480edo: Difference between revisions
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{{EDO intro|480}} | {{EDO intro|480}} | ||
480edo is | 480edo is [[consistent]] in the [[11-odd-limit]] with a sharp tendency in the first few [[harmonic]]s. | ||
It provides the [[optimal patent val]] for the 11-limit rank-3 [[semiporwell]] temperament, and the 7- and 11-limit [[twilight]] temperament. It also [[support]]s the 6th-octave [[hemidomain]] temperament and the 24th-octave [[chromium]] temperament on the [[patent val]] in the 11-limit and extends chromium via the 480fgg [[val]] into the 17-limit. It is worth tuning that 480fgg val has a lower [[TE error]] than the patent val. The 480bde val supports the 24th-octave rank-3 [[rabic]] temperament. | |||
=== Harmonics === | |||
{{Harmonics in equal|480}} | |||
=== Subsets and supersets === | |||
480edo is a [[Highly composite equal division #Largely composite numbers|largely composite edo]]. Since 480 factors into {{factorization|480}}, 480edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, and 240 }}. 960edo, which doubles it, corrects harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], and [[11/1|11]] to near-just qualities, and [[1920edo]] corrects harmonic [[3/1|3]]. | |||
Revision as of 06:34, 3 November 2023
| ← 479edo | 480edo | 481edo → |
480edo is consistent in the 11-odd-limit with a sharp tendency in the first few harmonics.
It provides the optimal patent val for the 11-limit rank-3 semiporwell temperament, and the 7- and 11-limit twilight temperament. It also supports the 6th-octave hemidomain temperament and the 24th-octave chromium temperament on the patent val in the 11-limit and extends chromium via the 480fgg val into the 17-limit. It is worth tuning that 480fgg val has a lower TE error than the patent val. The 480bde val supports the 24th-octave rank-3 rabic temperament.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.54 | +1.19 | +1.17 | +1.09 | +1.18 | -0.53 | -0.77 | +0.04 | -0.01 | -0.78 | -0.77 |
| Relative (%) | +21.8 | +47.5 | +47.0 | +43.6 | +47.3 | -21.1 | -30.7 | +1.8 | -0.5 | -31.2 | -31.0 | |
| Steps (reduced) |
761 (281) |
1115 (155) |
1348 (388) |
1522 (82) |
1661 (221) |
1776 (336) |
1875 (435) |
1962 (42) |
2039 (119) |
2108 (188) |
2171 (251) | |
Subsets and supersets
480edo is a largely composite edo. Since 480 factors into 25 × 3 × 5, 480edo has subset edos 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, and 240. 960edo, which doubles it, corrects harmonics 5, 7, 9, and 11 to near-just qualities, and 1920edo corrects harmonic 3.