2024edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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}. | 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}. | ||
In the 2.3.7.11.17.19, it tunes the 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}. | 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}. | ||
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. | 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. | ||
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== Music == | == Music == | ||
; [[Eliora]] | ; [[Eliora]] | ||
* ''[https://youtu.be/6wO9uONbJhY Piano Juice]'' (2024) - palladium[92] (from [[506edo]]), ruthenium[88] (from [[1012edo]]), 629 & 2024[25], major-arcana[88] (from [[506edo]]) | * ''[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]] | [[Category:Listen]] | ||