99edo

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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

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 pions 7mus
1 12.121 12.8485 15.515 (F.83E16)
2 24.242 25.697 31.03 (1F.07C16)
3 36.364 38.5455 46.5455 (2E.8BA16)
4 48.485 51.394 62.061 (3E.0F816)
5 60.606 64.242 77.576 (4D.93616)
6 72.727 77.091 93.091 (5D.17416)
7 84.8485 89.939 108.606 (6C.9B216)
8 96.97 102.788 124.121 (7C.1F0816)
9 109.091 115.636 139.636 (8B.A2F16)
10 121.212 128.485 155.1515 (9B.26D16)
11 133.333 141.333 170.667 (AA.AAB16)
12 145.4545 154.182 186.182 (BA.2E916)
13 157.576 167.03 201.697 (C9.B2716)
14 169.697 179.879 217.212 (D9.36516)
15 181.818 192.727 232.727 (E8.BA316)
16 193.939 205.576 248.242 (F8.3E116)
17 206.061 218.424 263.758 (107.C1F16)
18 218.182 231.273 279.273 (117.45D16)
19 230.303 244.121 294.788 (126.C9B16)
20 242.424 256.97 310.303 (136.4D916)
21 254.5455 269.818 325.818 (145.D1716)
22 266.667 282.666 341.333 (155.55516)
23 278.788 295.515 356.8485 (164.D9316)
24 290.909 308.364 372.364 (174.5D116)
25 303.03 321.212 387.879 (183.E0F816)
26 315.1515 334.061 403.394 (193.64E16)
27 327.273 346.909 418.909 (1A2.E8C16)
28 339.394 359.758 434.424 (1B2.6CA16)
29 351.515 372.606 449.939 (1C1.F0816)
30 363.636 385.4545 465.4545 (1D1.74616)
31 375.758 398.303 480.97 (1E0.F8416)
32 387.879 411.1515 496.485 (1F0.7C216)
33 400 424 512 (20016)
34 412.121 436.8485 527.515 (20F.83E16)
35 424.242 449.697 543.03 (21F.07C16)
36 436.364 462.5455 558.5455 (22E.8BA16)
37 448.485 475.394 574.061 (23E.0F816)
38 460.606 488.2424 589.576 (24D.93616)
39 472.727 501.091 605.091 (5D.17416)
40 484.8485 513.939 620.606 (26C.9B216)
41 496.97 526.788 636.121 (27C.1F0816)
42 509.091 539.636 651.636 (28B.A2F16)
43 521.212 552.485 667.1515 (29B.26D16)
44 533.333 565.333 692.667 (2AA.AAB16)
45 545.4545 578.182 698.182 (2BA.2E916)
46 557.576 591.03 713.697 (2C9.B2716)
47 569.697 603.879 729.212 (2D9.36516)
48 581.818 616.727 744.727 (2E8.BA316)
49 593.939 629.576 760.242 (2F8.3E116)
50 606.061 642.424 775.758 (307.C1F16)
51 618.182 655.273 791.273 (317.45D16)
52 630.303 668.121 806.788 (326.C9B16)
53 642.424 680.97 822.303 (336.4D916)
54 654.5455 693.8181 837.818 (345.D1716)
55 666.667 706.667 853.333 (355.55516)
56 678.788 719.515 868.8485 (364.D9316)
57 690.909 732.363 884.364 (374.5D116)
58 703.03 745.212 899.879 (383.E0F816)
59 715.1515 758.061 915.394 (393.64E16)
60 727.273 770.909 930.909 (3A2.E8C16)
61 739.394 783.758 946.424 (3B2.6CA16)
62 751.515 796.606 961.939 (3C1.F0816)
63 763.636 809.4545 977.4545 (3D1.74616)
64 775.758 822.303 992.97 (3E0.F8416)
65 787.879 835.1515 1008.485 (3F0.7C216)
66 800 848 1024 (40016)
67 812.121 860.8485 1039.515 (40F.83E16)
68 824.242 873.697 1055.03 (41F.07C16)
69 836.364 886.5455 1070.5455 (42E.8BA16)
70 848.485 899.394 1086.061 (43E.0F816)
71 860.606 912.242 1101.576 (44D.93616)
72 872.727 925.091 1117.091 (45D.17416)
73 884.8485 937.939 1132.606 (46C.9B216)
74 896.97 950.788 1148.121 (47C.1F0816)
75 909.091 963.636 1163.636 (48B.A2F16)
76 921.212 976.485 1179.1515 (49B.26D16)
77 933.333 989.333 1194.667 (4AA.AAB16)
78 945.4545 1002.182 1210.182 (4BA.2E916)
79 957.576 1015.030 1225.697 (4C9.B2716)
80 969.697 1027.879 1241.212 (4D9.36516)
81 981.818 1040.727 1256.727 (4E8.BA316)
82 993.939 1053.576 1272.242 (4F8.3E116)
83 1006.061 1066.424 1287.758 (507.C1F16)
84 1018.182 1079.272 1303.273 (517.45D16)
85 1030.303 1092.121 1318.788 (526.C9B16)
86 1042.424 1104.97 1334.303 (536.4D916)
87 1054.5455 1117.818 1349.818 (545.D1716)
88 1066.667 1130.667 1365.333 (555.55516)
89 1078.788 1143.515 1380.8485 (564.D9316)
90 1090.909 1156.364 1396.364 (574.5D116)
91 1103.03 1169.212 1411.879 (583.E0F816)
92 1115.1515 1182.061 1427.394 (593.64E16)
93 1127.273 1194.909 1442.909 (5A2.E8C16)
94 1139.394 1207.758 1458.424 (5B2.6CA16)
95 1151.515 1220.606 1473.939 (5C1.F0816)
96 1163.636 1233.4545 1489.4545 (5D1.74616)
97 1175.758 1246.303 1504.97 (5E0.F8416)
98 1187.879 1259.1515 1520.485 (5F0.7C216)
99 1200 1272 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