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.

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

In the 17-limit on the patent val, it is a tuning for the [[leaves]] temperament~~. 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 * 172~~.

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

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

{| class="wikitable center-all left-4"

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

!Periods

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

per 8ve

|-

!Generator

! Periods per 8ve

~~(Reduced)~~

! Generator*

!Cents

! Cents*

~~(Reduced)~~

! Associated ratio*

!Associated

! Temperaments

~~Ratio~~

!~~Temperament~~

|-

|17

| 17

|144\2023

| 144\2023 (25\2023)

(25\2023)

| 85.417 (14.829)

|85.417

| 1024/975 (8192/8125)

(14.829)

| [[Leaves]]

|1024/975

(?)

|[[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: @@
 {{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.
-edo is enfactored in the 5-limit, with the same mapping as [[289edo]].
-In the 17-limit on the patent val, it is a tuning for the [[leaves]] temperament. 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 represented by 289edo are not included.
+Note: 5-limit temperaments supported by 289edo are not included.
-{| class="wikitable center-all left-4"
+{| class="wikitable center-all left-5"
-!Periods
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-per 8ve
+|-
-!Generator
+! Periods<br />per 8ve
-(Reduced)
+! Generator*
-!Cents
+! Cents*
-(Reduced)
+! Associated<br />ratio*
-!Associated
+! Temperaments
-Ratio
-!Temperament
 |-
-|17
+| 17
-|144\2023
+| 144\2023<br />(25\2023)
-(25\2023)
+| 85.417<br />(14.829)
-|85.417
+| 1024/975<br />(8192/8125)
-(14.829)
+| [[Leaves]]
-|1024/975
-(?)
-|[[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]]