576edo: Difference between revisions
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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]], assining [[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, | 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]], assining [[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]]. | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
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|- | |- | ||
| 12 | | 12 | ||
| 239\576<br>(1\576) | | 239\576<br />(1\576) | ||
| 497.916<br>(2.083) | | 497.916<br />(2.083) | ||
| 4/3<br>(32805/32768) | | 4/3<br />(32805/32768) | ||
| [[Atomic]] (576) | | [[Atomic]] (576) | ||
{{rank-2 end}} | |||
{{orf}} | |||