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'''472edo''' is the [[EDO|equal division of the octave]] into 472 parts of 2.54237 [[cent]]s each.
{{Infobox ET}}
{{ED intro}}


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.
== Theory ==
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]].  


It is a [[zeta peak integer edo]].
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 ===
{{Harmonics in equal|472}}
{{Harmonics in equal|472}}


[[Category:Equal divisions of the octave]]
=== Subsets and supersets ===
[[Category:Zeta]]
Since 472 factors into {{factorization|472}}, 472edo has subset edos {{EDOs| 2, 4, 8, 59, 118, and 236 }}.
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3.5.7
| 2401/2400, 32805/32768, {{monzo| 8 14 -13 }}
| [{{val| 472 748 1096 1325 }}]
| +0.0435
| 0.0814
| 3.20
|-
| 2.3.5.7.11
| 2401/2400, 9801/9800, 32805/32768, 46656/46585
| [{{val| 472 748 1096 1325 1633 }}]
| +0.0130
| 0.0950
| 3.74
|-
| 2.3.5.7.11.13
| 729/728, 1575/1573, 2200/2197, 2401/2400, 4096/4095
| [{{val| 472 748 1096 1325 1633 1747 }}]
| −0.0341
| 0.1365
| 5.37
|}
 
=== Rank-2 temperaments ===
Note: 5-limit temperaments supported by [[118edo|118et]] are not included.
 
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
|-
| 1
| 69\472
| 175.42
| 448/405
| [[Sesquiquartififths]]
|-
| 1
| 137\472
| 348.31
| 57344/46875
| [[Subneutral]]
|-
| 1
| 205\472
| 521.19
| 875/648
| [[Maviloid]]
|-
| 2
| 69\472
| 175.42
| 448/405
| [[Bisesqui]]
|-
| 8
| 196\472<br />(19\472)
| 498.31<br />(48.31)
| 4/3<br />(36/35)
| [[Octant]]
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
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