratios of 15 are well represented, especially [[15/13]]. For that reason [[3/2]] is in that diamond, but other intervals of 3 are not. A notable chord using these odds is the 10:13:15 triad, though a much better system of around the same size to utilise it is [[313edo]], which tempers out [[676/675]]. While this system could be interesting, its is nowhere near the best of its size, and for most purposes [[311edo]] is better instead. | |||
It is part of the [[optimal ET sequence]] for the [[31-5-commatic]], [[fantastic]], [[quadrasruta]] and [[wizard]] temperaments. | It is part of the [[optimal ET sequence]] for the [[31-5-commatic]], [[fantastic]], [[quadrasruta]] and [[wizard]] temperaments. | ||
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== Odd harmonics == | == Odd harmonics == | ||
{{Harmonics in equal|310}} | {{Harmonics in equal|310}} | ||