2023edo: Difference between revisions

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== Theory ==

~~{{Harmonics in equal~~|~~2023}}~~

2023edo is [[Enfactoring|enfactored]] in the 5-limit, with the same mapping as [[289edo]]. As such it maps the period to [[25/24]], which means [[septendecima]] is also tempered out. In the 17-limit on the [[patent val]], it is a tuning for the [[leaves]] temperament.

~~It is~~ enfactored in the 5-limit, with the same mapping as [[289edo~~]].~~

~~In the patent val, it is good in the no-11s 17-limit, a property which it shares with [[323edo~~]]. As such~~, a 2.3.5.7.13.17 temperament can be created by merging 323 & 2023, which gives the comma basis {57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000}. It is also period-17, and~~ maps the period to 25/24, which means [[septendecima]] is also tempered out.

If we impose a stricter harmonic approach, and require all errors to be below 25%, the subgroup consisting of first 7 such harmonics for 2023edo is 2.13.17.23.47.61.71.

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In the 2023e val, it supports the altierran rank-3 temperament tempering out the [[schisma]] and the [[quartisma]].

~~The divisors of~~ 2023 ~~are~~ {{EDOs|1, 7, 17, 119, 289}}. ~~It factors as 7~~ * 17<~~sup~~>2</~~sup~~>.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 2023 factors as {{factorization|2023}}, 2023edo has subset edos {{EDOs| 7, 17, 119, and 289 }}.

== Regular temperament properties ==

=== Rank-2 temperaments ===

Note: 5-limit temperaments supported by 289edo are not included.

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

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ratio*

! Temperaments

|-

| 17

| 144\2023 (25\2023)

| 85.417 (14.829)

| 1024/975 (8192/8125)

| [[Leaves]]

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

== Music ==

; [[Eliora]]

* [https://www.youtube.com/watch?v=8K2RYO_oCnM ''Bagatelle in 11/8♭ Leaves''] (2023)

[[Category:~~Equal divisions of the octave|####]]~~

[[Category:Listen]]

~~[[Category:Quartismic~~]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|2023}}
+{{ED intro}}
 == Theory ==
-{{Harmonics in equal|2023}}
+edo is [[Enfactoring|enfactored]] in the 5-limit, with the same mapping as [[289edo]]. As such it maps the period to [[25/24]], which means [[septendecima]] is also tempered out. In the 17-limit on the [[patent val]], it is a tuning for the [[leaves]] temperament.
-It is enfactored in the 5-limit, with the same mapping as [[289edo]].
-In the patent val, it is good in the no-11s 17-limit, a property which it shares with [[323edo]]. As such, a 2.3.5.7.13.17 temperament can be created by merging 323 & 2023, which gives the comma basis {57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000}. It is also period-17, and maps the period to 25/24, which means [[septendecima]] is also tempered out.
 If we impose a stricter harmonic approach, and require all errors to be below 25%, the subgroup consisting of first 7 such harmonics for 2023edo is 2.13.17.23.47.61.71.
@@ Line 11: / Line 9: @@
 In the 2023e val, it supports the altierran rank-3 temperament tempering out the [[schisma]] and the [[quartisma]].
-The divisors of 2023 are {{EDOs|1, 7, 17, 119, 289}}. It factors as 7 * 17<sup>2</sup>.
+=== Prime harmonics ===
+{{Harmonics in equal|2023}}
+=== Subsets and supersets ===
+Since 2023 factors as {{factorization|2023}}, 2023edo has subset edos {{EDOs| 7, 17, 119, and 289 }}.
+== Regular temperament properties ==
+=== Rank-2 temperaments ===
+Note: 5-limit temperaments supported by 289edo are not included.
+{| 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
+|-
+| 17
+| 144\2023<br />(25\2023)
+| 85.417<br />(14.829)
+| 1024/975<br />(8192/8125)
+| [[Leaves]]
+|}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+== Music ==
+; [[Eliora]]
+* [https://www.youtube.com/watch?v=8K2RYO_oCnM ''Bagatelle in 11/8♭ Leaves''] (2023)
-[[Category:Equal divisions of the octave|####]]<!-- 4-digit number -->
+[[Category:Listen]]
-[[Category:Quartismic]]