48edo: Difference between revisions

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! #
! #
! Cents
! Cents
! [[Ups and downs notation|Ups and Downs Notation]]
! [[Ups and downs notation|Ups and downs notation]]
|-
|-
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== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Ups and downs notation ===
48edo can be notated using [[ups and downs notation]]. This can be accomplished by combining [[Helmholtz-Ellis]] accidentals with semisharps and semiflats:
48edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Sharpness-sharp4|48}}
{{Sharpness-sharp4a}}
 
[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp4}}
=== Sagittal notation ===
=== Sagittal notation ===
This notation is a superset of the notations for EDOs [[24edo#Sagittal notation|24]], [[12edo#Sagittal notation|12]], [[8edo#Sagittal notation|8]], and [[6edo#Sagittal notation|6]].
This notation is a superset of the notations for EDOs [[24edo#Sagittal notation|24]], [[12edo#Sagittal notation|12]], [[8edo#Sagittal notation|8]], and [[6edo#Sagittal notation|6]].
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default [[File:48-EDO_Evo-SZ_Sagittal.svg]]
default [[File:48-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
</imagemap>
== Approximation to JI ==
=== Zeta peak index ===
{| class="wikitable center-all"
|-
! colspan="3" | Tuning
! colspan="3" | Strength
! colspan="2" | Closest edo
! colspan="2" | Integer limit
|-
! ZPI
! Steps per octave
! Step size (cents)
! Height
! Integral
! Gap
! Edo
! Octave (cents)
! Consistent
! Distinct
|-
| [[226zpi]]
| 47.9883202080850
| 25.0060847055410
| 5.843508
| 0.890480
| 13.888482
| 48edo
| 1200.29206586597
| 6
| 6
|}


== 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 "Elements - Fire"] from ''Elements'' (2019–2020)
* [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" &ndash; [https://norokusi.bandcamp.com/track/cruise-for-strings-48-tone-microtonal-music-48edo-48tet Bandcamp] | [https://youtu.be/ayilWbYWr54?si=b-H-SR1inT00quT8 YouTube]
** ''Cruise for strings'' &ndash; [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" &ndash; [https://norokusi.bandcamp.com/track/rigel-for-strings-48-tone-microtonal-music-48edo-48tet Bandcamp] | [https://youtu.be/XjjI6NVRVDs?si=-S_Vcx-8ypvxaODx YouTube]
** ''Rigel for Strings'' &ndash; [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}}
== Instruments ==
* [[Lumatone mapping for 48edo]]
* [[Skip fretting system 48 2 13]]


== See also ==
== See also ==