32edo: Difference between revisions

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=== Subsets and supersets ===

Since 32 factors ~~into primes~~ as 2<sup>5</sup>, 32edo contains subset edos {{EDOs| 2, 4, 8, and 16 }}.

Since 32 is a power of two and factors as 2<sup>5</sup>, 32edo contains subset edos {{EDOs| 2, 4, 8, and 16 }}.

See also [[32nd-octave temperaments]].

== Intervals ==

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== Notation ==

=== ~~Ups and downs~~ notation ===

=== Stein–Zimmermann–Gould notation ===

~~32edo can be notated with~~ [[~~ups and downs~~]]~~, spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc.~~ and ~~down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).~~

[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:

~~Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here~~, ~~this can~~ be ~~done~~ using ~~sharps and flats with~~ arrows~~, borrowed from extended [[Helmholtz–Ellis notation]]:~~

If the arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best denoted using triple arrows.

=== Kite's ups and downs notation ===

32edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).

~~If the arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best denoted using triple arrows.~~

=== Sagittal notation ===

This notation uses the same sagittal sequence as [[25edo#Sagittal notation|~~25-EDO~~]], and is a subset of the notation for [[64edo#Second-best fifth notation|64b]].

This notation uses the same sagittal sequence as [[25edo #Sagittal notation|25edo]], and is a subset of the notation for [[64edo #Second-best fifth notation|64b-edo]].

==== Evo flavor ====

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== Approximation to JI ==

~~=== Zeta properties ===~~

Below is a plot of the [[Zeta]] function, showing how its peak (ie most negative) value is shifted above 32, corresponding to a zeta tuning with octaves flattened to 1197.375 cents. This will improve the fifth, at the expense of the third.

~~[[File:plot32.png|alt=plot32.png|plot32.png]]~~

== Regular temperament properties ==

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| [[Sedecic]] (32)

|}

<nowiki/>* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if distinct

<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

== Delta-rational harmony ==

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| 0.00026

|}

== Octave stretch or compression ==

Whether [[octave stretch]], shrink or neither is advised for 32edo depends on which [[val]]s one wishes to use.

For 32, pure-octaves, or slight compression (~0.5{{c}}), works well.

For 32f, moderate compression (~2{{c}}) works well. This is close to [[zpi|133zpi]] (32.07edo).

For 32c or 32cf, substantial compression (3-4{{c}}) is well suited.

For 32be, substantial ''stretch'' works (~5{{c}}). This is close to [[zpi|132zpi]] (31.86edo).

The graph shows [[zeta]] near 32edo.

[[File:plot32.png|alt=plot32.png|plot32.png]]

== Instruments ==

[[Lumatone mapping for 32edo]]

* [[Lumatone mapping for 32edo]]

== Music ==

=== Modern renderings ===

; {{W|Koji Kondo}}

* [https://www.youtube.com/shorts/OUlNwN-bAsc "Lost Woods" from ''The Legend of Zelda: Ocarina of Time OST''] (1998) – covered by [[Bryan Deister]] (2025)

=== 21st century ===

; [[Brody Bigwood]]

* [https://www.youtube.com/watch?v=yMokW3-0vIs ''Beyond the Grid''] (2024)

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/nTQfjPjeee8 ''32edo improv''] (2025)

* ''Licorice Hearted'' (2026)

** [https://www.youtube.com/shorts/zFgw-AfGEcQ short 1] · [https://www.youtube.com/shorts/ocgMIf4xopo short 2]

; [[groundfault]]

* "Winter's Mortal Hope", from ''A New Dusk'' (2024) – [https://groundfco.bandcamp.com/track/winters-mortal-hope-32edo Bandcamp] | [https://www.youtube.com/watch?v=1bnEO8vGvbo&t=1357 YouTube (22:37–26:00)]

; [[Claudi Meneghin]]

* [https://www.youtube.com/watch?v=y2G6Fs2HMUs ~~''Canon on Twinkle Twinkle Little Star'',~~ for organ] (2023) ~~– (~~[https://www.youtube.com/watch?v=JWRGLa59ZwY for ~~Baroque Oboe~~ & ~~Viola~~])

