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→62-EDO Intervals: Removed 7mus column
Line 16: Line 16:
{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2" | [[Degree|Degree]]
! [[Degree|Degree]]
! colspan="2" | Size
! rowspan="2" | Armodue notation
! rowspan="2" | Approximate intervals
|-
![[cent|Cents]]
![[cent|Cents]]
!7mus
! Armodue notation
! Approximate intervals
|-
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:right;" | 0.0000
| style="text-align:right;" | 0.0000
|0
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| |  
| |  
Line 32: Line 28:
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:right;" | 19.3548
| style="text-align:right;" | 19.3548
|24.7742 (18.C632<sub>16</sub>)
| style="text-align:center;" | 1Ɨ
| style="text-align:center;" | 1Ɨ
| |  
| |  
Line 38: Line 33:
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:right;" | 38.7097
| style="text-align:right;" | 38.7097
|49.5484 (31.8C63<sub>16</sub>)
| style="text-align:center;" | 1‡ (9#)
| style="text-align:center;" | 1‡ (9#)
| |  
| |  
Line 44: Line 38:
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:right;" | 58.0645
| style="text-align:right;" | 58.0645
|74.3226 (4A.5295<sub>16</sub>)
| style="text-align:center;" | 2b
| style="text-align:center;" | 2b
| |  
| |  
Line 50: Line 43:
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:right;" | 77.41935
| style="text-align:right;" | 77.41935
|99.0968 (63.18C6<sub>16</sub>)
| style="text-align:center;" | 1◊2
| style="text-align:center;" | 1◊2
| |  
| |  
Line 56: Line 48:
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:right;" | 96.7742
| style="text-align:right;" | 96.7742
|123.871 (7B.DEF8<sub>16</sub>)
| style="text-align:center;" | 1#
| style="text-align:center;" | 1#
| |  
| |  
Line 62: Line 53:
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| style="text-align:right;" | 116.129
| style="text-align:right;" | 116.129
|148.6452 (94.A529<sub>16</sub>)
| style="text-align:center;" | 2v
| style="text-align:center;" | 2v
| |  
| |  
Line 68: Line 58:
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| style="text-align:right;" | 135.4839
| style="text-align:right;" | 135.4839
|173.41935 (AD.7B5B<sub>16</sub>)
| style="text-align:center;" | 2⌐
| style="text-align:center;" | 2⌐
| |  
| |  
Line 74: Line 63:
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| style="text-align:right;" | 154.8387
| style="text-align:right;" | 154.8387
|198.19355 (C6.318C<sub>16</sub>)
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| |  
| |  
Line 80: Line 68:
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| style="text-align:right;" | 174.19355
| style="text-align:right;" | 174.19355
|222.9677 (DE.F7BE<sub>16</sub>)
| style="text-align:center;" | 2Ɨ
| style="text-align:center;" | 2Ɨ
| |  
| |  
Line 86: Line 73:
| style="text-align:center;" | 10
| style="text-align:center;" | 10
| style="text-align:right;" | 193.5484
| style="text-align:right;" | 193.5484
|247.7419 (F7.BDEF8<sub>16</sub>)
| style="text-align:center;" | 2‡
| style="text-align:center;" | 2‡
| |  
| |  
Line 92: Line 78:
| style="text-align:center;" | 11
| style="text-align:center;" | 11
| style="text-align:right;" | 212.9032
| style="text-align:right;" | 212.9032
|272.5161 (110.8421<sub>16</sub>)
| style="text-align:center;" | 3b
| style="text-align:center;" | 3b
| | ·
| | ·
Line 98: Line 83:
| style="text-align:center;" | 12
| style="text-align:center;" | 12
| style="text-align:right;" | 232.2581
| style="text-align:right;" | 232.2581
|297.2903 (129.4A53<sub>16</sub>)
| style="text-align:center;" | 2◊3
| style="text-align:center;" | 2◊3
| |  
| |  
Line 104: Line 88:
| style="text-align:center;" | 13
| style="text-align:center;" | 13
| style="text-align:right;" | 251.6129
| style="text-align:right;" | 251.6129
|322.0645 (142.1084<sub>16</sub>)
| style="text-align:center;" | 2#
| style="text-align:center;" | 2#
| |  
| |  
Line 110: Line 93:
| style="text-align:center;" | 14
| style="text-align:center;" | 14
| style="text-align:right;" | 270.9677
