2023edo: Difference between revisions

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~~{{novelty}}{{stub}}~~{{Infobox ET}}

== Theory ==

2023edo is 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.

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.

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.

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

=== Prime harmonics ===

=== Subsets and supersets ===

~~The divisors of~~ 2023 ~~are~~ {{EDOs|1, 7, 17, 119, 289}}~~. It factors as 7 * 172~~.

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 ~~represented~~ by 289edo are not included.

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

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

~~!Periods~~

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

~~per 8ve~~

~~!Generator~~

~~(Reduced)~~

~~!Cents~~

~~(Reduced)~~

~~!Associated~~

~~Ratio~~

~~!Temperament~~

|-

|17

! Periods per 8ve

|144\2023 (25\2023)

! Generator*

|85.417 (14.829)

! Cents*

|1024/975 (8192/8125)

! Associated ratio*

|[[Leaves]]

! 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)

* [https://www.youtube.com/watch?v=8K2RYO_oCnM Bagatelle in 11/8♭ Leaves, (Op. 2, No. 2)] by [[Eliora]]

[[Category:Listen]]

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

[[Category:~~Quartismic~~]]

@@ Line 1: / Line 1: @@
-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-{{EDO intro|2023}}
+{{ED intro}}
 == Theory ==
-edo is 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.
+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.
 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.
 In the 2023e val, it supports the altierran rank-3 temperament tempering out the [[schisma]] and the [[quartisma]].
 === Prime harmonics ===
-{{harmonics in equal|2023}}
+{{Harmonics in equal|2023}}
 === Subsets and supersets ===
-The divisors of 2023 are {{EDOs|1, 7, 17, 119, 289}}. It factors as 7 * 17<sup>2</sup>.
+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 represented by 289edo are not included.
+Note: 5-limit temperaments supported by 289edo are not included.
 {| class="wikitable center-all left-5"
-!Periods
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-per 8ve
-!Generator
-(Reduced)
-!Cents
-(Reduced)
-!Associated
-Ratio
-!Temperament
 |-
-|17
+! Periods<br />per 8ve
-|144\2023<br>(25\2023)
+! Generator*
-|85.417<br>(14.829)
+! Cents*
-|1024/975<br>(8192/8125)
+! Associated<br />ratio*
-|[[Leaves]]
+! 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)
-* [https://www.youtube.com/watch?v=8K2RYO_oCnM Bagatelle in 11/8♭ Leaves, (Op. 2, No. 2)] by [[Eliora]]
+[[Category:Listen]]
-[[Category:Equal divisions of the octave|####]]<!-- 4-digit number -->
-[[Category:Quartismic]]