1323edo: Difference between revisions
Rank 2 temps, also notated 441 & 1308 despite not having a name, because it is listed on the augmented-cloudy equivalence continuum page. |
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 | 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 === | ||
{{Harmonics in equal|1323}} | {{Harmonics in equal|1323}} | ||
[[ | === Subsets and supersets === | ||
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 == | ||
=== Rank-2 temperaments === | |||
Note: 7-limit temperaments supported by 441et are not included. | |||
{| class="wikitable center-all left-5" | {| 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 | |||
|- | |- | ||
|27 | | 27 | ||
|299\1323 | | 299\1323<br />(5\1323) | ||
(5\1323) | | 271.201<br />(4.535) | ||
|271.201 | | 1375/1176<br />(?) | ||
(4.535) | | [[Trinealimmal]] | ||
|1375/1176 | |} | ||
<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 | |||
(?) | |||
|Trinealimmal | |||
|}< | |||