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.

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=== 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 forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct~~

== Music ==

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 == 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.
@@ Line 14: / Line 14: @@
 === 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 forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 == Music ==