320edo: Difference between revisions

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The '''320 equal ~~division~~''' divides the [[octave]] into 320 [[equal]] parts of precisely 3.75 [[cent]]s each.

{{Infobox ET

| Prime factorization = 2<sup>6</sup> × 5

| Step size = 3.75000¢

| Fifth = 187\320 (701.25¢)

| Semitones = 29:25 (108.75¢ : 93.75¢)

| Consistency = 19

}}

The '''320 equal divisions of the octave''' ('''320edo'''), or the '''320(-tone) equal temperament''' ('''320tet''', '''320et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 320 [[equal]] parts of precisely 3.75 [[cent]]s each.

It tempers out 65625/65536 (horwell) and 420175/419904 (wizma) in the 7-limit and [[441/440]], [[8019/8000]] and [[9801/9800]] in the 11-limit, and so supports the [[varuna]] temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the [[optimal patent val]]. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out [[729/728]], [[1001/1000]], [[1575/1573]], [[4225/4224]] and [[6656/6655]] in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to a rank-3 temperament.

== Theory ==

320et tempers out 65625/65536 (horwell) and 420175/419904 (wizma) in the 7-limit and [[441/440]], [[8019/8000]] and [[9801/9800]] in the 11-limit, and so supports the [[varuna]] temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the [[optimal patent val]]. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out [[729/728]], [[1001/1000]], [[1575/1573]], [[4225/4224]] and [[6656/6655]] in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to a rank-3 temperament.

=== Prime harmonics ===

@@ Line 1: / Line 1: @@
-The '''320 equal division''' divides the [[octave]] into 320 [[equal]] parts of precisely 3.75 [[cent]]s each.
+{{Infobox ET
+| Prime factorization = 2<sup>6</sup> × 5
+| Step size = 3.75000¢
+| Fifth = 187\320 (701.25¢)
+| Semitones = 29:25 (108.75¢ : 93.75¢)
+| Consistency = 19
+}}
+The '''320 equal divisions of the octave''' ('''320edo'''), or the '''320(-tone) equal temperament''' ('''320tet''', '''320et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 320 [[equal]] parts of precisely 3.75 [[cent]]s each.
-It tempers out 65625/65536 (horwell) and 420175/419904 (wizma) in the 7-limit and [[441/440]], [[8019/8000]] and [[9801/9800]] in the 11-limit, and so supports the [[varuna]] temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the [[optimal patent val]]. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out [[729/728]], [[1001/1000]], [[1575/1573]], [[4225/4224]] and [[6656/6655]] in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to a rank-3 temperament.
+== Theory ==
+et tempers out 65625/65536 (horwell) and 420175/419904 (wizma) in the 7-limit and [[441/440]], [[8019/8000]] and [[9801/9800]] in the 11-limit, and so supports the [[varuna]] temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the [[optimal patent val]]. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out [[729/728]], [[1001/1000]], [[1575/1573]], [[4225/4224]] and [[6656/6655]] in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to a rank-3 temperament.
 === Prime harmonics ===