84edo: Difference between revisions

'''84edo''' divides the [[octave]] into 84 equal parts of size 14.286 [[cent]]s each and it is the highest edo where the size of 3 has a common factor with its cardinality. It makes for an excellent orwell tuning and also a good one for compton, and the 84e val, {{val| 84 133 195 236 290 }}, is almost identical to the 11-limit POTE tuning for orwell. In the [[13-limit]] it is the [[optimal patent val]] for the rank five temperament tempering out [[144/143]].

[[5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152

[[7-limit]] commas: 225/224, 1728/1715, 2430/2401, 6144/6125

[[11-limit]] commas: 441/440, 1344/1331, 1375/1372

[[13-limit]] commas: 144/143, 351/350, 364/363, 625/625

== Music ==

* ''Ten'' by John Cage, 1991, for chamber ensemble. [http://youtu.be/PE_2Ds_6qGk Ives Ensemble recording (YouTube)]

* ''Two4'' by John Cage, 1991, for violin and piano or shō. [http://youtu.be/sLOrpd5onCs Harr & Miyata recording (YouTube)]

* ''Two5'' by John Cage, 1991, for tenor trombone and piano. [http://youtu.be/YOtQZIqfY1w Fulkerson & Denyer recording (YouTube)].

* ''Two6'' by John Cage, 1992, for violin and piano. [http://youtu.be/XkX37zH6AbU Haar & Snijders recording (YouTube)].

[[Category:Compton]]

[[Category:John Cage]]

[[Category:Listen]]

[[Category:Orwell]]

[[Category:Grossmic]]