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__FORCETOC__
__FORCETOC__
=25 tone equal temperament=
=Theory=


25EDO divides the [[Octave|octave]] in 25 equal steps of exact size 48 [[cent|cent]]s each. It is a good way to tune the [[Blackwood_temperament|Blackwood temperament]], which takes the very sharp fifths of [[5edo|5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 ([[5/4|5/4]]) and 7 ([[7/4|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 divides the [[Octave|octave]] in 25 equal steps of exact size 48 [[cent|cent]]s each. It is a good way to tune the [[Blackwood_temperament|Blackwood temperament]], which takes the very sharp fifths of [[5edo|5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 ([[5/4|5/4]]) and 7 ([[7/4|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.
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If 5/4 and 7/4 aren't 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 aren't 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.
=Music=
''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3 Study in Fives]'' by [http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29 Paul Rapoport]
[http://chrisvaisvil.com/?p=2377 Fantasy for Piano in 25 Note per Octave Tuning] ''[http://micro.soonlabel.com/25edo/fantasy_for_piano_in_25_edo.mp3 play]'' by Chris Vaisvil
''[http://micro.soonlabel.com/gene_ward_smith/Others/Fiale/flat%20fourth%20blues.mp3 Flat fourth blues]'' by Fabrizio Fulvio Fausto Fiale
[[File:25edochorale.mid]] [[:File:25edochorale.mid|25edochorale.mid]] Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded "The <span style="">25edo</span> canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.")
[[File:25_edo_prelude_largo.mid]] [[:File:25_edo_prelude_largo.mid|25 edo prelude largo.mid]] Peter Kosmorsky (2011, Blackwood)


=Intervals=
=Intervals=
{| class="wikitable"
{| class="wikitable"
|-
|-
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| style="text-align:center;" | ^1, ^m2
| style="text-align:center;" | ^1, ^m2
| style="text-align:center;" | up 1sn, upminor 2nd
| style="text-align:center;" | up 1sn, upminor 2nd
| style="text-align:center;" | D^, Eb^
| style="text-align:center;" | ^D, ^Eb
|-
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 2
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| style="text-align:center;" | ^^m2
| style="text-align:center;" | ^^m2
| style="text-align:center;" | double-upminor 2nd
| style="text-align:center;" | double-upminor 2nd
| style="text-align:center;" | Eb^^
| style="text-align:center;" | ^^Eb
|-
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 3
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| style="text-align:center;" | vvM2
| style="text-align:center;" | vvM2
| style="text-align:center;" | double-downmajor 2nd
| style="text-align:center;" | double-downmajor 2nd
| style="text-align:center;" | Evv
| style="text-align:center;" | vvE
|-
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 4
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| style="text-align:center;" | vM2
| style="text-align:center;" | vM2
| style="text-align:center;" | downmajor 2nd
| style="text-align:center;" | downmajor 2nd
| style="text-align:center;" | Ev
| style="text-align:center;" | vE
|-
|-
| style="text-align:center;" | 5·
| style="text-align:center;" | 5·
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| style="text-align:center;" | ^m3
| style="text-align:center;" | ^m3
| style="text-align:center;" | upminor 3rd
| style="text-align:center;" | upminor 3rd
| style="text-align:center;" | F^
| style="text-align:center;" | ^F
|-
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 7
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| style="text-align:center;" | ^^m3
| style="text-align:center;" | ^^m3
| style="text-align:center;" | double-upminor 3rd
| style="text-align:center;" | double-upminor 3rd
| style="text-align:center;" | F^^
| style="text-align:center;" | ^^F
|-
|-
| style="text-align:center;" | 8·
| style="text-align:center;" | 8·
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| style="text-align:center;" | vvM3
| style="text-align:center;" | vvM3
| style="text-align:center;" | double-downmajor 3rd
| style="text-align:center;" | double-downmajor 3rd
| style="text-align:center;" | F#vv
| style="text-align:center;" | vvF#
|-
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 9
