62edo: Difference between revisions

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→62-EDO Intervals: Removed 7mus column
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→62-EDO Intervals: Started adding approximate intervals.
Line 29: Line 29:
| style="text-align:right;" | 19.3548
| style="text-align:right;" | 19.3548
| style="text-align:center;" | 1Ɨ
| style="text-align:center;" | 1Ɨ
| |  
| | 90/89
|-
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:right;" | 38.7097
| style="text-align:right;" | 38.7097
| style="text-align:center;" | 1‡ (9#)
| style="text-align:center;" | 1‡ (9#)
| |  
| | 45/44
|-
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:right;" | 58.0645
| style="text-align:right;" | 58.0645
| style="text-align:center;" | 2b
| style="text-align:center;" | 2b
| |  
| | 30/29
|-
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:right;" | 77.41935
| style="text-align:right;" | 77.41935
| style="text-align:center;" | 1◊2
| style="text-align:center;" | 1◊2
| |  
| | 23/22
|-
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:right;" | 96.7742
| style="text-align:right;" | 96.7742
| style="text-align:center;" | 1#
| style="text-align:center;" | 1#
| |  
| | 37/35, 18/17, 19/18
|-
|-
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| style="text-align:right;" | 116.129
| style="text-align:right;" | 116.129
| style="text-align:center;" | 2v
| style="text-align:center;" | 2v
| |  
| | 31/29, 15/14, 16/15
|-
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| style="text-align:right;" | 135.4839
| style="text-align:right;" | 135.4839
| style="text-align:center;" | 2⌐
| style="text-align:center;" | 2⌐
| |  
| | 27/25, 13/12, 14/13
|-
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| style="text-align:right;" | 154.8387
| style="text-align:right;" | 154.8387
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| |  
| | 12/11
|-
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| style="text-align:right;" | 174.19355
| style="text-align:right;" | 174.19355
| style="text-align:center;" | 2Ɨ
| style="text-align:center;" | 2Ɨ
| |  
| | 11/10
|-
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 10
| style="text-align:right;" | 193.5484
| style="text-align:right;" | 193.5484
| style="text-align:center;" | 2‡
| style="text-align:center;" | 2‡
| |  
| | 19/17, 9/8, 10/9
|-
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 11
| style="text-align:right;" | 212.9032
| style="text-align:right;" | 212.9032
| style="text-align:center;" | 3b
| style="text-align:center;" | 3b
| | ·
| | 17/15, 9/8
|-
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 12
| style="text-align:right;" | 232.2581
| style="text-align:right;" | 232.2581
| style="text-align:center;" | 2◊3
| style="text-align:center;" | 2◊3
| |  
| | 8/7
|-
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 13
| style="text-align:right;" | 251.6129
| style="text-align:right;" | 251.6129
| style="text-align:center;" | 2#
| style="text-align:center;" | 2#
| |  
| | 15/13
|-
|-
| style="text-align:center;" | 14
| style="text-align:center;" | 14
| style="text-align:right;" | 270.9677
| style="text-align:right;" | 270.9677
| style="text-align:center;" | 3v
| style="text-align:center;" | 3v
| |  
| | 7/6
|-
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 15
Line 104: Line 104:
| style="text-align:right;" | 309.6774
| style="text-align:right;" | 309.6774
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| |  
| | 6/5
|-
|-
| style="text-align:center;" | 17
| style="text-align:center;" | 17
Line 114: Line 114:
| style="text-align:right;" | 348.3871
| style="text-align:right;" | 348.3871
| style="text-align:center;" | 3‡
| style="text-align:center;" | 3‡
| |  
| | 11/9
|-
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 19
Line 124: Line 124:
| style="text-align:right;" | 387.0968
| style="text-align:right;" | 387.0968
| style="text-align:center;" | 3◊4
| style="text-align:center;" | 3◊4
| |  
| | 5/4
|-
|-
| style="text-align:center;" | 21
| style="text-align:center;" | 21
Line 154: Line 154:
| style="text-align:right;" | 503.2258
| style="text-align:right;" | 503.2258
| style="text-align:center;" | 5⌐ (4‡)
| style="text-align:center;" | 5⌐ (4‡)
| |  
| | 4/3
|-
|-
| style="text-align:center;" | 27
| style="text-align:center;" | 27
Line 174: Line 174:
| style="text-align:right;" | 580.6452
| style="text-align:right;" | 580.6452
| style="text-align:center;" | 6b
| style="text-align:center;" | 6b
| |  
| | 7/5
|-
|-
| style="text-align:center;" | 31
| style="text-align:center;" | 31
Line 184: Line 184:
| style="text-align:right;" | 619.3548
| style="text-align:right;" | 619.3548
| style="text-align:center;" | 5#
| style="text-align:center;" | 5#
| |  
| | 10/7
|-
|-
| style="text-align:center;" | 33
| style="text-align:center;" | 33
Line 204: Line 204:
| style="text-align:right;" | 696.7742
| style="text-align:right;" | 696.7742
| style="text-align:center;" | 6Ɨ
| style="text-align:center;" | 6Ɨ
| |  
| |3/2
|-
|-
| style="text-align:center;" | 37
| style="text-align:center;" | 37
Line 234: Line 234:
| style="text-align:right;" | 812.9032
| style="text-align:right;" | 812.9032
| style="text-align:center;" | 7⌐
| style="text-align:center;" | 7⌐
| |  
| | 8/5
|-
|-
| style="text-align:center;" | 43
| style="text-align:center;" | 43
Line 244: Line 244:
| style="text-align:right;" | 851.6129
| style="text-align:right;" | 851.6129
| style="text-align:center;" | 7Ɨ
| style="text-align:center;" | 7Ɨ
| |  
| | 18/11
|-
|-
| style="text-align:center;" | 45
| style="text-align:center;" | 45
Line 254: Line 254:
| style="text-align:right;" | 890.3226
| style="text-align:right;" | 890.3226
| style="text-align:center;" | 8b
| style="text-align:center;" | 8b
| |  
| | 5/3
|-
|-
| style="text-align:center;" | 47
| style="text-align:center;" | 47
Line 264: Line 264:
| style="text-align:right;" | 929.0323
| style="text-align:right;" | 929.0323
| style="text-align:center;" | 7#
| style="text-align:center;" | 7#
| |  
| | 12/7
|-
|-
| style="text-align:center;" | 49
| style="text-align:center;" | 49
| style="text-align:right;" | 948.3871
| style="text-align:right;" | 948.3871
| style="text-align:center;" | 8v
| style="text-align:center;" | 8v
| |  
| | 26/15
|-
|-
| style="text-align:center;" | 50
| style="text-align:center;" | 50
| style="text-align:right;" | 967.7419
| style="text-align:right;" | 967.7419
| style="text-align:center;" | 8⌐
| style="text-align:center;" | 8⌐
| |  
| | 7/4
|-
|-
| style="text-align:center;" | 51
| style="text-align:center;" | 51
| style="text-align:right;" | 987.0968
| style="text-align:right;" | 987.0968
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| | ·
| | 16/9
|-
|-
| style="text-align:center;" | 52
| style="text-align:center;" | 52

