84edo: Difference between revisions
No edit summary Tags: Mobile edit Mobile web edit |
No edit summary |
||
| Line 1: | Line 1: | ||
'''84edo''' divides the [[octave]] into 84 equal parts of size 14.286 [[cent]]s each | '''84edo''' divides the [[octave]] into 84 equal parts of size 14.286 [[cent]]s each. | ||
== Theory == | |||
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]]. | |||
84edo is where the '''[[orwell]]''' temperament takes its name from, since the generator of 7/6 is equal to 19 steps of the EDO, referencing the [[Wikipedia:Nineteen Eighty-Four|book 1984]]. The maximum evenness orwell in this temperament is a 31 note scale. | |||
{{Primes in edo|84}} | |||
== Table of intervals == | |||
{| class="wikitable" | |||
|+Table of 84edo intervals | |||
!Step | |||
!Size (Cents) | |||
!Orwell[31] Name | |||
!Associated ratio | |||
|- | |||
|0 | |||
|0.000 | |||
|unison, prime | |||
|1/1 | |||
|- | |||
|3 | |||
|42.857 | |||
|second | |||
| | |||
|- | |||
|6 | |||
|85.714 | |||
|third | |||
| | |||
|- | |||
|9 | |||
|128.571 | |||
| | |||
| | |||
|- | |||
|11 | |||
|157.142 | |||
| | |||
| | |||
|- | |||
|14 | |||
|200.000 | |||
| | |||
| | |||
|- | |||
|17 | |||
|242.857 | |||
| | |||
| | |||
|- | |||
|19 | |||
|271.428 | |||
|eighth | |||
|7/6 | |||
|- | |||
|38 | |||
| | |||
|fifteenth | |||
|11/8 | |||
|- | |||
|57 | |||
| | |||
|twenty-second | |||
|5/3 | |||
|} | |||
== Tempered commas == | |||
[[5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152 | [[5-limit]] commas: 78732/78125, 531441/524288, 2109375/2097152 | ||
| Line 12: | Line 79: | ||
84e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000 | 84e: 275/273, 640/637, 351/350, 352/351, 625/624, 1001/1000 | ||
== Music == | == Music == | ||
Revision as of 17:28, 24 January 2022
84edo divides the octave into 84 equal parts of size 14.286 cents each.
Theory
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.
84edo is where the orwell temperament takes its name from, since the generator of 7/6 is equal to 19 steps of the EDO, referencing the book 1984. The maximum evenness orwell in this temperament is a 31 note scale.
Script error: No such module "primes_in_edo".
Table of intervals
| Step | Size (Cents) | Orwell[31] Name | Associated ratio |
|---|---|---|---|
| 0 | 0.000 | unison, prime | 1/1 |
| 3 | 42.857 | second | |
| 6 | 85.714 | third | |
| 9 | 128.571 | ||
| 11 | 157.142 | ||
| 14 | 200.000 | ||
| 17 | 242.857 | ||
| 19 | 271.428 | eighth | 7/6 |
| 38 | fifteenth | 11/8 | |
| 57 | twenty-second | 5/3 |
Tempered commas
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).