99edo

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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

tutone6

tutone7

tutone13

zeus7tri

zeus8tri

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
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

  • 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