1323edo: Difference between revisions
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
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}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1323edo is the smallest edo [[consistency|distinctly consistent]] in the [[29-odd-limit]]. | 1323edo is the smallest edo [[consistency|distinctly consistent]] in the [[29-odd-limit]]. It is [[enfactoring|enfactored]] in the 7-limit, sharing the same excellent 7-limit approximation with [[441edo]], but it makes for a great higher-limit system by splitting each step of 441edo into three. | ||
It provides the [[optimal patent val]] for the 11-limit [[trinealimmal]] temperament, which has a period of 1\27 octave | It provides the [[optimal patent val]] for the 11-limit [[trinealimmal]] temperament, which has a period of 1\27 octave. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
1323 | Since 1323 factors into {{factorization|1323}}, 1323edo has subset edos {{EDOs| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 7, 27, and 441edo are members of the [[zeta edo]]s. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
! Periods<br>per 8ve | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| 27 | | 27 | ||
| 299\1323<br>(5\1323) | | 299\1323<br />(5\1323) | ||
| 271.201<br>(4.535) | | 271.201<br />(4.535) | ||
| 1375/1176<br>(?) | | 1375/1176<br />(?) | ||
| [[Trinealimmal]] | | [[Trinealimmal]] | ||
|} | |} | ||
<nowiki>* | <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 | ||