476edo: Difference between revisions

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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|476}}
{{ED intro}}


== Theory ==
== Theory ==
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=== Subsets and supersets ===
=== Subsets and supersets ===
476 factors into 2<sup>2</sup> × 7 × 17, with subset edos {{EDOs| 2, 4, 7, 14, 17, 28, 34, 68, 119, and 238 }}. [[952edo]], which doubles it, gives a good correction to the harmonic 3, but unfortunately it is inconsistent in the [[5-odd-limit]].
476 factors into {{factorisation|476}}, with subset edos {{EDOs| 2, 4, 7, 14, 17, 28, 34, 68, 119, and 238 }}. [[952edo]], which doubles it, gives a good correction to the harmonic 3, but unfortunately it is inconsistent in the [[5-odd-limit]].


== Regular temperament properties ==
== Regular temperament properties ==
{{comma basis begin}}
{| 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]] (%)
|-
|-
| 2.9
| 2.9
| {{monzo| 1509 -476 }}
| {{monzo| 1509 -476 }}
| {{mapping| 476 1509 }}
| {{mapping| 476 1509 }}
| -0.0460
| −0.0460
| 0.0460
| 0.0460
| 1.82
| 1.82
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| 0.1586
| 0.1586
| 6.29
| 6.29
{{comma basis end}}
|}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{{rank-2 begin}}
{| 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
| 1
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| 4/3<br>(105/104)
| 4/3<br>(105/104)
| [[Oquatonic]] (5-limit)
| [[Oquatonic]] (5-limit)
{{rank-2 end}}
|}
{{orf}}
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct