User:Eliora/377edo: Difference between revisions
Created page with "{{Infobox ET}} {{ED intro}} 377edo is consistent only in the 3-limit and represents lower harmonics poorly. Nonetheless, 2.7/5.9.13.17 subgroup is represented quite well. Some commas 377edo tempers out in this subgroup are 2000033/2000000, 4303125/4302592, and 3955078125/3954653486. === Odd harmonics === {{harmonics in equal|377}} === Subsets and supersets === Since 377 factors as {{Factorization|377}}, 377edo contains 13edo and 29edo as its subsets. Given..." |
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377 equal divisions of the octave (abbreviated 377edo or 377ed2), also called 377-tone equal temperament (377tet) or 377 equal temperament (377et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 377 equal parts of about 3.18 ¢ each. Each step represents a frequency ratio of 21/377, or the 377th root of 2.
377edo is consistent only in the 3-limit and represents lower harmonics poorly. Nonetheless, 2.7/5.9.13.17 subgroup is represented quite well. Some commas 377edo tempers out in this subgroup are 2000033/2000000, 4303125/4302592, and 3955078125/3954653486.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.49 | -1.17 | -1.19 | -0.20 | -0.65 | -0.21 | +0.33 | +0.08 | -1.49 | +0.31 | -1.22 |
| Relative (%) | +46.9 | -36.7 | -37.3 | -6.2 | -20.6 | -6.6 | +10.2 | +2.7 | -46.9 | +9.6 | -38.3 | |
| Steps (reduced) |
598 (221) |
875 (121) |
1058 (304) |
1195 (64) |
1304 (173) |
1395 (264) |
1473 (342) |
1541 (33) |
1601 (93) |
1656 (148) |
1705 (197) | |
Subsets and supersets
Since 377 factors as 13 × 29, 377edo contains 13edo and 29edo as its subsets.
Given the fact that this equal division does not support any obvious temperaments, the best way to use it is as a polychromatic tuning that is a superposition of 13edo and 29edo.