99edo
The 99 equal temperament, often abbreviated 99-tET, 99-EDO, or 99-ET, is the scale derived by dividing the octave into 99 equally-sized steps, where each step represents a frequency ratio of 12.1212 cents. It is a very strong 7-limit (and 9 odd limit) temperament, but extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far of the mark. It tempers out 3136/3125, 5120/5103, 6144/6125, 2401/2400 and 4375/4374, and supports hemififths, amity, parakleismic, hemiwürschmidt and ennealimmal temperaments, and is pretty well a perfect tuning for hendecatonic temperament. It has a sound defined by the slight sharpness (1.075, 1.565, 0.871 cents) of its 3, 5, and 7.
Using the patent val, <99 157 230 278 342|, 99 is the optimal patent val for the rank four temperament tempering out 121/120; zeus, the rank three temperament tempering out 121/120 and 176/175; hemiwur, one of the rank two 11-limit extensions of hemiwürschmidt; and hitchcock (11-limit amity), the rank two temperament which also tempers out 2200/2187. Using the <99 157 230 278 343| ("99e") val, 99 tempers out 896/891, 243/242, 441/440 and 540/539, and is an excellent tuning for the 11-limit version of hemififths temperament. Hence 99, in spite of the fact that it tunes 11 relatively badly, is an important 11-limit tuning in more than one way.
Scales[edit]
Music in 99edo[edit]
Nonaginta et Novem play by Gene Ward Smith
Benny Smith-Palestrina in zeus7tri
Intervals[edit]
See Table of 99edo intervals for the ratios the intervals approximate.
| Degrees | Cents Value |
|---|---|
| 1 | 12.121 |
| 2 | 24.242 |
| 3 | 36.364 |
| 4 | 48.485 |
| 5 | 60.606 |
| 6 | 72.727 |
| 7 | 84.848 |
| 8 | 96.97 |
| 9 | 109.091 |
| 10 | 121.212 |
| 11 | 133.333 |
| 12 | 145.455 |
| 13 | 157.576 |
| 14 | 169.697 |
| 15 | 181.818 |
| 16 | 193.939 |
| 17 | 206.061 |
| 18 | 218.182 |
| 19 | 230.303 |
| 20 | 242.424 |
| 21 | 254.545 |
| 22 | 266.667 |
| 23 | 278.788 |
| 24 | 290.909 |
| 25 | 303.03 |
| 26 | 315.152 |
| 27 | 327.273 |
| 28 | 339.394 |
| 29 | 351.515 |
| 30 | 363.636 |
| 31 | 375.758 |
| 32 | 387.879 |
| 33 | 400 |
| 34 | 412.121 |
| 35 | 424.242 |
| 36 | 436.364 |
| 37 | 448.485 |
| 38 | 460.606 |
| 39 | 472.727 |
| 40 | 484.848 |
| 41 | 496.97 |
| 42 | 509.091 |
| 43 | 521.212 |
| 44 | 533.333 |
| 45 | 545.455 |
| 46 | 557.576 |
| 47 | 569.697 |
| 48 | 581.818 |
| 49 | 593.939 |
| 50 | 606.061 |
| 51 | 618.182 |
| 52 | 630.303 |
| 53 | 642.424 |
| 54 | 654.545 |
| 55 | 666.667 |
| 56 | 678.788 |
| 57 | 690.909 |
| 58 | 703.03 |
| 59 | 715.152 |
| 60 | 727.273 |
| 61 | 739.394 |
| 62 | 751.515 |
| 63 | 763.636 |
| 64 | 775.758 |
| 65 | 787.879 |
| 66 | 800 |
| 67 | 812.121 |
| 68 | 824.242 |
| 69 | 836.364 |
| 70 | 848.485 |
| 71 | 860.606 |
| 72 | 872.727 |
| 73 | 884.848 |
| 74 | 896.97 |
| 75 | 909.091 |
| 76 | 921.212 |
| 77 | 933.333 |
| 78 | 945.455 |
| 79 | 957.576 |
| 80 | 969.697 |
| 81 | 981.818 |
| 82 | 993.939 |
| 83 | 1006.061 |
| 84 | 1018.182 |
| 85 | 1030.303 |
| 86 | 1042.424 |
| 87 | 1054.545 |
| 88 | 1066.667 |
| 89 | 1078.788 |
| 90 | 1090.909 |
| 91 | 1103.03 |
| 92 | 1115.152 |
| 93 | 1127.273 |
| 94 | 1139.394 |
| 95 | 1151.515 |
| 96 | 1163.636 |
| 97 | 1175.758 |
| 98 | 1187.879 |
| 99 | 1200 |
See also[edit]
- 94edo, a similarly sized edo with a very accurate 3 and consistency in 23-odd-limit
- 105edo, a similarly sized edo that is meantone, septimal meantone, undecimal meantone and grosstone