472edo: Difference between revisions

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'''472edo''' is the [[EDO|equal division of the octave]] into 472 parts of 2.~~54237~~ [[cent]]s each.

{{Infobox ET

| Prime factorization = 2<sup>3</sup> × 59

| Step size = 2.54237¢

| Fifth = 276\472 (701.69¢) (→ [[118edo|69\118]])

| Semitones = 44:36 (111.86¢ : 91.53¢)

| Consistency = 11

}}

The '''472 equal divisions of the octave''' ('''472edo'''), or the '''472(-tone) equal temperament''' ('''472tet''', '''472et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 472 parts of about 2.54 [[cent]]s each.

== Theory ==

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.

@@ Line 1: / Line 1: @@
-'''472edo''' is the [[EDO|equal division of the octave]] into 472 parts of 2.54237 [[cent]]s each.
+{{Infobox ET
+| Prime factorization = 2<sup>3</sup> × 59
+| Step size = 2.54237¢
+| Fifth = 276\472 (701.69¢) (→ [[118edo|69\118]])
+| Semitones = 44:36 (111.86¢ : 91.53¢)
+| Consistency = 11
+}}
+The '''472 equal divisions of the octave''' ('''472edo'''), or the '''472(-tone) equal temperament''' ('''472tet''', '''472et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 472 parts of about 2.54 [[cent]]s each.
+== Theory ==
 edo 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.