1323edo: Difference between revisions

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== 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~~. In addition, it tunes well 441 & 1308 temperament, which is a member of the augmented-cloudy equivalence continuum~~.

It provides the [[optimal patent val]] for the 11-limit [[trinealimmal]] temperament, which has a period of 1\27 octave.

=== Prime harmonics ===

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=== Subsets and supersets ===

1323~~'s divisors are~~ {{EDOs| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 441edo is a member of the [[zeta edo]]s~~. 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~~.

Since 1323 factors into {{factorization|1323}}, 1323edo has subset edos {{EDOs| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 441edo is a member of the [[zeta edo]]s.

== Regular temperament properties ==

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{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

|-

! Periods<br>per 8ve

! Generator*

! Cents*

! Associated<br>Ratio

! Associated<br>Ratio*

! Temperaments

~~<!--~~

|-

~~| 3~~

~~| 177\1323~~

~~| 160.544~~

~~| 154478651796875/140737488355328~~

~~| [[Augmented-cloudy equivalence continuum#441 & 1308|441 & 1308]]~~

~~-->~~

|-

| 27

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is the smallest edo [[consistency|distinctly consistent]] in the [[29-odd-limit]].
+edo 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. In addition, it tunes well 441 & 1308 temperament, which is a member of the augmented-cloudy equivalence continuum.
+It provides the [[optimal patent val]] for the 11-limit [[trinealimmal]] temperament, which has a period of 1\27 octave.
 === Prime harmonics ===
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-'s divisors are {{EDOs| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 441edo is a member of the [[zeta edo]]s. 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.
+Since 1323 factors into {{factorization|1323}}, 1323edo has subset edos {{EDOs| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 441edo is a member of the [[zeta edo]]s.
 == Regular temperament properties ==
@@ Line 18: / Line 18: @@
 {| class="wikitable center-all left-5"
+|+Table of rank-2 temperaments by generator
+|-
 ! Periods<br>per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
-<!--
-|-
-| 3
-| 177\1323
-| 160.544
-| 154478651796875/140737488355328
-| [[Augmented-cloudy equivalence continuum#441 & 1308|441 & 1308]]
--->
 |-
 | 27