Revision as of 09:26, 18 June 2020

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 Cents Armodue notation Approximate intervals
0 0.0000 1
1 19.3548 1Ɨ 90/89
2 38.7097 1‡ (9#) 45/44
3 58.0645 2b 30/29
4 77.41935 1◊2 23/22
5 96.7742 1# 37/35, 18/17, 19/18
6 116.129 2v 31/29, 15/14, 16/15
7 135.4839 2⌐ 27/25, 13/12, 14/13
8 154.8387 2 12/11
9 174.19355 2Ɨ 11/10
10 193.5484 2‡ 19/17, 9/8, 10/9
11 212.9032 3b 17/15, 9/8
12 232.2581 2◊3 8/7
13 251.6129 2# 15/13
14 270.9677 3v 7/6
15 290.3226 3⌐
16 309.6774 3 6/5
17 329.0323 3Ɨ
18 348.3871 3‡ 11/9
19 367.7419 4b ·
20 387.0968 3◊4 5/4
21 406.4516 3#
22 425.80645 4v (5b)
23 445.1613 4⌐
24 464.5161 4
25 483.871 4Ɨ (5v)
26 503.2258 5⌐ (4‡) 4/3
27 522.58065 5 ·
28 541.9355 5Ɨ
29 561.2903 5‡ (4#)
30 580.6452 6b 7/5
31 600 5◊6
32 619.3548 5# 10/7
33 638.7097 6v
34 658.0645 6⌐
35 677.41935 6 ·
36 696.7742 6Ɨ 3/2
37 716.129 6‡
38 735.4839 7b
39 754.8387 6◊7
40 774.19355 6#
41 793.5484 7v
42 812.9032 7⌐ 8/5
43 832.2581 7 ·
44 851.6129 7Ɨ 18/11
45 870.9677 7‡
46 890.3226 8b 5/3
47 909.6774 7◊8
48 929.0323 7# 12/7
49 948.3871 8v 26/15
50 967.7419 8⌐ 7/4
51 987.0968 8 16/9
52 1006.4516 8Ɨ
53 1025.80645 8‡
54 1045.1613 9b
55 1064.5161 8◊9
56 1083.871 8#
57 1103.2258 9v (1b)
58 1122.58065 9⌐
59 1141.9355 9
60 1161.2903 9Ɨ (1v)
61 1180.6452 1⌐ (9‡)
62 1200 1
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