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In the [[7-limit|7-limit]], 96 has two possible mappings for 7/4, a sharp one of 975 cents from the patent val, and a flat one of 962.5 cents from 96d. Using the sharp mapping, 96 tempers out 225/224 and supports 7-limit würschmidt temperament, and using the flat mapping it tempers out 126/125 and supports worschmidt temperament. We can also dispense with 7 altogether, and use it as a no-sevens system, where it tempers out 243/242 in the 11-limit and 676/675 in the 13-limit. If we include 7, then the sharp mapping tempers out 99/98 and 176/175 in the 11-limit, and 169/168 in the 13-limit, and this provides the optimal patent val for [[Marvel_temperaments#Submajor-Interpental|interpental temperament]]. With the flat 7 it tempers out 385/384 in the 11-limit and 196/195 and 364/363 in the 13-limit, and serves for the various temperaments of the unicorn family.
In the [[7-limit|7-limit]], 96 has two possible mappings for 7/4, a sharp one of 975 cents from the patent val, and a flat one of 962.5 cents from 96d. Using the sharp mapping, 96 tempers out 225/224 and supports 7-limit würschmidt temperament, and using the flat mapping it tempers out 126/125 and supports worschmidt temperament. We can also dispense with 7 altogether, and use it as a no-sevens system, where it tempers out 243/242 in the 11-limit and 676/675 in the 13-limit. If we include 7, then the sharp mapping tempers out 99/98 and 176/175 in the 11-limit, and 169/168 in the 13-limit, and this provides the optimal patent val for [[Marvel_temperaments#Submajor-Interpental|interpental temperament]]. With the flat 7 it tempers out 385/384 in the 11-limit and 196/195 and 364/363 in the 13-limit, and serves for the various temperaments of the unicorn family.


Since 96edo has a step of 12.5 cents, it also allows one to use its MOS scales as circulating temperaments. It is the first 12n-edo which does this and the first edo which allows one to use an MOS scale with a step 20 degrees or larger as a circulating temperament.
{| class="wikitable"
|+Circulating temperaments in 96edo
!Tones
!Pattern
!L:s
|-
|5
|[[4L 1s]]
|20:19
|-
|6
|[[6edo]]
|equal
|-
|7
|[[5L 2s]]
|14:13
|-
|8
|[[8edo]]
|equal
|-
|9
|[[6L 3s]]
|11:10
|-
|10
|[[6L 4s]]
|10:9
|-
|11
|[[8L 3s]]
|9:8
|-
|12
|[[12edo]]
|equal
|-
| 13
|[[5L 8s]]
|8:7
|-
|14
|[[12L 2s]]
| rowspan="2" |7:6
|-
|15
|[[6L 9s]]
|-
|16
|[[16edo]]
|equal
|-
|17
|[[11L 6s]]
| rowspan="3" |6:5
|-
|18
|6L 12s
|-
| 19
|1L 18s
|-
|20
|16L 4s
| rowspan="4" |5:4
|-
|21
|12L 9s
|-
|22
|8L 14s
|-
|23
|4L 19s
|-
|24
|[[24edo]]
|equal
|-
|25
|21L 4s
| rowspan="7" |4:3
|-
|26
|18L 8s
|-
|27
|15L 12s
|-
|28
|12L 16s
|-
|29
|9L 20s
|-
|30
|6L 24s
|-
|31
|3L 28s
|-
|32
|[[32edo]]
|equal
|-
|33
|30L 3s
| rowspan="15" |3:2
|-
| 34
|28L 6s
|-
|35
|26L 9s
|-
|36
|24L 12s
|-
|37
|22L 15s
|-
| 38
|20L 18s
|-
|39
|18L 21s
|-
|40
|16L 24s
|-
|41
|14L 27s
|-
|42
|12L 30s
|-
|43
|10L 33s
|-
|44
|8L 36s
|-
|45
|6L 39s
|-
|46
|4L 42s
|-
|47
|2L 45s
|-
|48
|[[48edo]]
|equal
|-
|49
|47L 2s
| rowspan="28" |2:1
|-
|50
|46L 4s
|-
|51
|45L 6s
|-
|52
|44L 8s
|-
|53
|43L 10s
|-
|54
|42L 12s
|-
|55
|41L 14s
|-
|56
|40L 16s
|-
|57
|39L 18s
|-
|58
|38L 20s
|-
|59
|37L 22s
|-
|60
|36L 24s
|-
|61
|35L 26s
|-
|62
|34L 28s
|-
|63
|33L 30s
|-
|64
|32L 32s
|-
|65
|31L 34s
|-
|66
|30L 36s
|-
|67
|29L 38s
|-
|68
|28L 40s
|-
|69
|27L 42s
|-
|70
|26L 44s
|-
|71
|25L 46s
|-
|72
|24L 48s
|-
|73
|23L 50s
|-
|74
|22L 52s
|-
|75
|21L 54s
|-
|76
|20L 56s
|}
=History=
=History=
96 equal divisions of the octave was first used by the Mexican composer and theorist [[Julián_Carrillo|Julián Carrillo]]. It has subsequently been used by a number of other composers.
96 equal divisions of the octave was first used by the Mexican composer and theorist [[Julián Carrillo]]. It has subsequently been used by a number of other composers.


