1323edo: Difference between revisions
m Infobox ET added |
Rank 2 temps, also notated 441 & 1308 despite not having a name, because it is listed on the augmented-cloudy equivalence continuum page. |
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1323edo is the smallest uniquely consistent EDO in the 29-odd-limit. | 1323edo is the smallest uniquely consistent EDO in the 29-odd-limit. | ||
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. In additoin, it tunes well 441 & 1308 temperament, which is a member of the augmented-cloudy equivalence continuum. | ||
1323's divisors are {{EDOs|1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441}}, of which 441EDO is a member of the zeta edos. 1323edo shares the 7-limit mapping with 441edo. As such, it can be interpreted as an improvement for 441edo into the 29-limit by splitting each step of 441edo into three. | 1323's divisors are {{EDOs|1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441}}, of which 441EDO is a member of the zeta edos. 1323edo shares the 7-limit mapping with 441edo. As such, it can be interpreted as an improvement for 441edo into the 29-limit by splitting each step of 441edo into three. | ||
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{{Harmonics in equal|1323}} | {{Harmonics in equal|1323}} | ||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
!Periods | |||
per octave | |||
!Generator | |||
(reduced) | |||
!Cents | |||
(reduced) | |||
!Associated | |||
ratio | |||
!Temperaments | |||
|- | |||
|3 | |||
|177\1323 | |||
|160.544 | |||
|154478651796875/140737488355328 | |||
|441 & 1308 | |||
|- | |||
|27 | |||
|299\1323 | |||
(5\1323) | |||
|271.201 | |||
(4.535) | |||
|1375/1176 | |||
(?) | |||
|Trinealimmal | |||
|}<!-- 4-digit number --> | |||