62edo

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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 Armodue notation Approximate intervals
Cents pions 7mus
0 1
1 19.3548 20.5161 24.7742 (18.C63216)
2 38.7097 41.0323 49.5484 (31.8C6316) 1‡ (9#)
3 58.0645 61.5484 74.3226 (4A.529516) 2b
4 77.41935 82.0645 99.0968 (63.18C616) 1◊2
5 96.7742 102.58065 123.871 (7B.DEF816) 1#
6 116.129 123.0968 148.6452 (94.A52916) 2v
7 135.4839 143.6129 173.41935 (AD.7B5B16) 2⌐
8 154.8387 164.129 198.19355 (C6.318C16) 2
9 174.19355 184.6452 222.9677 (DE.F7BE16)
10 193.5484 205.1613 247.7419 (F7.BDEF816) 2‡
11 212.9032 225.6774 272.5161 (110.842116) 3b ·
12 232.2581 246.19355 297.2903 (129.4A5316) 2◊3
13 251.6129 266.7097 322.0645 (142.108416) 2#
14 270.9677 287.2258 346.8387 (15A.D6B616) 3v
15 290.3226 307.7419 371.6129 (173.9CE716) 3⌐
16 309.6774 328.2581 396.3871 (18C.631916) 3
17 329.0323 348.7742 421.1613 (1A5.294A16)
18 348.3871 369.2903 445.9355 (1BD.EF7C16) 3‡
19 367.7419 389.80645 470.7097 (1D6.B5AD16) 4b ·
20 387.0968 410.3225 495.4838 (1EF.7BDF16) 3◊4
21 406.4516 430.8387 520.2581 (208.4210816) 3#
22 425.80645 451.3548 545.0323 (221.084216) 4v (5b)
23 445.1613 471.871 569.80645 (239.CE7416) 4⌐
24 464.5161 492.3871 594.58065 (252.94A516) 4
25 483.871 512.9032 619.3548 (26B.5AD716) 4Ɨ (5v)
26 503.2258 533.41935 644.129 (284.210816) 5⌐ (4‡)
27 522.58065 553.9355 668.9032 (29C.E73A16) 5 ·
28 541.9355 574.4516 693.6774 (2B5.AD6B16)
29 561.2903 594.9677 718.4516 (2C4.739D16) 5‡ (4#)
30 580.6452 615.4839 743.2258 (2E7.39CD16) 6b
31 600 636 768 (30016) 5◊6
32 619.3548 656.5161 792.7742 (318.C63216) 5#
33 638.7097 677.0323 813.5484 (331.8C6316) 6v
34 658.0645 697.5484 842.3226 (34A.529516) 6⌐
35 677.41935 718.0645 867.0968 (363.18C616) 6 ·
36 696.7742 738.58065 891.871 (37B.DEF816)
37 716.129 759.0968 916.6452 (394.A52916) 6‡
38 735.4839 779.6129 941.41935 (3AD.7B5B16) 7b
39 754.8387 800.129 966.19355 (3C6.318C16) 6◊7
40 774.19355 820.6452 990.9677 (3DE.F7BE16) 6#
41 793.5484 841.1613 1015.7419 (3F7.BDEF816) 7v
42 812.9032 861.6774 1040.5161 (410.842116) 7⌐
43 832.2581 882.19355 1065.2903 (429.4A5316) 7 ·
44 851.6129 902.7097 1090.0645 (442.108416)
45 870.9677 923.2268 1114.8387 (45A.D6B616) 7‡
46 890.3226 943.7419 1139.6129 (473.9CE716) 8b
47 909.6774 964.2581 1164.3871 (48C.631916) 7◊8
48 929.0323 984.7742 1189.1613 (4A5.294A16) 7#
49 948.3871 1005.2903 1213.9355 (4BD.EF7C16) 8v
50 967.7419 1025.80645 1238.7097 (4D6.B5AD16) 8⌐
51 987.0968 1046.3225 1263.4838 (4EF.7BDF16) 8 ·
52 1006.4516 1066.8387 1288.2581 (508.4210816)
53 1025.80645 1087.3548 1313.0323 (521.084216) 8‡
54 1045.1613 1107.871 1337.80645 (539.CE7416) 9b
55 1064.5161 1128.3871 1362.58065 (552.94A516) 8◊9
56 1083.871 1148.9032 1387.3548 (56B.5AD716) 8#
57 1103.2258 1169.41935 1412.129 (584.210816) 9v (1b)
58 1122.58065 1189.9355 1436.9032 (59C.E73A16) 9⌐
59 1141.9355 1210.4516 1461.6774 (5B5.AD6B16) 9
60 1161.2903 1230.9677 1486.4516 (5C4.739D16) 9Ɨ (1v)
61 1180.6452 1251.4839 1411.2258 (5E7.39CD16) 1⌐ (9‡)
62 1200 1272 1536 (60016) 1