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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|25}}
{{ED intro}}


== Theory ==
== Theory ==
25edo is a good way to tune the [[blackwood]] temperament, which closes each circle of fifths at five fifths, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 ([[5/4]]) and 7 ([[7/4]]). It also tunes [[sixix]] temperament with a sharp fifth. It supplies the optimal patent val for the 11-limit 6&25 temperament tempering out 49/48, 77/75 and 605/576, and the 13-limit extension also tempering out 66/65.


25edo is a good way to tune the [[blackwood]] temperament, which takes the very sharp fifths of [[5edo]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 ([[5/4]]) and 7 ([[7/4]]). It also tunes [[sixix]] temperament with a sharp fifth. It supplies the optimal patent val for the 11-limit 6&25 temperament tempering out 49/48, 77/75 and 605/576, and the 13-limit extension also tempering out 66/65.
25edo has fifths 18 cents sharp, but its major thirds of 5/4 are excellent and its 7/4 is acceptable. Moreover, in full 7-limit including the 3, it is not [[consistent]]. It therefore makes sense to use it as a 2.5.7 [[subgroup]] tuning. Looking just at 2, 5, and 7, it equates five [[8/7]]'s with the octave, and so tempers out (8/7)<sup>5</sup> / 2 = 16807/16384. It also equates a [[128/125]] [[diesis]] and two [[septimal]] [[tritone]]s of [[7/5]] with the octave, and hence tempers out [[3136/3125]]. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50edo]]. An alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for [[trismegistus]] temperament (or [[mavila]] if it is interpreted as [[3/2]]). In fact, it is a convergent to a melodically optimal "golden" tuning of trismegistus or mavila, at around 672.7 cents.
 
25edo has fifths 18 cents sharp, but its major thirds of 5/4 are excellent and its 7/4 is acceptable. Moreover, in full 7-limit including the 3, it is not [[consistent]]. It therefore makes sense to use it as a 2.5.7 [[subgroup]] tuning. Looking just at 2, 5, and 7, it equates five [[8/7]]'s with the octave, and so tempers out (8/7)<sup>5</sup> / 2 = 16807/16384. It also equates a [[128/125]] [[diesis]] and two [[septimal]] [[tritone]]s of [[7/5]] with the octave, and hence tempers out [[3136/3125]]. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50edo]]. An alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for [[mavila]] temperament.


If 5/4 and 7/4 are not good enough, it also does 17/16 and 19/16, just like 12edo. In fact, on the [[k*N subgroups|2*25 subgroup]] 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for a wide range of harmony.  
If 5/4 and 7/4 are not good enough, it also does 17/16 and 19/16, just like 12edo. In fact, on the [[k*N subgroups|2*25 subgroup]] 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for a wide range of harmony.  


Since 25 is 5 x 5, 25edo is the smallest composite EDO that doesn't have any intervals in common with [[12edo]].  
Its step of 48{{c}}, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having a very high [[harmonic entropy]]. This is because the harmonic entropy model is usually tuned to reflect the general perception of quarter-tones being the most dissonant intervals. This property is shared with all edos between around 20 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.


=== Possible usage in Indonesian music ===
=== Possible usage in Indonesian music ===
Since 25edo contains [[5edo]] as a subset, and it features an [[antidiatonic]] scale generated by the 672 cent fifth, it can theoretically be used to represent Indonesian music in both [[Slendro]] (~5edo) and [[Pelog]] (~antidiatonic scale) tunings.
Since 25edo contains [[5edo]] as a subset, and it features an [[antidiatonic]] scale generated by the 672 cent fifth, it can theoretically be used to represent Indonesian music in both [[Slendro]] (~5edo) and [[Pelog]] (~antidiatonic scale) tunings. However, many tunings of pelog are also better represented by the tuning's native 3-2-6-3-2-3-6 [[omnidiatonic]] scale.  


=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|25}}
{{Harmonics in equal|25}}
=== Subsets and supersets ===
Since 25 is 5 x 5, 25edo is the smallest composite EDO that doesn't have any intervals in common with [[12edo]]. Doubling 25edo to get [[50edo]] produces a good [[meantone]] tuning.


== Intervals ==
== Intervals ==
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
| Degrees
! Degrees
| Cents
! Cents
| Approximate <br> Ratios*
! Approximate <br> Ratios*
| Armodue <br> Notation
! Armodue <br> Notation
| colspan="3" | [[Ups and Downs notation]]
! colspan="3" | [[Ups and Downs notation]]
|-
|-
| 0
| 0
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| C#, D
| C#, D
|}
|}
*based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.
<nowiki>*</nowiki> based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.
25-edo chords can be named with ups and downs, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
 
25-edo chords can be named with ups and downs, see [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]].


