2023edo: Difference between revisions

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== Theory ==

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~~.

2023edo is [[enfactoring|enfactored]] in the 5-limit, with the same mapping and commas as [[289edo]].

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 ===

Since 2023 factors as ~~7 × 172~~, 2023edo has subset edos {{EDOs| 7, 17, 119, and 289 }}.

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

== ~~Regular temperament properties ==~~

=== Other uses ===

=== ~~Rank-2 temperaments~~ ===

2023edo also supports a high badness 323 & 2023 temperament, which [[Eliora]] designated as [[User:Eliora/Leaves|leaves]].

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

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

~~! Periods per 8ve~~

! Generator*

! Cents*

~~! Associated Ratio~~

~~! Temperament~~

|-

~~| 17~~

~~| 144\~~2023~~ (25\2023)~~

~~| 85.417 (14.829)~~

~~| 1024/975 (8192/8125)~~

| [[~~Leaves~~]]

|}

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

== Music ==

; [[Eliora]]

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

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|2023}}
+{{ED intro}}
 == Theory ==
-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.
+edo is [[enfactoring|enfactored]] in the 5-limit, with the same mapping and commas as [[289edo]].
 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}}
 === Subsets and supersets ===
-Since 2023 factors as 7 × 17<sup>2</sup>, 2023edo has subset edos {{EDOs| 7, 17, 119, and 289 }}.
+Since 2023 factors as {{factorization|2023}}, 2023edo has subset edos {{EDOs| 7, 17, 119, and 289 }}.
-== Regular temperament properties ==
+=== Other uses ===
-=== Rank-2 temperaments ===
+edo also supports a high badness 323 & 2023 temperament, which [[Eliora]] designated as [[User:Eliora/Leaves|leaves]].
-Note: 5-limit temperaments supported by 289edo are not included.
-{| class="wikitable center-all left-5"
-! Periods<br>per 8ve
-! Generator*
-! Cents*
-! Associated<br>Ratio
-! Temperament
-|-
-| 17
-| 144\2023<br>(25\2023)
-| 85.417<br>(14.829)
-| 1024/975<br>(8192/8125)
-| [[Leaves]]
-|}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 == Music ==
 ; [[Eliora]]
 * [https://www.youtube.com/watch?v=8K2RYO_oCnM ''Bagatelle in 11/8♭ Leaves''] (2023)
+[[Category:Listen]]