472edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Cmloegcmluin (talk | contribs)
link to new page for Supports
Cleanup and expansion
Line 1: Line 1:
'''472edo''' is the [[EDO|equal division of the octave]] into 472 parts of 2.54237 cents each. It is consistent to the 11-limit, tempering out 32805/32768 (schisma) and 1224440064/1220703125 (parakleisma) in the 5-limit; 2401/2400, 2460375/2458624, and 30623756184/30517578125 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 234375/234256 in the 11-limit, [[support|supporting]] the [[Breedsmic temperaments|maviloid temperament]], the [[Schismatic family|bisesqui temperament]], and the [[Schismatic family|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.
'''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]].


{{Primes in edo|472|prec=3}}
=== 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

Approximation of prime harmonics in 472edo
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)