[[File:25ed2-001.svg|alt=alt : Your browser has no SVG support.]]
[[File:25ed2-001.svg|alt=alt : Your browser has no SVG support.]]
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== Notation ==
== Notation ==
=== Stein–Zimmermann–Gould notation ===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
{{Sharpness-sharp5-szg}}


===Sagittal 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.
This notation uses the same sagittal sequence as [[32edo#Sagittal notation|32-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]].
 
=== Kite's ups and downs notation ===
25edo can 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).
{{Sharpness-sharp5a}}
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[32edo #Sagittal notation|32edo]], and is a superset of the notation for [[5edo #Sagittal notation|5edo]].


<imagemap>
<imagemap>
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rect 20 80 415 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
rect 20 80 415 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:25-EDO_Sagittal.svg]]
default [[File:25-EDO_Sagittal.svg]]
</imagemap>[[MisterShafXen’s 25edo notation]]
</imagemap>
 
=== Second-best fifth (mavila) notation ===
{{Mavila}}


== Regular temperament properties ==
== Regular temperament properties ==
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|}
|}
<references/>
<references/>
== Octave stretch or compression ==
25edo's [[prime]] 3 is very sharp, and its sharp and flat mapping of 11 and 13 are about equally bad, it can benefit from [[octave shrinking]]. Some compressed-octave 25edo tunings include [[ed12|90ed12]], [[ed6|65ed6]] or [[zpi|96zpi]].


== Scales ==
== Scales ==
; [[Antipental blues]]
; [[Antipental blues]]


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Approximated from a [[hexatonic]] subset of the [[dwarf17marv]] scale. Contains lots of [[consonance]]s from the 2.3.7.11 [[subgroup]] while excluding the familiar [[harmonic]] 5.
Approximated from a [[hexatonic]] subset of the [[dwarf17marv]] scale. Contains lots of [[consonance]]s from the 2.3.7.11 [[subgroup]] while excluding the familiar [[harmonic]] 5.


 
; [[Armodue (temperament)|Armodue]]/[[Pelogic]][5]
; [[Armodue]]/[[pelogic]][5]


; 3 3 8 3 8
; 3 3 8 3 8


A [[pentatonic]] and [[MOS]] scale somewhat resembling [[pelog]].
A [[pentatonic]] [[mos]] scale somewhat resembling [[pelog]].
 


; Armodue/pelogic[9]
; Armodue/Pelogic[9]


; 3 3 2 3 3 3 2 2 3 3
; 3 3 2 3 3 3 2 2 3 3


A [[:Category:9-tone scales|9-tone]] MOS scale somewhat resembling pelog.
A [[:Category:9-tone scales|9-tone]] mos scale somewhat resembling pelog.
 


; [[Equipentatonic]]
; [[Equipentatonic]]
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; 5 5 5 5 5
; 5 5 5 5 5


Somewhat resembles [[slendro]]. Is the [[blacksmith]]/[[blackwood]][5] MOS. Is the same as [[5edo]].
Identical to [[5edo]], and [[Blackwood]][5]. Somewhat resembles [[slendro]].  
 


; [[Mabila]]/[[trismegistus]] justified pentatonic
; [[Mabila]]/[[trismegistus]] justified pentatonic
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; 3 3 9 2 8
; 3 3 9 2 8


A pentatonic subset of the mabila/trismegistus[16] MOS scale, it is those temperaments' pentatonic MOS, but with their complex 3/2 substituted in.
A pentatonic subset of the Mabila/Trismegistus[16], it is those temperaments' pentatonic mos, but with their complex 3/2 substituted in.


 
; Mabila/trismegistus justified enneatonic
; Mabila/trismegistus justified nonatonic


; 3 3 2 3 4 2 2 2 3 3
; 3 3 2 3 4 2 2 2 3 3


A 9-tone subset of the mabila/trismegistus[16] MOS scale, it is those temperaments' 9-tone MOS, but with their complex 3/2 substituted in.
A 9-tone subset of the Mabila/Trismegistus[16], it is those temperaments' 9-tone mos, but with their complex 3/2 substituted in.
 