* ''Canon on Twinkle Twinkle Little Star''

** [https://www.youtube.com/watch?v=y2G6Fs2HMUs for organ] (2023) · [https://www.youtube.com/watch?v=JWRGLa59ZwY for baroque oboe & viola] (2024)

; [[Petr Pařízek]]

* [http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg ''Sixix'']

* [https://web.archive.org/web/20201127014118/http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg ''Sixix'']

; [[Billy Stiltner]]

* [https://billystiltner.bandcamp.com/album/1332 ''1332'']

* [https://billystiltner.bandcamp.com/album/1332 ''1332''] (2019)

; [[Chris Vaisvil]]

* [http://micro.soonlabel.com/32edo/32-32-32-nothing-less-will-do.mp3 ''32 32 32 Nothing Less Will Do'']

* [https://web.archive.org/web/20201127013223/http://micro.soonlabel.com/32edo/32-32-32-nothing-less-will-do.mp3 ''32 32 32 Nothing Less Will Do'']

; [[Stephen Weigel]]

* [https://www.youtube.com/watch?v=00kH3CqSgMY "Zinnia Riplet" ~~(32-EDO)~~] (featured in [https://spectropolrecords.bandcamp.com/album/possible-worlds-vol-4 ''Possible Worlds Vol. 4''] of Spectropol Records)

* [https://www.youtube.com/watch?v=00kH3CqSgMY "Zinnia Riplet"], featured in [https://spectropolrecords.bandcamp.com/album/possible-worlds-vol-4 ''Possible Worlds Vol. 4''] (2019) of Spectropol Records

* [https://soundcloud.com/overtoneshock/admins-hot-tub-32-edo ''Admin's Hot Tub'']

* [https://soundcloud.com/overtoneshock/admins-hot-tub-32-edo ''Admin's Hot Tub''] (2019)

[[Category:Listen]]

[[Category:Sixix]]

