381edo: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
Expand |
||
| Line 2: | Line 2: | ||
{{ED intro}} | {{ED intro}} | ||
381edo is [[consistent]] to the [[13-odd-limit]] | 381edo is [[consistent]] to the [[13-odd-limit]] and almost the [[15-odd-limit]]; the only inconsistently mapped intervals in the 15-odd-limit are [[15/11]] and its [[octave complement]]. It has a sharp tendency, with odd [[harmonic]]s 3 through 15 all tuned sharp except for 11, which is very slightly flat. | ||
As an equal temperament, it [[tempering out|tempers out]] the [[vulture comma]], {{monzo| 24 -21 4 }}, in the 5-limit and 6144/6125 ([[porwell comma]]) and 250047/250000 ([[landscape comma]]) in the 7-limit. It provides the [[optimal patent val]] for the porwell planar temperament tempering out 6144/6125, and [[nessafof]], the {{nowrap| 99 & 282 }} temperament tempering out it and the landscape comma 250047/250000. | |||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 8: | Line 10: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 381 factors into {{ | Since 381 factors into primes as {{nowrap| 3 × 127 }}, 381edo contains [[3edo]] and [[127edo]] as subsets. | ||
[[Category:Porwell]] | [[Category:Porwell]] | ||
[[Category:Nessafof]] | [[Category:Nessafof]] | ||
Revision as of 10:44, 24 October 2025
| ← 380edo | 381edo | 382edo → |
381 equal divisions of the octave (abbreviated 381edo or 381ed2), also called 381-tone equal temperament (381tet) or 381 equal temperament (381et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 381 equal parts of about 3.15 ¢ each. Each step represents a frequency ratio of 21/381, or the 381st root of 2.
381edo is consistent to the 13-odd-limit and almost the 15-odd-limit; the only inconsistently mapped intervals in the 15-odd-limit are 15/11 and its octave complement. It has a sharp tendency, with odd harmonics 3 through 15 all tuned sharp except for 11, which is very slightly flat.
As an equal temperament, it tempers out the vulture comma, [24 -21 4⟩, in the 5-limit and 6144/6125 (porwell comma) and 250047/250000 (landscape comma) in the 7-limit. It provides the optimal patent val for the porwell planar temperament tempering out 6144/6125, and nessafof, the 99 & 282 temperament tempering out it and the landscape comma 250047/250000.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.41 | +1.09 | +1.25 | -0.14 | +0.42 | -1.02 | -1.45 | -1.50 | +0.34 | +1.42 |
| Relative (%) | +0.0 | +12.9 | +34.5 | +39.8 | -4.3 | +13.2 | -32.3 | -46.0 | -47.7 | +10.9 | +45.1 | |
| Steps (reduced) |
381 (0) |
604 (223) |
885 (123) |
1070 (308) |
1318 (175) |
1410 (267) |
1557 (33) |
1618 (94) |
1723 (199) |
1851 (327) |
1888 (364) | |
Subsets and supersets
Since 381 factors into primes as 3 × 127, 381edo contains 3edo and 127edo as subsets.