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| style="text-align:center;" | vM3
| style="text-align:center;" | vM3
| style="text-align:center;" | downmajor
| style="text-align:center;" | downmajor
| style="text-align:center;" | F#v
| style="text-align:center;" | vF#
|-
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 10
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| style="text-align:center;" | ^4
| style="text-align:center;" | ^4
| style="text-align:center;" | up 4th
| style="text-align:center;" | up 4th
| style="text-align:center;" | G^
| style="text-align:center;" | ^G
|-
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 12
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double-up dim 5th
double-up dim 5th
| style="text-align:center;" | G^^, Ab^^
| style="text-align:center;" | ^^G, ^^Ab
|-
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 13
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double-down 5th
double-down 5th
| style="text-align:center;" | G#vv, Avv
| style="text-align:center;" | vvG#, vvA
|-
|-
| style="text-align:center;" | 14·
| style="text-align:center;" | 14·
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| style="text-align:center;" | v5
| style="text-align:center;" | v5
| style="text-align:center;" | down 5th
| style="text-align:center;" | down 5th
| style="text-align:center;" | Av
| style="text-align:center;" | vA
|-
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 15
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| style="text-align:center;" | ^m6
| style="text-align:center;" | ^m6
| style="text-align:center;" | upminor 6th
| style="text-align:center;" | upminor 6th
| style="text-align:center;" | Bb^
| style="text-align:center;" | ^Bb
|-
|-
| style="text-align:center;" | 17·
| style="text-align:center;" | 17·
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| style="text-align:center;" | ^^m6
| style="text-align:center;" | ^^m6
| style="text-align:center;" | double-upminor 6th
| style="text-align:center;" | double-upminor 6th
| style="text-align:center;" | Bb^^
| style="text-align:center;" | ^^Bb
|-
|-
| style="text-align:center;" | 18
| style="text-align:center;" | 18
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| style="text-align:center;" | vvM6
| style="text-align:center;" | vvM6
| style="text-align:center;" | double-downmajor 6th
| style="text-align:center;" | double-downmajor 6th
| style="text-align:center;" | Bvv
| style="text-align:center;" | vvB
|-
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 19
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| style="text-align:center;" | vM6
| style="text-align:center;" | vM6
| style="text-align:center;" | downmajor 6th
| style="text-align:center;" | downmajor 6th
| style="text-align:center;" | Bv
| style="text-align:center;" | vB
|-
|-
| style="text-align:center;" | 20·
| style="text-align:center;" | 20·
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| style="text-align:center;" | ^m7
| style="text-align:center;" | ^m7
| style="text-align:center;" | upminor 7th
| style="text-align:center;" | upminor 7th
| style="text-align:center;" | C^
| style="text-align:center;" | ^C
|-
|-
| style="text-align:center;" | 22
| style="text-align:center;" | 22
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| style="text-align:center;" | ^^m7
| style="text-align:center;" | ^^m7
| style="text-align:center;" | double-upminor 7th
| style="text-align:center;" | double-upminor 7th
| style="text-align:center;" | C^^
| style="text-align:center;" | ^^C
|-
|-
| style="text-align:center;" | 23
| style="text-align:center;" | 23
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| style="text-align:center;" | vvM7
| style="text-align:center;" | vvM7
| style="text-align:center;" | double-downmajor 7th
| style="text-align:center;" | double-downmajor 7th
| style="text-align:center;" | C#vv
| style="text-align:center;" | vvC#
|-
|-
| style="text-align:center;" | 24
| style="text-align:center;" | 24
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| style="text-align:center;" | vM7
| style="text-align:center;" | vM7
| style="text-align:center;" | downmajor 7th
| style="text-align:center;" | downmajor 7th
| style="text-align:center;" | C#v
| style="text-align:center;" | vC#
|-
|-
| style="text-align:center;" | 25
| style="text-align:center;" | 25
Line 256: Line 244:


