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62 tone equal temperament


62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for gallium, semivalentine and hemimeantone temperaments.

Using the 35\62 generator, which leads to the <62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143 172| supports hornbostel.

62-EDO Intervals


ARMODUE NOMENCLATURE 8;3 RELATION
  • Ɨ = Thick (1/8-tone up)
  • = Semisharp (1/4-tone up)
  • b = Flat (5/8-tone down)
  • = Node (sharp/flat blindspot 1/2-tone)
  • # = Sharp (5/8-tone up)
  • v = Semiflat (1/4-tone down)
  • = Thin (1/8-tone down)

Degree
Size (Cents)
Armodue notation
Approximate intervals
0
0.0000
1

1
19.3548


2
38.7097
1‡ (9#)

3
58.0645
2b

4
77.4194
1◊2

5
96.7742
1#

6
116.1290
2v

7
135.4839
2⌐

8
154.8387
2

9
174.1935


10
193.5484
2‡

11
212.9032
3b
·
12
232.2581
2◊3

13
251.6129
2#

14
270.9677
3v

15
290.3226
3⌐

16
309.6774
3

17
329.0323


18
348.3871
3‡

19
367.7419
4b
·
20
387.0968
3◊4

21
406.4516
3#

22
425.8065
4v (5b)

23
445.1613
4⌐

24
464.5161
4

25
483.8710
4Ɨ (5v)

26
503.2258
5⌐ (4‡)

27
522.5806
5
·
28
541.9355


29
561.2903
5‡ (4#)

30
580.6452
6b

31
600.0000
5◊6

32
619.3548
5#

33
638.7097
6v

34
658.0645
6⌐

35
677.4194
6
·
36
696.7742


37
716.1290
6‡

38
735.4839
7b

39
754.8387
6◊7

40
774.1935
6#

41
793.5484
7v

42
812.9032
7⌐

43
832.2581
7
·
44
851.6129


45
870.9677
7‡

46
890.3226
8b

47
909.6774
7◊8

48
929.0323
7#

49
948.3871
8v

50
967.7419
8⌐

51
987.0968
8
·
52
1006.4516


53
1025.8065
8‡

54
1045.1613
9b

55
1064.5161
8◊9

56
1083.8710
8#

57
1103.2258
9v (1b)

58
1122.5806
9⌐

59
1141.9355
9

60
1161.2903
9Ɨ (1v)

61
1180.6452
1⌐ (9‡)

62
1200.0000
1