576edo: Difference between revisions
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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== Theory == | == Theory == | ||
576edo is [[consistent]] in the 7-odd-limit, though the error on harmonic [[5/4|5]] is quite large. As a corollary, 576edo is an excellent 2.3.7 subgroup tuning. It tempers out the [[septimal ennealimma]], | 576edo is [[consistent]] in the 7-odd-limit, though the error on harmonic [[5/4|5]] is quite large. As a corollary, 576edo is an excellent 2.3.7 subgroup tuning. It tempers out the [[septimal ennealimma]], assigning [[7/6]] to 2\9, as well as {{monzo| 99 -66 0 2 }}, {{monzo| 110 -57 0 -7 }} , and {{monzo| 88 -75 0 11 }}. In the 5-limit, the patent val of 576edo [[support]]s the [[atomic]] temperament and the [[amity]] temperament. The 576c val supports [[maquila]]. The 576ccd val, {{val| 576 913 1336 1618 }}, is a tuning for the [[garibaldi]] temperament in the 7-limit. In addition, in this case 5/4 comes from [[72edo]], and 7/4 comes form 288edo. | ||
In higher limits, the 2.3.7 subgroup can be used with optional additions of [[19/16|19]] or [[29/16|29]], or fractional subgroups using [[13/10]]. | In higher limits, the 2.3.7 subgroup can be used with optional additions of [[19/16|19]] or [[29/16|29]], or fractional subgroups using [[13/10]]. | ||