380edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | |||
== Theory == | == Theory == | ||
380edo notably provides the [[optimal patent val]] for the 2.3.11 [[neutral]] temperament. It has particularly accurate approximations of primes 23 and 29. Approximations of 7, 13, 17, and 19 are also very good. | 380edo notably provides the [[optimal patent val]] for the 2.3.11 [[subgroup]] [[neutral]] temperament. It has particularly accurate approximations of primes 23 and 29. Approximations of 7, 13, 17, and 19 are also very good. | ||
[[File:neutral_380edo.png|thumb|alt=neutral_380edo.png|Neutral in 380edo]] | [[File:neutral_380edo.png|thumb|alt=neutral_380edo.png|Neutral in 380edo]] | ||
=== Odd harmonics === | |||
{{Harmonics in equal|380}} | |||
=== Subsets and supersets === | |||
Since 380 factors into {{factorization|380}}, 380edo has subset edos {{EDOs| 2, 4, 5, 10, 19, 20, 38, 76, 95, and 190 }}. | |||
== Scales == | == Scales == | ||
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* [[Omahat]] | * [[Omahat]] | ||
[[Category:Neutral]] | [[Category:Neutral]] | ||
Latest revision as of 14:48, 20 February 2025
| ← 379edo | 380edo | 381edo → |
380 equal divisions of the octave (abbreviated 380edo or 380ed2), also called 380-tone equal temperament (380tet) or 380 equal temperament (380et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 380 equal parts of about 3.16 ¢ each. Each step represents a frequency ratio of 21/380, or the 380th root of 2.
Theory
380edo notably provides the optimal patent val for the 2.3.11 subgroup neutral temperament. It has particularly accurate approximations of primes 23 and 29. Approximations of 7, 13, 17, and 19 are also very good.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.90 | -1.05 | +0.65 | +1.35 | +1.31 | -0.53 | +1.20 | -0.74 | -0.67 | -0.25 | +0.15 |
| Relative (%) | -28.6 | -33.3 | +20.5 | +42.8 | +41.6 | -16.7 | +38.2 | -23.6 | -21.2 | -8.1 | +4.6 | |
| Steps (reduced) |
602 (222) |
882 (122) |
1067 (307) |
1205 (65) |
1315 (175) |
1406 (266) |
1485 (345) |
1553 (33) |
1614 (94) |
1669 (149) |
1719 (199) | |
Subsets and supersets
Since 380 factors into 22 × 5 × 19, 380edo has subset edos 2, 4, 5, 10, 19, 20, 38, 76, 95, and 190.