388edo: Difference between revisions

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 about 3.09 [[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.

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 [[Very high accuracy temperaments #Raider|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. [[neusec]], the 190&198 temperament. By tempering out cuthbert it [[support]]s the [[cuthbert triad]], in addition to [[sinbadmic chords]].

! rowspan="2" | Subgroup

! rowspan="2" | [[Comma list]]

! rowspan="2" | Optimal<br>8ve stretch (¢)

! colspan="2" | Tuning error

! Generator<br>(reduced)

! Cents<br>(reduced)

! Associated<br>ratio