576edo: Difference between revisions

{{ED intro}}

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]].

Since 576 factors as {{factorization|576}}, 576edo has subset edos {{EDOs| 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, and 288 }}, of which {{EDOs|12, 24, 72, and 96}} are particularly notable. Overall, 576edo contains a number of notable divisions that are multiples of 12, and it is a [[Highly composite equal division#Highly factorable numbers|highly factorable]] edo.

 

[[1152edo]], which is also a highly factorable edo, divides the edostep in two and corrects the mapping for 5.

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Periods<br />per 8ve

! Generator*

! Cents*

! Associated<br />ratio*

| [[Amity]] (576)

| 239\576<br />(1\576)

| 497.916<br />(2.083)

| 4/3<br />(32805/32768)

| [[Atomic]] (576)

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct