# 60edo

The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the Pythagorean comma, 531441/524288 = |-19 12>. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports magic, compton and tritonic temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 bleu temperament.

# Intervals

degrees of 60edo | cents value | approximate ratios in the 2.3.5.13 subgroup | additional ratios of 7 and 11 (assuming flat values for primes) |

0 | 0 | ||

1 | 20 | ||

2 | 40 | ||

3 | 60 | ||

4 | 80 | ||

5 | 100 | ||

6 | 120 | 16/15 | |

7 | 140 | ||

8 | 160 | 12/11, 11/10 | |

9 | 180 | 10/9 | |

10 | 200 | 9/8 | |

11 | 220 | ||

12 | 240 | 15/13 | 8/7 |

13 | 260 | 7/6 | |

14 | 280 | ||

15 | 300 | ||

16 | 320 | ||

17 | 340 | 11/9 | |

18 | 360 | 16/13 | |

19 | 380 | ||

20 | 400 | ||

21 | 420 | 14/11 | |

22 | 440 | 9/7 | |

23 | 460 | 13/10 | |

24 | 480 | ||

25 | 500 | 4/3 | |

26 | 520 | ||

27 | 540 | 11/8, 15/11 | |

28 | 560 | 18/13 | |

29 | 580 | 7/5 | |

30 | 600 | ||

31 | 620 | 10/7 | |

32 | 640 | 13/8 | |

33 | 660 | 16/11, 22/15 | |

34 | 680 | ||

35 | 700 | 3/2 | |

36 | 720 | ||

37 | 740 | 20/13 | |

38 | 760 | 14/9 | |

39 | 780 | 11/7 | |

40 | 800 | ||

41 | 820 | ||

42 | 840 | 13/8 | |

43 | 860 | 18/11 | |

44 | 880 | ||

45 | 900 | ||

46 | 920 | ||

47 | 940 | 12/7 | |

48 | 960 | 26/15 | 7/4 |

49 | 980 | ||

50 | 1000 | 16/9 | |

51 | 1020 | 9/5 | |

52 | 1040 | 11/6, 20/11 | |

53 | 1060 | ||

54 | 1080 | 15/8 | |

55 | 1100 | ||

56 | 1120 | ||

57 | 1140 | ||

58 | 1160 | ||

59 | 1180 | ||

60 | 1200 |

# Compositions

Rojqoq (So-Called Peace) play by William Sethares

Black Salt - White Pepper play

all by Robin Perry

Dingshi and

Gene's Jitterbug (ogg) Gene's Jitterbug (mp3) Score

by Graham Breed

# Images

Robin Perry guitar