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Properties

The 96 equal division divides the octave into 96 equal parts of exactly 12.5 cents each. As a 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>. It therefore has the same familiar 700 cent fifth as 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 of temperaments. It also tempers out the unicorn comma, and serves a way of tuning temperaments in the unicorn family.

In the 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 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. It has subsequently been used by a number of other composers.

Links

Carrillo

See Julián Carrillo .

Other composers

Works for the Sauter's 1/16tone microtone piano by the composers Ernest Helmuth Flammer, Marc Kilchenmann, Bernfried E. G. Pröve, Martin Imholz, Franck Cristoph Yeznikian, Werner Grimmel, and Alain Bancquart, are recompilated on this CD: 'The Carrillo tone piano' .
Mohajeri, Shaahin
Marie, Jean-Etienne
Criton, Pascale
Martin Salinas, J.A. 'Autumn' conic bellophone & mixed quintet.mp3 / Pictures of the 96edo conic bellophone
Haas, Georg Friedrich, "flow and friction"

Music

4gah for brass by Shahiin Mohajeri
Endless life by Shahiin Mohajeri
Heroic elegy by Shahiin Mohajeri
Autumn for conic bellophone and mixed quintet by Tony Salinas
Cromometrofonía #1 by Julián Carrillo