editing disabled

84edo divides the octave into 84 equal parts of size 14.286 cents 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, <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
84e: 99/98, 121/120, 176/175, 385/384, 540/539, 5632/5625

13-limit commas: 144/143, 351/350, 364/363, 625/625
84e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000

Music


Ten by John Cage, 1991, for chamber ensemble. Ives Ensemble recording (YouTube).
Two4 by John Cage, 1991, for violin and piano or shō. Harr & Miyata recording (YouTube).
Two5 by John Cage, 1991, for tenor trombone and piano. Fulkerson & Denyer recording (YouTube).
Two6 by John Cage, 1992, for violin and piano. Haar & Snijders recording (YouTube).