576edo: Difference between revisions
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In the 5-limit, 576edo supports 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|garibaldi]] temperament in the 7-limit. In addition, in this case 5/4 comes from [[72edo]], and 7/4 comes form 288edo. | In the 5-limit, 576edo supports 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|garibaldi]] temperament in the 7-limit. In addition, in this case 5/4 comes from [[72edo]], and 7/4 comes form 288edo. | ||
576edo supports a messed-up version of the [[Rectified Hebrew]] scale, but with step hardness of 5:3 instead of 3:2. | 576edo supports a messed-up version of the [[Rectified Hebrew]] scale, but with step hardness of 5:3 instead of 3:2, and from regular temperament theory perspective, 5/4 is reached via 359 third-tone generators down instead of 6 generators up. The relationship that 7/4 is 15 generators and 13/8 is 13 steps is still preserved. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|576|columns=11}} | {{Harmonics in equal|576|columns=11}} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 163\576 | |||
| 339.583 | |||
| 243/200 | |||
| [[Amity]] | |||
|- | |||
| 12 | |||
| 239\576<br>(1\576) | |||
| 497.916<br>(2.083) | |||
| 4/3<br>(32805/32768) | |||
| [[Atomic]] | |||
|} | |||
<!-- 3-digit number --> | |||
[[Category:Amity]] | [[Category:Amity]] | ||
[[Category:Atomic]] | [[Category:Atomic]] | ||