; [[Magic]][13]
; [[Magic]][13]
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; 1 1 5 1 1 1 5 1 1 1 5 1 1
; 1 1 5 1 1 1 5 1 1 1 5 1 1


A [[:Category:13-tone scales|13-tone]] MOS scale. A useful starting point for a [[scalesmith]] to find [[MODMOS]]es, or to find 4- to 9-tone subsets.  
A [[:Category:13-tone scales|13-tone]] mos scale. A useful starting point for a [[scalesmith]] to find [[modmos]]es, or to find 4- to 9-tone subsets.  
 


; Amulet{{idiosyncratic}}
; Amulet{{idiosyncratic}}
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; 2 1 2 2 1 2 3 2 2 1 2 3 2
; 2 1 2 2 1 2 3 2 2 1 2 3 2


A MODMOS of Magic[13]. It is the same as Magic[13], but with 4 tones shifted over by one [[chroma]] (the difference between MOS step sizes, in this case 4\25). This gives its intervals a more even spread, which makes it very useable as a chromatic-like scale. Can also be used to take 4- to 9-tone subsets.
A modmos of Magic[13]. It is the same as Magic[13], but with 4 tones shifted over by one [[chroma]] (the difference between mos step sizes, in this case 4\25). This gives its intervals a more even spread, which makes it very useable as a chromatic-like scale. Can also be used to take 4- to 9-tone subsets.
 


; Fennec{{idiosyncratic}}
; Fennec{{idiosyncratic}}
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A subset of the amulet scale. Approximated from the original fennec scale of [[14edo]].
A subset of the amulet scale. Approximated from the original fennec scale of [[14edo]].


; [[Passion]][13]
; [[Passion]][13]
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; 2 2 2 2 2 2 1 2 2 2 2 2 2
; 2 2 2 2 2 2 1 2 2 2 2 2 2


A 13-tone MOS scale with a lot of consonances available. Can be used as a chromatic-like scale. Can also be used to take 4- to 9-tone subsets.
A 13-tone mos scale with a lot of consonances available. Can be used as a chromatic-like scale. Can also be used to take 4- to 9-tone subsets.
 


; Akebono I
; Akebono I
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A subset of the Passion[13] scale. Approximated from the original Akebono I scale of [[12edo]].
A subset of the Passion[13] scale. Approximated from the original Akebono I scale of [[12edo]].


; Unfair [[blackwood]][10]  
; Unfair [[Blackwood]][10]  


; 4 1 4 1 4 1 4 1 4 1
; 4 1 4 1 4 1 4 1 4 1
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Named "unfair" (by Igliashon Jones) because of the predominance of the larger interval. The major triads come with the large supermajor third.
Named "unfair" (by Igliashon Jones) because of the predominance of the larger interval. The major triads come with the large supermajor third.


 
; Fair [[Blackwood]][10]  
; Fair [[blackwood]][10]  


; 3 2 3 2 3 2 3 2 3 2
; 3 2 3 2 3 2 3 2 3 2


Named "fair" (by Igliashon Jones) because larger and smaller interval are more balanced. The major triads come with the nice 5/4 major third.
Named "fair" (by Igliashon Jones) because larger and smaller interval are more balanced. The major triads come with the nice 5/4 major third.
{{Todo|expand scales list}}


== Relationship to Armodue ==
== Relationship to Armodue ==
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== Keyboard layout ==
== Keyboard layout ==
'''Piano keyboard'''
; Piano keyboard
[[File:mm25.PNG|alt=mm25.PNG|mm25.PNG]]
[[File:mm25.PNG|alt=mm25.PNG|mm25.PNG]]


 
; Lumatone
'''Lumatone'''


See [[Lumatone mapping for 25edo]]
See [[Lumatone mapping for 25edo]]
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* [https://www.youtube.com/watch?v=tMtFIfpju7c ''StartingnStoppinLeftnRight''] (2024)
* [https://www.youtube.com/watch?v=tMtFIfpju7c ''StartingnStoppinLeftnRight''] (2024)


; [[Fabrizio Fulvio Fausto Fiale]]
; [[Bryan Deister]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Fiale/flat%20fourth%20blues.mp3 ''Flat fourth blues'']
* [https://www.youtube.com/shorts/flOUjg09uAY ''25edo''] (2023)
* [https://www.youtube.com/shorts/4WZo1loLbeI ''Waltz in 25edo (short clip)''] (2024)
 
; [[Fabrizio Fiale]]
* [https://web.archive.org/web/20201127012528/http://micro.soonlabel.com/gene_ward_smith/Others/Fiale/flat%20fourth%20blues.mp3 ''Flat fourth blues'']
 
