388edo: Difference between revisions

Line 1:

The '''388 equal divisions of the octave''' ('''~~388edo~~'''), or the '''388(-tone) equal temperament''' ('''~~388tet~~''', '''~~388et~~''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 388 [[equal]] parts of 3.0928 [[cent]]s each.

The '''388 equal divisions of the octave''' ('''388EDO'''), or the '''388(-tone) equal temperament''' ('''388TET''', '''388ET''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 388 [[equal]] parts of 3.0928 [[cent]]s each.

~~388edo~~ is the first ~~edo~~ that is uniquely [[consistent]] through to the [[27-odd-limit]]; it is also consistent through the 37-odd-limit.

388EDO is the first EDO that is uniquely [[consistent]] through to the [[27-odd-limit]]; it is also consistent through the 37-odd-limit.

~~388et~~ tempers out the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[tricot comma]], {{monzo| 39 -29 3 }}, the [[minortone comma]], {{monzo| -16 35 -17 }}, and the [[raider comma]], {{monzo| 71 -99 31 }}, in the 5-limit, and provides a tuning with less error than any previous equal temperaments. It tempers out [[4375/4374]] and [[235298/234375]] in the 7-limit, and 5632/5625, [[3025/3024]] and [[9801/9800]] in the 11-limit and [[847/845]], [[1001/1000]] and [[4096/4095]] in the 13-limit. It is the [[optimal patent val]] for cuthbert temperament, which tempers out cuthbert, the 847/845 comma, and for a number of other temperaments tempering out cuthbert, e.g. 198&388. By tempering out cuthbert it supports the [[cuthbert triad]].

388EDO tempers out the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[tricot comma]], {{monzo| 39 -29 3 }}, the [[minortone comma]], {{monzo| -16 35 -17 }}, and the [[Very high accuracy temperaments|raider comma]], {{monzo| 71 -99 31 }}, in the 5-limit, and provides a tuning with less error than any previous equal temperaments. It tempers out [[4375/4374]] and [[Triwellismic temperaments|235298/234375]] in the 7-limit, and 5632/5625, [[3025/3024]] and [[9801/9800]] in the 11-limit and [[847/845]], [[1001/1000]] and [[4096/4095]] in the 13-limit. It is the [[optimal patent val]] for cuthbert temperament, which tempers out cuthbert, the 847/845 comma, and for a number of other temperaments tempering out cuthbert, e.g. 198&388. By tempering out cuthbert it supports the [[cuthbert triad]].

[[Category:Equal divisions of the octave]]

~~[[Category:Consistent]]~~

[[Category:Cuthbert]]

@@ Line 1: / Line 1: @@
-The '''388 equal divisions of the octave''' ('''388edo'''), or the '''388(-tone) equal temperament''' ('''388tet''', '''388et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 388 [[equal]] parts of 3.0928 [[cent]]s each.
+The '''388 equal divisions of the octave''' ('''388EDO'''), or the '''388(-tone) equal temperament''' ('''388TET''', '''388ET''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 388 [[equal]] parts of 3.0928 [[cent]]s each.
-edo is the first edo that is uniquely [[consistent]] through to the [[27-odd-limit]]; it is also consistent through the 37-odd-limit.
+EDO is the first EDO that is uniquely [[consistent]] through to the [[27-odd-limit]]; it is also consistent through the 37-odd-limit.
-et tempers out the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[tricot comma]], {{monzo| 39 -29 3 }}, the [[minortone comma]], {{monzo| -16 35 -17 }}, and the [[raider comma]], {{monzo| 71 -99 31 }}, in the 5-limit, and provides a tuning with less error than any previous equal temperaments. It tempers out [[4375/4374]] and [[235298/234375]] in the 7-limit, and 5632/5625, [[3025/3024]] and [[9801/9800]] in the 11-limit and [[847/845]], [[1001/1000]] and [[4096/4095]] in the 13-limit. It is the [[optimal patent val]] for cuthbert temperament, which tempers out cuthbert, the 847/845 comma, and for a number of other temperaments tempering out cuthbert, e.g. 198&amp;388. By tempering out cuthbert it supports the [[cuthbert triad]].
+EDO tempers out the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[tricot comma]], {{monzo| 39 -29 3 }}, the [[minortone comma]], {{monzo| -16 35 -17 }}, and the [[Very high accuracy temperaments|raider comma]], {{monzo| 71 -99 31 }}, in the 5-limit, and provides a tuning with less error than any previous equal temperaments. It tempers out [[4375/4374]] and [[Triwellismic temperaments|235298/234375]] in the 7-limit, and 5632/5625, [[3025/3024]] and [[9801/9800]] in the 11-limit and [[847/845]], [[1001/1000]] and [[4096/4095]] in the 13-limit. It is the [[optimal patent val]] for cuthbert temperament, which tempers out cuthbert, the 847/845 comma, and for a number of other temperaments tempering out cuthbert, e.g. 198&amp;388. By tempering out cuthbert it supports the [[cuthbert triad]].
+{{Primes in edo|edo=388|columns=11|start=2|prec=3}}
 [[Category:Equal divisions of the octave]]
-[[Category:Consistent]]
 [[Category:Cuthbert]]