388edo: Difference between revisions
Cleanup |
Mention more 5-limit commas by community request |
||
| Line 3: | Line 3: | ||
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 }}, in the 5-limit, [[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]]. | 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]]. | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Consistent]] | [[Category:Consistent]] | ||
[[Category:Cuthbert]] | [[Category:Cuthbert]] | ||
Revision as of 14:50, 19 July 2021
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 cents 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, [23 6 -14⟩, the tricot comma, [39 -29 3⟩, the minortone comma, [-16 35 -17⟩, and the raider comma, [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.