96edo: Difference between revisions

<span style="display: block; text-align: right;">Other languages: [[:de:96edo Deutsch]]</span>

<youtube>3O3H01c2SjE</youtube>

=Properties=

The 96 equal division divides the octave into 96 equal parts of exactly 12.5 cents each. As a [[5-limit|5-limit]] system, it can be characterized by the fact that it tempers out both the Pythagorean comma, 531441/524288, Würschmidt's comma, 393216/390625, the unicorn comma, 1594323/1562500, and the kwazy comma, |-53 10 16&gt;. It therefore has the same familiar 700 cent fifth as [[12edo|12edo]], and has a best major third of 387.5 cents, a bit over a cent sharp. There is therefore nothing to complain of with its representation of the 5-limit and it can be recommended as an approach to the [[Würschmidt_family|Würschmidt family]] of temperaments. It also tempers out the unicorn comma, and serves a way of tuning temperaments in the [[Unicorn_family|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.

=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.

 

=Links=

 

==Carrillo==

See [[Julián_Carrillo|Julián Carrillo]] .

 

==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'] .

 

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

 

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

 

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

 

[http://www.tonysalinas.com/ Martin Salinas, J.A.] [[Autumn|'Autumn' conic bellophone &amp; mixed quintet.mp3]] / [[Conic_Bellophone_in_96edo|Pictures of the 96edo conic bellophone]]

 

[http://en.wikipedia.org/wiki/Georg_Friedrich_Haas Haas, Georg Friedrich], "flow and friction"

 

=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/Endless%20life.mp3 Endless life] by Shahiin Mohajeri

 

[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Heroic%20elegy.mp3 Heroic elegy] by Shahiin Mohajeri

 

[[: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]]      [[Category:edo]]