| style="text-align:right;" | 270.9677
|346.8387 (15A.D6B6<sub>16</sub>)
| style="text-align:center;" | 3v
| style="text-align:center;" | 3v
| |  
| |  
Line 116: Line 98:
| style="text-align:center;" | 15
| style="text-align:center;" | 15
| style="text-align:right;" | 290.3226
| style="text-align:right;" | 290.3226
|371.6129 (173.9CE7<sub>16</sub>)
| style="text-align:center;" | 3⌐
| style="text-align:center;" | 3⌐
| |  
| |  
Line 122: Line 103:
| style="text-align:center;" | 16
| style="text-align:center;" | 16
| style="text-align:right;" | 309.6774
| style="text-align:right;" | 309.6774
|396.3871 (18C.6319<sub>16</sub>)
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| |  
| |  
Line 128: Line 108:
| style="text-align:center;" | 17
| style="text-align:center;" | 17
| style="text-align:right;" | 329.0323
| style="text-align:right;" | 329.0323
|421.1613 (1A5.294A<sub>16</sub>)
| style="text-align:center;" | 3Ɨ
| style="text-align:center;" | 3Ɨ
| |  
| |  
Line 134: Line 113:
| style="text-align:center;" | 18
| style="text-align:center;" | 18
| style="text-align:right;" | 348.3871
| style="text-align:right;" | 348.3871
|445.9355 (1BD.EF7C<sub>16</sub>)
| style="text-align:center;" | 3‡
| style="text-align:center;" | 3‡
| |  
| |  
Line 140: Line 118:
| style="text-align:center;" | 19
| style="text-align:center;" | 19
| style="text-align:right;" | 367.7419
| style="text-align:right;" | 367.7419
|470.7097 (1D6.B5AD<sub>16</sub>)
| style="text-align:center;" | 4b
| style="text-align:center;" | 4b
| | ·
| | ·
Line 146: Line 123:
| style="text-align:center;" | 20
| style="text-align:center;" | 20
| style="text-align:right;" | 387.0968
| style="text-align:right;" | 387.0968
|495.4838 (1EF.7BDF<sub>16</sub>)
| style="text-align:center;" | 3◊4
| style="text-align:center;" | 3◊4
| |  
| |  
Line 152: Line 128:
| style="text-align:center;" | 21
| style="text-align:center;" | 21
| style="text-align:right;" | 406.4516
| style="text-align:right;" | 406.4516
|520.2581 (208.42108<sub>16</sub>)
| style="text-align:center;" | 3#
| style="text-align:center;" | 3#
| |  
| |  
Line 158: Line 133:
| style="text-align:center;" | 22
| style="text-align:center;" | 22
| style="text-align:right;" | 425.80645
| style="text-align:right;" | 425.80645
|545.0323 (221.0842<sub>16</sub>)
| style="text-align:center;" | 4v (5b)
| style="text-align:center;" | 4v (5b)
| |  
| |  
Line 164: Line 138:
| style="text-align:center;" | 23
| style="text-align:center;" | 23
| style="text-align:right;" | 445.1613
| style="text-align:right;" | 445.1613
|569.80645 (239.CE74<sub>16</sub>)
| style="text-align:center;" | 4⌐
| style="text-align:center;" | 4⌐
| |  
| |  
Line 170: Line 143:
| style="text-align:center;" | 24
| style="text-align:center;" | 24
| style="text-align:right;" | 464.5161
| style="text-align:right;" | 464.5161
|594.58065 (252.94A5<sub>16</sub>)
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| |  
| |  
Line 176: Line 148:
| style="text-align:center;" | 25
| style="text-align:center;" | 25
| style="text-align:right;" | 483.871
| style="text-align:right;" | 483.871
|619.3548 (26B.5AD7<sub>16</sub>)
| style="text-align:center;" | 4Ɨ (5v)
| style="text-align:center;" | 4Ɨ (5v)
| |  
| |  
Line 182: Line 153:
| style="text-align:center;" | 26
| style="text-align:center;" | 26
| style="text-align:right;" | 503.2258
| style="text-align:right;" | 503.2258
|644.129 (284.2108<sub>16</sub>)
| style="text-align:center;" | 5⌐ (4‡)
| style="text-align:center;" | 5⌐ (4‡)
| |  
| |  
Line 188: Line 158:
| style="text-align:center;" | 27
| style="text-align:center;" | 27
| style="text-align:right;" | 522.58065
| style="text-align:right;" | 522.58065
|668.9032 (29C.E73A<sub>16</sub>)
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| | ·
| | ·
Line 194: Line 163:
| style="text-align:center;" | 28
| style="text-align:center;" | 28
| style="text-align:right;" | 541.9355
| style="text-align:right;" | 541.9355
|693.6774 (2B5.AD6B<sub>16</sub>)
| style="text-align:center;" | 5Ɨ
| style="text-align:center;" | 5Ɨ