=Links=
=Links=


==Carrillo==
==Carrillo==
See [[Julián_Carrillo|Julián Carrillo]] .
See [[Julián Carrillo]] .


==Other composers==
== Other composers==
Works for the [http://www.sauter-pianos.de/english/pianos/microtone.html Sauter's 1/16tone microtone piano] by the composers [http://presence.or.at/einklang/Archiv/archiv_Komponisten_E.htm#flammer Ernest Helmuth Flammer], Marc Kilchenmann, Bernfried E. G. Pröve, [http://www.musinfo.ch/index.php?content=maske_werke&pers_id=150&name=Imholz&vorname=Martin&setLanguage=en Martin Imholz], Franck Cristoph Yeznikian, [http://www.schauhoer-verlag.de/cms/file_download/13/Vita_WMG_lang.pdf Werner Grimmel], and [http://www.moderecords.com/catalog/120_121bancquart.html Alain Bancquart], are recompilated on this CD: [http://www.dominikblum.ch/carillo_d.shtml 'The Carrillo tone piano'] .
Works for the [http://www.sauter-pianos.de/english/pianos/microtone.html Sauter's 1/16tone microtone piano] by the composers [http://presence.or.at/einklang/Archiv/archiv_Komponisten_E.htm#flammer Ernest Helmuth Flammer], Marc Kilchenmann, Bernfried E. G. Pröve, [http://www.musinfo.ch/index.php?content=maske_werke&pers_id=150&name=Imholz&vorname=Martin&setLanguage=en Martin Imholz], Franck Cristoph Yeznikian, [http://www.schauhoer-verlag.de/cms/file_download/13/Vita_WMG_lang.pdf Werner Grimmel], and [http://www.moderecords.com/catalog/120_121bancquart.html Alain Bancquart], are recompilated on this CD: [http://www.dominikblum.ch/carillo_d.shtml 'The Carrillo tone piano'] .


[http://www.96edo.com/ Mohajeri, Shaahin]
[http://www.96edo.com/ Mohajeri, Shaahin]


[http://mac-texier.ircam.fr/textes/c00001420/ Marie, Jean-Etienne ]
[http://mac-texier.ircam.fr/textes/c00001420/ Marie, Jean-Etienne]


[http://en.wikipedia.org/wiki/Pascale_Criton Criton, Pascale]
[http://en.wikipedia.org/wiki/Pascale_Criton Criton, Pascale]
Line 34: Line 277:


=Music=
=Music=
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/4gahforbrass-880821.mp3 4gah for brass] by [[Shahiin_Mohajeri|Shahiin Mohajeri]]
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/4gahforbrass-880821.mp3 4gah for brass] by [[Shahiin Mohajeri]]


[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Endless%20life.mp3 Endless life] by Shahiin Mohajeri
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Endless%20life.mp3 Endless life] by Shahiin Mohajeri
Line 42: Line 285:
[[:File:01_-_Autumn_1.mp3|Autumn for conic bellophone and mixed quintet]] by Tony Salinas
[[:File:01_-_Autumn_1.mp3|Autumn for conic bellophone and mixed quintet]] by Tony Salinas


[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Carrillo/Cromometrofon%eda%20%231.mp3 Cromometrofonía #1] by [[Julián_Carrillo|Julián Carrillo]]     
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Carrillo/Cromometrofon%eda%20%231.mp3 Cromometrofonía #1] by [[Julián Carrillo]]     


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
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