2024edo: Difference between revisions

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

==Theory==

== Theory ==

2024edo is [[enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] ~~EDO~~. ~~Beyond that~~, ~~it does make for~~ a ~~reasonable~~ 17~~- an~~ 19~~-limit system~~.

2024edo is [[Enfactoring|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}.

~~It has two suitable mappings for 5th harmonic, one which derives from 1012edo, and other in~~ the ~~2024c val~~. ~~In the 2024c val~~, it ~~tempers out~~ the ~~[[wizma]]~~, ~~420175/419904 in the 7-limit, as well as~~ [[~~3025~~/~~3024]], [[4225/4224~~]] and [[~~10648~~/~~10647~~]] in the ~~13-limit~~.

In the 2.3.7.11.17.19, it tunes the {{nowrap|629 & 2024}} temperament, which has [[19/17]] as a generator and reaches [[17/16]] in 13 steps. The comma basis in the 2.3.7.11.17.19 subgroup is {23409/23408, 131072/131043, 323456/323433, 818107136/817887699}.

If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 subgroup tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374~~]] and [[117649/117612~~]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.

It has two suitable mappings for [[5/1|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.

===~~Harmonics~~===

=== Prime harmonics ===

=== Subsets and supersets ===

Since 2024 factors into {{factorization|2024}}, 2024edo has subset edos {{EDOs| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}.

== Music ==

; [[Eliora]]

* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), {{nowrap|629 & 2024[25]}}, major-arcana[88] (from [[506edo]])

[[Category:Listen]]

@@ Line 1: / Line 1: @@
-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-{{EDO intro|2024}}
+{{ED intro}}
-==Theory==
+== Theory ==
-edo is [[enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] EDO. Beyond that, it does make for a reasonable 17- an 19-limit system.
+edo is [[Enfactoring|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. It corrects 1012edo's mapping for 17, being a strong 2.3.7.11.17.19 subgroup temperament. A comma basis for the said subgroup is {23409/23408, 117649/117612, 323456/323433, 131072/131043, 26042368/26040609}.
-It has two suitable mappings for 5th harmonic, one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it tempers out the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit.
+In the 2.3.7.11.17.19, it tunes the {{nowrap|629 &amp; 2024}} temperament, which has [[19/17]] as a generator and reaches [[17/16]] in 13 steps. The comma basis in the 2.3.7.11.17.19 subgroup is {23409/23408, 131072/131043, 323456/323433, 818107136/817887699}.
-If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 subgroup tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and [[117649/117612]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.
+It has two suitable mappings for [[5/1|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.
-===Harmonics===
-{{harmonics in equal|2024}}
+=== Prime harmonics ===
+{{Harmonics in equal|2024}}
+=== Subsets and supersets ===
+Since 2024 factors into {{factorization|2024}}, 2024edo has subset edos {{EDOs| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}.
+== Music ==
+; [[Eliora]]
+* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), {{nowrap|629 &amp; 2024[25]}}, major-arcana[88] (from [[506edo]])
+[[Category:Listen]]