48edo: Difference between revisions
→Theory: + ''It is recommended to read the page regular temperament first to understand this section.'' Tag: Reverted |
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== Theory == | == Theory == | ||
Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the [[5-limit]], but [[tempering out|tempers out]] [[2401/2400]] in the [[7-limit]], making it a tuning for [[squares]] temperament. In the [[11-limit]] we can add [[99/98]] and [[121/120]] to the list, and in the [[13-limit]], [[66/65]]. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes. | Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the [[5-limit]], but [[tempering out|tempers out]] [[2401/2400]] in the [[7-limit]], making it a tuning for [[squares]] temperament. In the [[11-limit]] we can add [[99/98]] and [[121/120]] to the list, and in the [[13-limit]], [[66/65]]. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes. | ||
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! # | ! # | ||
! Cents | ! Cents | ||
! [[Ups and downs notation|Ups and | ! [[Ups and downs notation|Ups and downs notation]] | ||
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default [[File:48-EDO_Evo-SZ_Sagittal.svg]] | default [[File:48-EDO_Evo-SZ_Sagittal.svg]] | ||
</imagemap> | </imagemap> | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Instruments == | |||
* [[Lumatone mapping for 48edo]] | |||
* [[Skip fretting system 48 2 13]] | |||
== Music == | == Music == | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/w1m9PMj0Ato ''48edo layout''] (2025) | |||
; [[E8 Heterotic]] | ; [[E8 Heterotic]] | ||
* [https://youtu.be/puADOWdfjSQ?si=FWEqYKwud-yoI6ae | * [https://youtu.be/puADOWdfjSQ?si=FWEqYKwud-yoI6ae ''Elements - Fire''] from ''Elements'' (2019–2020) | ||
; [[norokusi]] | ; [[norokusi]] | ||
* from ''Works for Strings Vol.1'' (2020) | * from ''Works for Strings Vol.1'' (2020) | ||
** | ** ''Cruise for strings'' – [https://norokusi.bandcamp.com/track/cruise-for-strings-48-tone-microtonal-music-48edo-48tet Bandcamp] | [https://youtu.be/ayilWbYWr54?si=b-H-SR1inT00quT8 YouTube] | ||
** | ** ''Rigel for Strings'' – [https://norokusi.bandcamp.com/track/rigel-for-strings-48-tone-microtonal-music-48edo-48tet Bandcamp] | [https://youtu.be/XjjI6NVRVDs?si=-S_Vcx-8ypvxaODx YouTube] | ||
* [https://youtu.be/bfPx121QqJ4?si=Yfspa9i9Rq2FKbZP ''Elysium Planitia for strings''] (2022) | * [https://youtu.be/bfPx121QqJ4?si=Yfspa9i9Rq2FKbZP ''Elysium Planitia for strings''] (2022) | ||
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; [[Jon Lyle Smith]] | ; [[Jon Lyle Smith]] | ||
* [https://archive.org/download/Quincunx/Quincunx.mp3 ''Quincunx'']{{dead link}} | * [https://archive.org/download/Quincunx/Quincunx.mp3 ''Quincunx'']{{dead link}} | ||
== See also == | == See also == | ||