| |  
| |  
Line 200: Line 168:
| style="text-align:center;" | 29
| style="text-align:center;" | 29
| style="text-align:right;" | 561.2903
| style="text-align:right;" | 561.2903
|718.4516 (2C4.739D<sub>16</sub>)
| style="text-align:center;" | 5‡ (4#)
| style="text-align:center;" | 5‡ (4#)
| |  
| |  
Line 206: Line 173:
| style="text-align:center;" | 30
| style="text-align:center;" | 30
| style="text-align:right;" | 580.6452
| style="text-align:right;" | 580.6452
|743.2258 (2E7.39CD<sub>16</sub>)
| style="text-align:center;" | 6b
| style="text-align:center;" | 6b
| |  
| |  
Line 212: Line 178:
| style="text-align:center;" | 31
| style="text-align:center;" | 31
| style="text-align:right;" | 600
| style="text-align:right;" | 600
|768 (300<sub>16</sub>)
| style="text-align:center;" | 5◊6
| style="text-align:center;" | 5◊6
| |  
| |  
Line 218: Line 183:
| style="text-align:center;" | 32
| style="text-align:center;" | 32
| style="text-align:right;" | 619.3548
| style="text-align:right;" | 619.3548
|792.7742 (318.C632<sub>16</sub>)
| style="text-align:center;" | 5#
| style="text-align:center;" | 5#
| |  
| |  
Line 224: Line 188:
| style="text-align:center;" | 33
| style="text-align:center;" | 33
| style="text-align:right;" | 638.7097
| style="text-align:right;" | 638.7097
|813.5484 (331.8C63<sub>16</sub>)
| style="text-align:center;" | 6v
| style="text-align:center;" | 6v
| |  
| |  
Line 230: Line 193:
| style="text-align:center;" | 34
| style="text-align:center;" | 34
| style="text-align:right;" | 658.0645
| style="text-align:right;" | 658.0645
|842.3226 (34A.5295<sub>16</sub>)
| style="text-align:center;" | 6⌐
| style="text-align:center;" | 6⌐
| |  
| |  
Line 236: Line 198:
| style="text-align:center;" | 35
| style="text-align:center;" | 35
| style="text-align:right;" | 677.41935
| style="text-align:right;" | 677.41935
|867.0968 (363.18C6<sub>16</sub>)
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| | ·
| | ·
Line 242: Line 203:
| style="text-align:center;" | 36
| style="text-align:center;" | 36
| style="text-align:right;" | 696.7742
| style="text-align:right;" | 696.7742
|891.871 (37B.DEF8<sub>16</sub>)
| style="text-align:center;" | 6Ɨ
| style="text-align:center;" | 6Ɨ
| |  
| |  
Line 248: Line 208:
| style="text-align:center;" | 37
| style="text-align:center;" | 37
| style="text-align:right;" | 716.129
| style="text-align:right;" | 716.129
|916.6452 (394.A529<sub>16</sub>)
| style="text-align:center;" | 6‡
| style="text-align:center;" | 6‡
| |  
| |  
Line 254: Line 213:
| style="text-align:center;" | 38
| style="text-align:center;" | 38
| style="text-align:right;" | 735.4839
| style="text-align:right;" | 735.4839
|941.41935 (3AD.7B5B<sub>16</sub>)
| style="text-align:center;" | 7b
| style="text-align:center;" | 7b
| |  
| |  
Line 260: Line 218:
| style="text-align:center;" | 39
| style="text-align:center;" | 39
| style="text-align:right;" | 754.8387
| style="text-align:right;" | 754.8387
|966.19355 (3C6.318C<sub>16</sub>)
| style="text-align:center;" | 6◊7
| style="text-align:center;" | 6◊7
| |  
| |  
Line 266: Line 223:
| style="text-align:center;" | 40
| style="text-align:center;" | 40
| style="text-align:right;" | 774.19355
| style="text-align:right;" | 774.19355
|990.9677 (3DE.F7BE<sub>16</sub>)
| style="text-align:center;" | 6#
| style="text-align:center;" | 6#
| |  
| |  
Line 272: Line 228:
| style="text-align:center;" | 41
| style="text-align:center;" | 41
| style="text-align:right;" | 793.5484
| style="text-align:right;" | 793.5484
|1015.7419 (3F7.BDEF8<sub>16</sub>)
| style="text-align:center;" | 7v
| style="text-align:center;" | 7v
| |  
| |  
Line 278: Line 233:
| style="text-align:center;" | 42
| style="text-align:center;" | 42
| style="text-align:right;" | 812.9032
| style="text-align:right;" | 812.9032
|1040.5161 (410.8421<sub>16</sub>)
| style="text-align:center;" | 7⌐
| style="text-align:center;" | 7⌐
| |  
| |  
Line 284: Line 238:
| style="text-align:center;" | 43
| style="text-align:center;" | 43
| style="text-align:right;" | 832.2581
