332edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
332edo tempers out 118098/117649, | 332edo is [[consistent]] to the [[7-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], [[19683/19600]], 118098/117649, and 29360128/29296875 in the 7-limit. It provides the [[optimal patent val]] for 11-, 13-, and 17-limit [[sedia]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal}} | {{Harmonics in equal|332}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
332 factors into | Since 332 factors into {{factorisation|332}}, 332edo has subset edos {{EDOs| 2, 4, 83, and 166 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| 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 | ||
| | |||
|- | |- | ||
|2.3.5 | ! [[TE error|Absolute]] (¢) | ||
|{{monzo|-13 17 -6}}, {{monzo|-53 10 16}} | ! [[TE simple badness|Relative]] (%) | ||
|{{mapping|332 526 771}} | |- | ||
| 0.0955 | | 2.3.5 | ||
| {{monzo| -13 17 -6 }}, {{monzo| -53 10 16 }} | |||
| {{mapping| 332 526 771 }} | |||
| +0.0955 | |||
| 0.2778 | | 0.2778 | ||
| 7.69 | | 7.69 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|2401/2400, 19683/19600, 29360128/29296875 | | 2401/2400, 19683/19600, 29360128/29296875 | ||
|{{mapping|332 526 771 932}} | | {{mapping| 332 526 771 932 }} | ||
| 0.0851 | | +0.0851 | ||
| 0.2412 | | 0.2412 | ||
| 6.67 | | 6.67 | ||
| Line 42: | Line 40: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|33\332 | | 33\332 | ||
|119.28 | | 119.28 | ||
|15/14 | | 15/14 | ||
|[[Septidiasemi]] | | [[Septidiasemi]] | ||
|- | |- | ||
|1 | | 1 | ||
|75\332 | | 75\332 | ||
|271.08 | | 271.08 | ||
|1024/875 | | 1024/875 | ||
|[[Quasiorwell]] | | [[Quasiorwell]] | ||
|- | |- | ||
|1 | | 1 | ||
|127\332 | | 127\332 | ||
|459.04 | | 459.04 | ||
|125/96 | | 125/96 | ||
|[[Majvam]] | | [[Majvam]] | ||
|- | |- | ||
|1 | | 1 | ||
|143\332 | | 143\332 | ||
|516.87 | | 516.87 | ||
|27/20 | | 27/20 | ||
|[[Gravity]] | | [[Gravity]] | ||
|- | |- | ||
|2 | | 2 | ||
|143\332<br>(23\332) | | 143\332<br />(23\332) | ||
|516.87<br>(83.13) | | 516.87<br />(83.13) | ||
|27/20<br>(21/20) | | 27/20<br />(21/20) | ||
|[[Harry]] | | [[Harry]] | ||
|- | |- | ||
|2 | | 2 | ||
|45\332 | | 45\332 | ||
|162.65 | | 162.65 | ||
|1125/1024 | | 1125/1024 | ||
|[[Kwazy]] | | [[Kwazy]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
[[Category:Sedia]] | |||