472edo: Difference between revisions
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
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== Theory == | == Theory == | ||
472edo is [[ | 472edo is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by [[tempering out]] the [[schisma]] and the [[parakleisma]], but the approximation to higher harmonics are much improved. It is a [[zeta peak integer edo]], [[consistent]] to the [[11-odd-limit]] or the no-13 [[29-odd-limit]]. | ||
In the 7-limit, the equal temperament tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[maviloid]] temperament, the [[Schismatic family #Bisesqui|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. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 472 factors into | Since 472 factors into {{factorization|472}}, 472edo has subset edos {{EDOs| 2, 4, 8, 59, 118, and 236 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| [[Octant]] | | [[Octant]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
[[ | |||