@@ Line 16: / Line 16: @@
 === Subsets and supersets ===
-Since 32 factors into primes as 2<sup>5</sup>, 32edo contains subset edos {{EDOs| 2, 4, 8, and 16 }}.
+Since 32 is a power of two and factors as 2<sup>5</sup>, 32edo contains subset edos {{EDOs| 2, 4, 8, and 16 }}.
+See also [[32nd-octave temperaments]].
 == Intervals ==
@@ Line 290: / Line 292: @@
 == Notation ==
-=== Ups and downs notation ===
+=== Stein–Zimmermann–Gould notation ===
-edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
+[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
-{{Sharpness-sharp5a}}
+{{Sharpness-sharp5-szg}}
-Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
+If the arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best denoted using triple arrows.
-{{Sharpness-sharp5}}
+=== Kite's ups and downs notation ===
+edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
-If the arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best denoted using triple arrows.
+{{Ups and downs sharpness}}
 === Sagittal notation ===
-This notation uses the same sagittal sequence as [[25edo#Sagittal notation|25-EDO]], and is a subset of the notation for [[64edo#Second-best fifth notation|64b]].
+This notation uses the same sagittal sequence as [[25edo #Sagittal notation|25edo]], and is a subset of the notation for [[64edo #Second-best fifth notation|64b-edo]].
 ==== Evo flavor ====
@@ Line 325: / Line 327: @@
 == Approximation to JI ==
 {{Q-odd-limit intervals|32}}
-=== Zeta properties ===
-Below is a plot of the [[Zeta]] function, showing how its peak (ie most negative) value is shifted above 32, corresponding to a zeta tuning with octaves flattened to 1197.375 cents. This will improve the fifth, at the expense of the third.
-[[File:plot32.png|alt=plot32.png|plot32.png]]
 == Regular temperament properties ==
@@ Line 444: / Line 441: @@
 | [[Sedecic]] (32)
 |}
-<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 == Delta-rational harmony ==
@@ Line 1,260: / Line 1,257: @@
 | 0.00026
 |}
+== Octave stretch or compression ==
+Whether [[octave stretch]], shrink or neither is advised for 32edo depends on which [[val]]s one wishes to use.
+For 32, pure-octaves, or slight compression (~0.5{{c}}), works well.
+For 32f, moderate compression (~2{{c}}) works well. This is close to [[zpi|133zpi]] (32.07edo).
+For 32c or 32cf, substantial compression (3-4{{c}}) is well suited.
+For 32be, substantial ''stretch'' works (~5{{c}}). This is close to [[zpi|132zpi]] (31.86edo).
+The graph shows [[zeta]] near 32edo.
+[[File:plot32.png|alt=plot32.png|plot32.png]]
 == Instruments ==
-[[Lumatone mapping for 32edo]]
+* [[Lumatone mapping for 32edo]]
 == Music ==
+=== Modern renderings ===
+; {{W|Koji Kondo}}
+* [https://www.youtube.com/shorts/OUlNwN-bAsc "Lost Woods" from ''The Legend of Zelda: Ocarina of Time OST''] (1998) – covered by [[Bryan Deister]] (2025)
+=== 21st century ===
 ; [[Brody Bigwood]]
 * [https://www.youtube.com/watch?v=yMokW3-0vIs ''Beyond the Grid''] (2024)
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/nTQfjPjeee8 ''32edo improv''] (2025)
+* ''Licorice Hearted'' (2026)
+** [https://www.youtube.com/shorts/zFgw-AfGEcQ short 1] · [https://www.youtube.com/shorts/ocgMIf4xopo short 2]
+; [[groundfault]]
+* "Winter's Mortal Hope", from ''A New Dusk'' (2024) – [https://groundfco.bandcamp.com/track/winters-mortal-hope-32edo Bandcamp] | [https://www.youtube.com/watch?v=1bnEO8vGvbo&t=1357 YouTube (22:37–26:00)]
 ; [[Claudi Meneghin]]
-* [https://www.youtube.com/watch?v=y2G6Fs2HMUs ''Canon on Twinkle Twinkle Little Star'', for organ] (2023) – ([https://www.youtube.com/watch?v=JWRGLa59ZwY for Baroque Oboe & Viola])
+* ''Canon on Twinkle Twinkle Little Star''
+** [https://www.youtube.com/watch?v=y2G6Fs2HMUs for organ] (2023) · [https://www.youtube.com/watch?v=JWRGLa59ZwY for baroque oboe & viola] (2024)
 ; [[Petr Pařízek]]
-* [http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg ''Sixix'']
+* [https://web.archive.org/web/20201127014118/http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg ''Sixix'']
 ; [[Billy Stiltner]]
-* [https://billystiltner.bandcamp.com/album/1332 ''1332'']
+* [https://billystiltner.bandcamp.com/album/1332 ''1332''] (2019)
 ; [[Chris Vaisvil]]
-* [http://micro.soonlabel.com/32edo/32-32-32-nothing-less-will-do.mp3 ''32 32 32 Nothing Less Will Do'']
+* [https://web.archive.org/web/20201127013223/http://micro.soonlabel.com/32edo/32-32-32-nothing-less-will-do.mp3 ''32 32 32 Nothing Less Will Do'']
 ; [[Stephen Weigel]]
-* [https://www.youtube.com/watch?v=00kH3CqSgMY "Zinnia Riplet" (32-EDO)] (featured in [https://spectropolrecords.bandcamp.com/album/possible-worlds-vol-4 ''Possible Worlds Vol. 4''] of Spectropol Records)
+* [https://www.youtube.com/watch?v=00kH3CqSgMY "Zinnia Riplet"], featured in [https://spectropolrecords.bandcamp.com/album/possible-worlds-vol-4 ''Possible Worlds Vol. 4''] (2019) of Spectropol Records
-* [https://soundcloud.com/overtoneshock/admins-hot-tub-32-edo ''Admin's Hot Tub'']
+* [https://soundcloud.com/overtoneshock/admins-hot-tub-32-edo ''Admin's Hot Tub''] (2019)
 [[Category:Listen]]
 [[Category:Sixix]]
+{{Todo|add scales list}}