=Commas=
=Commas=
25 EDO tempers out the following commas. (Note: This assumes the val &lt; 25 40 58 70 86 93 |.)
25 EDO tempers out the following [[commas]]. (Note: This assumes the val &lt; 25 40 58 70 86 93 |.)


{| class="wikitable"
{| class="wikitable"
|-
|-
! | Comma
! | [[Ratio]]
! | Monzo
! | [[Monzo]]
! | Value (Cents)
! | [[Cents]]
![[Color notation/Temperament Names|Color Name]]
! | Name 1
! | Name 1
! | Name 2
! | Name 2
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| |<nowiki> | 8 -5 </nowiki>&gt;
| |<nowiki> | 8 -5 </nowiki>&gt;
| style="text-align:right;" | 90.22
| style="text-align:right;" | 90.22
| style="text-align:center;" |Sawa
| style="text-align:center;" | Limma
| style="text-align:center;" | Limma
| style="text-align:center;" | Pythagorean Minor 2nd
| style="text-align:center;" | Pythagorean Minor 2nd
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| |<nowiki> | -10 -1 5 </nowiki>&gt;
| |<nowiki> | -10 -1 5 </nowiki>&gt;
| style="text-align:right;" | 29.61
| style="text-align:right;" | 29.61
| style="text-align:center;" |Laquinyo
| style="text-align:center;" | Small Diesis
| style="text-align:center;" | Small Diesis
| style="text-align:center;" | Magic Comma
| style="text-align:center;" | Magic Comma
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| |<nowiki> | 38 -2 -15 </nowiki>&gt;
| |<nowiki> | 38 -2 -15 </nowiki>&gt;
| style="text-align:right;" | 1.38
| style="text-align:right;" | 1.38
| style="text-align:center;" |Sasa-quintrigu
| style="text-align:center;" | Hemithirds Comma
| style="text-align:center;" | Hemithirds Comma
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | -14 0 0 5 </nowiki>&gt;
| |<nowiki> | -14 0 0 5 </nowiki>&gt;
| style="text-align:right;" | 44.13
| style="text-align:right;" | 44.13
| style="text-align:center;" |Laquinzo
| |  
| |  
| |  
| |  
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| |<nowiki> | -4 -1 0 2 </nowiki>&gt;
| |<nowiki> | -4 -1 0 2 </nowiki>&gt;
| style="text-align:right;" | 35.70
| style="text-align:right;" | 35.70
| style="text-align:center;" |Zozo
| style="text-align:center;" | Slendro Diesis
| style="text-align:center;" | Slendro Diesis
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | 6 -2 0 -1 </nowiki>&gt;
| |<nowiki> | 6 -2 0 -1 </nowiki>&gt;
| style="text-align:right;" | 27.26
| style="text-align:right;" | 27.26
| style="text-align:center;" |Ru
| style="text-align:center;" | Septimal Comma
| style="text-align:center;" | Septimal Comma
| style="text-align:center;" | Archytas' Comma
| style="text-align:center;" | Archytas' Comma
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| |<nowiki> | 0 -2 5 -3 </nowiki>&gt;
| |<nowiki> | 0 -2 5 -3 </nowiki>&gt;
| style="text-align:right;" | 21.18
| style="text-align:right;" | 21.18
| style="text-align:center;" |Triru-aquinyo
| style="text-align:center;" | Gariboh
| style="text-align:center;" | Gariboh
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | -4 1 -5 5 </nowiki>&gt;
| |<nowiki> | -4 1 -5 5 </nowiki>&gt;
| style="text-align:right;" | 14.52
| style="text-align:right;" | 14.52
| style="text-align:center;" |Quinzogu
| style="text-align:center;" | Trimyna
| style="text-align:center;" | Trimyna
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | -10 1 0 3 </nowiki>&gt;
| |<nowiki> | -10 1 0 3 </nowiki>&gt;
| style="text-align:right;" | 8.43
| style="text-align:right;" | 8.43
| style="text-align:center;" |Latrizo
| style="text-align:center;" | Gamelisma
| style="text-align:center;" | Gamelisma
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | 6 0 -5 2 </nowiki>&gt;
| |<nowiki> | 6 0 -5 2 </nowiki>&gt;
| style="text-align:right;" | 6.08
| style="text-align:right;" | 6.08
| style="text-align:center;" |Zozoquingu
| style="text-align:center;" | Hemimean
| style="text-align:center;" | Hemimean
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | -16 1 5 1 </nowiki>&gt;
| |<nowiki> | -16 1 5 1 </nowiki>&gt;
| style="text-align:right;" | 2.35
| style="text-align:right;" | 2.35
| style="text-align:center;" |Lazoquinyo
| style="text-align:center;" | Horwell
| style="text-align:center;" | Horwell
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;
| style="text-align:right;" | 17.40
| style="text-align:right;" | 17.40
| style="text-align:center;" |Luyoyo
| style="text-align:center;" | Ptolemisma
| style="text-align:center;" | Ptolemisma
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| style="text-align:right;" | 9.86
| style="text-align:right;" | 9.86
| style="text-align:center;" |Lorugugu
| style="text-align:center;" | Valinorsma
| style="text-align:center;" | Valinorsma
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | -1 -2 -1 1 0 1 </nowiki>&gt;
| |<nowiki> | -1 -2 -1 1 0 1 </nowiki>&gt;
| style="text-align:right;" | 19.13
| style="text-align:right;" | 19.13
| style="text-align:center;" |Thozogu
| style="text-align:center;" | Superleap
| style="text-align:center;" | Superleap
| style="text-align:center;" |  
| style="text-align:center;" |  
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| |<nowiki> | 2 -3 -2 0 0 2 </nowiki>&gt;
| |<nowiki> | 2 -3 -2 0 0 2 </nowiki>&gt;
| style="text-align:right;" | 2.56
| style="text-align:right;" | 2.56
| style="text-align:center;" |Bithogu
| style="text-align:center;" | Parizeksma
| style="text-align:center;" | Parizeksma
| style="text-align:center;" |  
| style="text-align:center;" |  
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=A 25edo keyboard=
=A 25edo keyboard=


[[File:mm25.PNG|alt=mm25.PNG|mm25.PNG]]    
[[File:mm25.PNG|alt=mm25.PNG|mm25.PNG]]
=Music=
''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3 Study in Fives]'' by [http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29 Paul Rapoport]
 
[http://chrisvaisvil.com/?p=2377 Fantasy for Piano in 25 Note per Octave Tuning] ''[http://micro.soonlabel.com/25edo/fantasy_for_piano_in_25_edo.mp3 play]'' by Chris Vaisvil
 
''[http://micro.soonlabel.com/gene_ward_smith/Others/Fiale/flat%20fourth%20blues.mp3 Flat fourth blues]'' by Fabrizio Fulvio Fausto Fiale
 
[[File:25edochorale.mid]] [[:File:25edochorale.mid|25edochorale.mid]] Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded "The <span style="">25edo</span> canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.")
 
[[File:25_edo_prelude_largo.mid]] [[:File:25_edo_prelude_largo.mid|25 edo prelude largo.mid]] Peter Kosmorsky (2011, Blackwood)
[[Category:25edo]]
[[Category:25edo]]
[[Category:edo]]
[[Category:edo]]
Retrieved from "https://en.xen.wiki/w/25edo"