2024edo: Difference between revisions

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~~==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.~~

~~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.

2024edo is [[Enfactoring|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.

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 tempers out the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit.

===~~Harmonics~~===

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.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 2024 factors into 2<sup>3</sup> × 11 × 23, 2024edo has subset edos {{EDOs| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}.

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 {{Infobox ET}}
 {{EDO intro|2024}}
-==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.
-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.
+edo is [[Enfactoring|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.
-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 tempers out the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit.
-===Harmonics===
-{{harmonics in equal|2024}}
+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.
+=== Prime harmonics ===
+{{Harmonics in equal|2024}}
+=== Subsets and supersets ===
+Since 2024 factors into 2<sup>3</sup> × 11 × 23, 2024edo has subset edos {{EDOs| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}.