# 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.

## Contents

# 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 |
---|---|

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