67edo

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67 equal divisions of the octave divides the octave into 67 equal parts of 17.910 cents each. It tempers out 81/80, supporting meantone temperament, with a tuning which is approximately 1/6 comma (the tuning favored by Mozart and contemporaries), or 0.16 comma, meantone. In the 7-limit the patent val tempers out 1029/1024 and 1728/1715, so that it supports mothra temperament. In the 11-limit it tempers out 176/175 and 540/539, supporting mosura, an alternative 11-limit mothra. In the 13-limit it tempers out 144/143 and 196/195, supporting 13-limit mosura. It tempers out the orgonisma, and on the 2.7.11 subgroup it supports orgone temperament.

A promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both meantone (26 could be called meantone, but it's more of a flattone) and an orgone temperament. It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th harmonics, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33+34 can be used to construct this temperament explaining some of its properties.

67edo is the 19th prime edo.

Music:

Beginning of a piece in 67 tone, Peter Kosmorsky

Cents

0: 1/1 0.000 unison, perfect prime

1: 17.910 cents 17.910

2: 35.821 cents 35.821

3: 53.731 cents 53.731

4: 71.642 cents 71.642

5: 89.552 cents 89.552

6: 107.463 cents 107.463

7: 125.373 cents 125.373

8: 143.284 cents 143.284

9: 161.194 cents 161.194

10: 179.104 cents 179.104

11: 197.015 cents 197.015

12: 214.925 cents 214.925

13: 232.836 cents 232.836

14: 250.746 cents 250.746

15: 268.657 cents 7/6

16: 286.567 cents 286.567

17: 304.478 cents 304.478

18: 322.388 cents 322.388

19: 340.299 cents 340.299

20: 358.209 cents 358.209

21: 376.119 cents 5/4 -

22: 394.030 cents 5/4 +

23: 411.940 cents 411.940

24: 429.851 cents 429.851

25: 447.761 cents 447.761

26: 465.672 cents 21/16

27: 483.582 cents 483.582

28: 501.493 cents 501.493

29: 519.403 cents 519.403

30: 537.313 cents 537.313

31: 555.224 cents 11/8

32: 573.134 cents 573.134

33: 591.045 cents 591.045

34: 608.955 cents 608.955

35: 626.866 cents 626.866

36: 644.776 cents 644.776

37: 662.687 cents 662.687

38: 680.597 cents 680.597

39: 698.507 cents 3/2

40: 716.418 cents 716.418

41: 734.328 cents 734.328

42: 752.239 cents 752.239

43: 770.149 cents 770.149

44: 788.060 cents 788.060

45: 805.970 cents 805.970

46: 823.881 cents 823.881

47: 841.791 cents 841.791

48: 859.701 cents 859.701

49: 877.612 cents 877.612

50: 895.522 cents 895.522

51: 913.433 cents 913.433

52: 931.343 cents 931.343

53: 949.254 cents 949.254

54: 967.164 cents 7/4

55: 985.075 cents 985.075

56: 1002.985 cents 1002.985

57: 1020.896 cents 1020.896

58: 1038.806 cents 1038.806

59: 1056.716 cents 1056.716

60: 1074.627 cents 1074.627

61: 1092.537 cents 1092.537

62: 1110.448 cents 1110.448

63: 1128.358 cents 1128.358

64: 1146.269 cents 1146.269

65: 1164.179 cents 1164.179

66: 1182.090 cents 1182.090

67: 2/1 1200.000 octave