84edo: Difference between revisions
m Cleanup; +category |
tried to include the patent val as well. Please reword if this reads bad! Thanks :) |
||
| Line 1: | Line 1: | ||
'''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. | '''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. Its [[patent val]] {{val| 84 133 195 236 291}} makes it 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 | [[5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152 | ||
Revision as of 19:04, 1 March 2021
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. Its patent val ⟨84 133 195 236 291] makes it 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).