472edo: Difference between revisions
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'''472edo''' is the [[EDO|equal division of the octave]] into 472 parts of 2.54237 | '''472edo''' is the [[EDO|equal division of the octave]] into 472 parts of 2.54237 [[cent]]s each. | ||
472edo is [[consistent]] to the [[11-odd-limit]]. It is [[Enfactoring|enfactored]] in the 5-limit, with the same tuning as 118edo, defined by tempering out the [[schisma]] and the [[parakleisma]]. In the 7-limit, it tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256 , [[Support|supporting]] the [[Breedsmic temperaments #Maviloid|maviloid]] temperament, the [[Schismatic family #Bisesqui|bisesqui temperament]], and the [[Schismatic family #Octant|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant. | |||
It is a [[zeta peak integer edo]]. | It is a [[zeta peak integer edo]]. | ||
{{ | === Prime harmonics === | ||
{{Harmonics in equal|472}} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Zeta]] | [[Category:Zeta]] | ||
Revision as of 18:28, 30 January 2022
472edo is the equal division of the octave into 472 parts of 2.54237 cents each.
472edo is consistent to the 11-odd-limit. It is enfactored in the 5-limit, with the same tuning as 118edo, defined by tempering out the schisma and the parakleisma. In the 7-limit, it tempers out 2401/2400, 2460375/2458624, and 30623756184/30517578125; in the 11-limit, 9801/9800, 46656/46585, 117649/117612, and 234375/234256 , supporting the maviloid temperament, the bisesqui temperament, and the octant temperament. Using the patent val, it tempers out 729/728, 1575/1573, 2200/2197, 4096/4095, and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.
It is a zeta peak integer edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.26 | +0.13 | -0.18 | +0.38 | +1.00 | -0.72 | -0.06 | -0.31 | +0.08 | -0.97 |
| Relative (%) | +0.0 | -10.2 | +5.0 | -7.2 | +14.8 | +39.2 | -28.2 | -2.2 | -12.1 | +3.3 | -38.1 | |
| Steps (reduced) |
472 (0) |
748 (276) |
1096 (152) |
1325 (381) |
1633 (217) |
1747 (331) |
1929 (41) |
2005 (117) |
2135 (247) |
2293 (405) |
2338 (450) | |