99edo
99edo is the equal division of the octave into 99 parts of 12.1212 cents each. 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 off the mark. It tempers out 393216/390625 (würschmidt comma) and 1600000/1594323 (amity comma) in the 5-limit; 2401/2400 (breedsma), 3136/3125 (hemimean comma), and 4375/4374 (ragisma) in the 7-limit, supporting 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, 99EDO 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; hemiwür, 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, it 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 equal divisions, in spite of the fact that it tunes 11 relatively badly, is an important 11-limit tuning in more than one way.
Scales
Music in 99edo
Nonaginta et Novem play by Gene Ward Smith
Benny Smith-Palestrina in zeus7tri
Intervals
See Table of 99edo intervals for the ratios the intervals approximate.
| Degrees | Cents Value | 7mus |
|---|---|---|
| 1 | 12.121 | 15.515 (F.83E16) |
| 2 | 24.242 | 31.03 (1F.07C16) |
| 3 | 36.364 | 46.5455 (2E.8BA16) |
| 4 | 48.485 | 62.061 (3E.0F816) |
| 5 | 60.606 | 77.576 (4D.93616) |
| 6 | 72.727 | 93.091 (5D.17416) |
| 7 | 84.8485 | 108.606 (6C.9B216) |
| 8 | 96.97 | 124.121 (7C.1F0816) |
| 9 | 109.091 | 139.636 (8B.A2F16) |
| 10 | 121.212 | 155.1515 (9B.26D16) |
| 11 | 133.333 | 170.667 (AA.AAB16) |
| 12 | 145.4545 | 186.182 (BA.2E916) |
| 13 | 157.576 | 201.697 (C9.B2716) |
| 14 | 169.697 | 217.212 (D9.36516) |
| 15 | 181.818 | 232.727 (E8.BA316) |
| 16 | 193.939 | 248.242 (F8.3E116) |
| 17 | 206.061 | 263.758 (107.C1F16) |
| 18 | 218.182 | 279.273 (117.45D16) |
| 19 | 230.303 | 294.788 (126.C9B16) |
| 20 | 242.424 | 310.303 (136.4D916) |
| 21 | 254.5455 | 325.818 (145.D1716) |
| 22 | 266.667 | 341.333 (155.55516) |
| 23 | 278.788 | 356.8485 (164.D9316) |
| 24 | 290.909 | 372.364 (174.5D116) |
| 25 | 303.03 | 387.879 (183.E0F816) |
| 26 | 315.1515 | 403.394 (193.64E16) |
| 27 | 327.273 | 418.909 (1A2.E8C16) |
| 28 | 339.394 | 434.424 (1B2.6CA16) |
| 29 | 351.515 | 449.939 (1C1.F0816) |
| 30 | 363.636 | 465.4545 (1D1.74616) |
| 31 | 375.758 | 480.97 (1E0.F8416) |
| 32 | 387.879 | 496.485 (1F0.7C216) |
| 33 | 400 | 512 (20016) |
| 34 | 412.121 | 527.515 (20F.83E16) |
| 35 | 424.242 | 543.03 (21F.07C16) |
| 36 | 436.364 | 558.5455 (22E.8BA16) |
| 37 | 448.485 | 574.061 (23E.0F816) |
| 38 | 460.606 | 589.576 (24D.93616) |
| 39 | 472.727 | 605.091 (5D.17416) |
| 40 | 484.8485 | 620.606 (26C.9B216) |
| 41 | 496.97 | 636.121 (27C.1F0816) |
| 42 | 509.091 | 651.636 (28B.A2F16) |
| 43 | 521.212 | 667.1515 (29B.26D16) |
| 44 | 533.333 | 692.667 (2AA.AAB16) |
| 45 | 545.4545 | 698.182 (2BA.2E916) |
| 46 | 557.576 | 713.697 (2C9.B2716) |
| 47 | 569.697 | 729.212 (2D9.36516) |
| 48 | 581.818 | 744.727 (2E8.BA316) |
| 49 | 593.939 | 760.242 (2F8.3E116) |
| 50 | 606.061 | 775.758 (307.C1F16) |
| 51 | 618.182 | 791.273 (317.45D16) |
| 52 | 630.303 | 806.788 (326.C9B16) |
| 53 | 642.424 | 822.303 (336.4D916) |
| 54 | 654.5455 | 837.818 (345.D1716) |
| 55 | 666.667 | 853.333 (355.55516) |
| 56 | 678.788 | 868.8485 (364.D9316) |
| 57 | 690.909 | 884.364 (374.5D116) |
| 58 | 703.03 | 899.879 (383.E0F816) |
| 59 | 715.1515 | 915.394 (393.64E16) |
| 60 | 727.273 | 930.909 (3A2.E8C16) |
| 61 | 739.394 | 946.424 (3B2.6CA16) |
| 62 | 751.515 | 961.939 (3C1.F0816) |
| 63 | 763.636 | 977.4545 (3D1.74616) |
| 64 | 775.758 | 992.97 (3E0.F8416) |
| 65 | 787.879 | 1008.485 (3F0.7C216) |
| 66 | 800 | 1024 (40016) |
| 67 | 812.121 | 1039.515 (40F.83E16) |
| 68 | 824.242 | 1055.03 (41F.07C16) |
| 69 | 836.364 | 1070.5455 (42E.8BA16) |
| 70 | 848.485 | 1086.061 (43E.0F816) |
| 71 | 860.606 | 1101.576 (44D.93616) |
| 72 | 872.727 | 1117.091 (45D.17416) |
| 73 | 884.8485 | 1132.606 (46C.9B216) |
| 74 | 896.97 | 1148.121 (47C.1F0816) |
| 75 | 909.091 | 1163.636 (48B.A2F16) |
| 76 | 921.212 | 1179.1515 (49B.26D16) |
| 77 | 933.333 | 1194.667 (4AA.AAB16) |
| 78 | 945.4545 | 1210.182 (4BA.2E916) |
| 79 | 957.576 | 1225.697 (4C9.B2716) |
| 80 | 969.697 | 1241.212 (4D9.36516) |
| 81 | 981.818 | 1256.727 (4E8.BA316) |
| 82 | 993.939 | 1272.242 (4F8.3E116) |
| 83 | 1006.061 | 1287.758 (507.C1F16) |
| 84 | 1018.182 | 1303.273 (517.45D16) |
| 85 | 1030.303 | 1318.788 (526.C9B16) |
| 86 | 1042.424 | 1334.303 (536.4D916) |
| 87 | 1054.5455 | 1349.818 (545.D1716) |
| 88 | 1066.667 | 1365.333 (555.55516) |
| 89 | 1078.788 | 1380.8485 (564.D9316) |
| 90 | 1090.909 | 1396.364 (574.5D116) |
| 91 | 1103.03 | 1411.879 (583.E0F816) |
| 92 | 1115.1515 | 1427.394 (593.64E16) |
| 93 | 1127.273 | 1442.909 (5A2.E8C16) |
| 94 | 1139.394 | 1458.424 (5B2.6CA16) |
| 95 | 1151.515 | 1473.939 (5C1.F0816) |
| 96 | 1163.636 | 1489.4545 (5D1.74616) |
| 97 | 1175.758 | 1504.97 (5E0.F8416) |
| 98 | 1187.879 | 1520.485 (5F0.7C216) |
| 99 | 1200 | 1536 (60016) |
See also
- 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