480edo: Difference between revisions
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480edo is [[consistent]] in the [[11-odd-limit]] with a sharp tendency in the first few [[harmonic]]s. | 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 | 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 noting that 480fgg val has a lower [[TE error]] than the patent val. The 480bde val supports the 24th-octave rank-3 [[rabic]] temperament. | ||
In the 2.7/5.11/7.23/13.17.19 subgroup ([[K*N subgroups|4*480 subgroup]]), 480edo is identical to [[1920edo]] and tempers out 44965/44954, 50578/50575, 2000033/2000000, 2283325/2283008, 163498496/163480075. | In the 2.7/5.11/7.23/13.17.19 subgroup ([[K*N subgroups|4*480 subgroup]]), 480edo is identical to [[1920edo]] and tempers out 44965/44954, 50578/50575, 2000033/2000000, 2283325/2283008, 163498496/163480075. | ||
Latest revision as of 05:38, 21 February 2025
| ← 479edo | 480edo | 481edo → |
480 equal divisions of the octave (abbreviated 480edo or 480ed2), also called 480-tone equal temperament (480tet) or 480 equal temperament (480et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 480 equal parts of exactly 2.5 ¢ each. Each step represents a frequency ratio of 21/480, or the 480th root of 2.
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 noting that 480fgg val has a lower TE error than the patent val. The 480bde val supports the 24th-octave rank-3 rabic temperament.
In the 2.7/5.11/7.23/13.17.19 subgroup (4*480 subgroup), 480edo is identical to 1920edo and tempers out 44965/44954, 50578/50575, 2000033/2000000, 2283325/2283008, 163498496/163480075.
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.