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" Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
476 factors into | 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 == | ||
{ | {| 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 | ||
| 1.82 | | 1.82 | ||
| Line 36: | Line 45: | ||
| 0.1586 | | 0.1586 | ||
| 6.29 | | 6.29 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| 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 | ||
| Line 58: | Line 74: | ||
| 4/3<br>(105/104) | | 4/3<br>(105/104) | ||
| [[Oquatonic]] (5-limit) | | [[Oquatonic]] (5-limit) | ||
|} | |||
<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 | |||