; [[Francium]]
* [https://www.youtube.com/watch?v=VrrnKs97NNY ''Plane Sonatina No. 3''] (2026)
 
; [[groundfault]]
* "Transpiration", from ''A New Dusk'' (2024) – [https://groundfco.bandcamp.com/track/transpiration-25edo Bandcamp] | [https://www.youtube.com/watch?v=1bnEO8vGvbo&t=1560 YouTube (26:00–27:43)]
* "Monolithium", from ''Souvenirs of the Affliction'' (2025) – [https://groundfco.bandcamp.com/track/monolithium-25edo-2 Bandcamp] | [https://www.youtube.com/watch?v=rrjuGmmodn0&t=382 YouTube (6:22–10:08)]


; [[JUMBLE]]
; [[JUMBLE]]
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; [[Budjarn Lambeth]]
; [[Budjarn Lambeth]]
* ''[https://www.youtube.com/watch?v=6VC5FWWMwR4 Improvisation in 25edo (Akebono I scale)]'' (2025)
* [https://www.youtube.com/watch?v=6VC5FWWMwR4 ''Improvisation in 25edo (Akebono I scale)''] (2025)
* ''[https://www.youtube.com/watch?v=ZVsQAZdbvMI Improvisation in 25edo (Antipental Blues scale, glass unison timbre)]'' (2025)
* [https://www.youtube.com/watch?v=ZVsQAZdbvMI ''Improvisation in 25edo (Antipental Blues scale, glass unison timbre)''] (2025)
* ''[https://www.youtube.com/watch?v=iy5Zwc8vipw Improvisation in 25edo (Antipental Blues scale, platinum inharmonic timbre)]'' (2025)
* [https://www.youtube.com/watch?v=iy5Zwc8vipw ''Improvisation in 25edo (Antipental Blues scale, platinum inharmonic timbre)''] (2025)
* ''[https://www.youtube.com/watch?v=B6HGVZzUze4 Improvisation in 25edo (Armodue5 scale)]'' (2025)
* [https://www.youtube.com/watch?v=B6HGVZzUze4 ''Improvisation in 25edo (Armodue5 scale)''] (2025)
* ''[https://www.youtube.com/watch?v=EK7O0SxI9dI Improvisation in 25edo (Fennec scale)]'' (2025)
* [https://www.youtube.com/watch?v=EK7O0SxI9dI ''Improvisation in 25edo (Fennec scale)''] (2025)


; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=oMJjfbdUddU ''Happy Birthday Canon · 6-in-1 Canon in 25edo]''
* [https://www.youtube.com/watch?v=oMJjfbdUddU ''Happy Birthday Canon · 6-in-1 Canon in 25edo'']


; [[Micronaive]]
; [[Micronaive]]
* [https://youtu.be/wCqVRcU9tec ''No.27.63'']
* [https://www.youtube.com/watch?v=wCqVRcU9tec ''No.27.63'']


; [[Herman Miller]]
; [[Herman Miller]]
* ''[https://soundcloud.com/morphosyntax-1/rabbit-tracks-in-the-snow Rabbit Tracks in the Snow]'' (2025)
* [https://soundcloud.com/morphosyntax-1/rabbit-tracks-in-the-snow ''Rabbit Tracks in the Snow''] (2025)


; [[No Clue Music]]
; [[No Clue Music]]
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; [[NullPointerException Music]]
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=kkPavppWUCg ''Edolian - Sepia''] (2020)
* [https://www.youtube.com/watch?v=kkPavppWUCg "Sepia"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)


; [[Paul Rapoport]]
; [[Paul Rapoport]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3 ''Study in Fives'']
* [https://web.archive.org/web/20201127012450/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3 ''Study in Fives'']


; [[Tapeworm Saga]]
; [[Tapeworm Saga]]
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; [[Chris Vaisvil]]
; [[Chris Vaisvil]]
* [http://chrisvaisvil.com/?p=2377 ''Fantasy for Piano in 25 Note per Octave Tuning'']  
* ''Fantasy for Piano in 25 Note per Octave Tuning'' (2012) – [https://www.chrisvaisvil.com/fantasy-for-piano-in-25-note-per-octave-tuning/ blog] | [http://micro.soonlabel.com/25edo/fantasy_for_piano_in_25_edo.mp3 play]
** ''[http://micro.soonlabel.com/25edo/fantasy_for_piano_in_25_edo.mp3 play]''


[[Category:Keyboard]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Twentuning]]
[[Category:Twentuning]]
Retrieved from "https://en.xen.wiki/w/25edo"