310edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|310}}
{{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.


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It is part of the [[optimal ET sequence]] for the [[31-5-commatic]], [[fantastic]], [[quadrasruta]] and [[wizard]] temperaments.
 
As a multiple of 10 and 31, it supports many [[10th-octave temperaments]] and [[31st-octave temperaments]].
 
== Odd harmonics ==
{{Harmonics in equal|310}}