| style="text-align:right;" | 832.2581
|1065.2903 (429.4A53<sub>16</sub>)
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| | ·
| | ·
Line 290: Line 243:
| style="text-align:center;" | 44
| style="text-align:center;" | 44
| style="text-align:right;" | 851.6129
| style="text-align:right;" | 851.6129
|1090.0645 (442.1084<sub>16</sub>)
| style="text-align:center;" | 7Ɨ
| style="text-align:center;" | 7Ɨ
| |  
| |  
Line 296: Line 248:
| style="text-align:center;" | 45
| style="text-align:center;" | 45
| style="text-align:right;" | 870.9677
| style="text-align:right;" | 870.9677
|1114.8387 (45A.D6B6<sub>16</sub>)
| style="text-align:center;" | 7‡
| style="text-align:center;" | 7‡
| |  
| |  
Line 302: Line 253:
| style="text-align:center;" | 46
| style="text-align:center;" | 46
| style="text-align:right;" | 890.3226
| style="text-align:right;" | 890.3226
|1139.6129 (473.9CE7<sub>16</sub>)
| style="text-align:center;" | 8b
| style="text-align:center;" | 8b
| |  
| |  
Line 308: Line 258:
| style="text-align:center;" | 47
| style="text-align:center;" | 47
| style="text-align:right;" | 909.6774
| style="text-align:right;" | 909.6774
|1164.3871 (48C.6319<sub>16</sub>)
| style="text-align:center;" | 7◊8
| style="text-align:center;" | 7◊8
| |  
| |  
Line 314: Line 263:
| style="text-align:center;" | 48
| style="text-align:center;" | 48
| style="text-align:right;" | 929.0323
| style="text-align:right;" | 929.0323
|1189.1613 (4A5.294A<sub>16</sub>)
| style="text-align:center;" | 7#
| style="text-align:center;" | 7#
| |  
| |  
Line 320: Line 268:
| style="text-align:center;" | 49
| style="text-align:center;" | 49
| style="text-align:right;" | 948.3871
| style="text-align:right;" | 948.3871
|1213.9355 (4BD.EF7C<sub>16</sub>)
| style="text-align:center;" | 8v
| style="text-align:center;" | 8v
| |  
| |  
Line 326: Line 273:
| style="text-align:center;" | 50
| style="text-align:center;" | 50
| style="text-align:right;" | 967.7419
| style="text-align:right;" | 967.7419
|1238.7097 (4D6.B5AD<sub>16</sub>)
| style="text-align:center;" | 8⌐
| style="text-align:center;" | 8⌐
| |  
| |  
Line 332: Line 278:
| style="text-align:center;" | 51
| style="text-align:center;" | 51
| style="text-align:right;" | 987.0968
| style="text-align:right;" | 987.0968
|1263.4838 (4EF.7BDF<sub>16</sub>)
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| | ·
| | ·
Line 338: Line 283:
| style="text-align:center;" | 52
| style="text-align:center;" | 52
| style="text-align:right;" | 1006.4516
| style="text-align:right;" | 1006.4516
|1288.2581 (508.42108<sub>16</sub>)
| style="text-align:center;" | 8Ɨ
| style="text-align:center;" | 8Ɨ
| |  
| |  
Line 344: Line 288:
| style="text-align:center;" | 53
| style="text-align:center;" | 53
| style="text-align:right;" | 1025.80645
| style="text-align:right;" | 1025.80645
|1313.0323 (521.0842<sub>16</sub>)
| style="text-align:center;" | 8‡
| style="text-align:center;" | 8‡
| |  
| |  
Line 350: Line 293:
| style="text-align:center;" | 54
| style="text-align:center;" | 54
| style="text-align:right;" | 1045.1613
| style="text-align:right;" | 1045.1613
|1337.80645 (539.CE74<sub>16</sub>)
| style="text-align:center;" | 9b
| style="text-align:center;" | 9b
| |  
| |  
Line 356: Line 298:
| style="text-align:center;" | 55
| style="text-align:center;" | 55
| style="text-align:right;" | 1064.5161
| style="text-align:right;" | 1064.5161
|1362.58065 (552.94A5<sub>16</sub>)
| style="text-align:center;" | 8◊9
| style="text-align:center;" | 8◊9
| |  
| |  
Line 362: Line 303:
| style="text-align:center;" | 56
| style="text-align:center;" | 56
| style="text-align:right;" | 1083.871
| style="text-align:right;" | 1083.871
|1387.3548 (56B.5AD7<sub>16</sub>)
| style="text-align:center;" | 8#
| style="text-align:center;" | 8#
| |  
| |  
Line 368: Line 308:
| style="text-align:center;" | 57
| style="text-align:center;" | 57
| style="text-align:right;" | 1103.2258
| style="text-align:right;" | 1103.2258
|1412.129 (584.2108<sub>16</sub>)
| style="text-align:center;" | 9v (1b)
| style="text-align:center;" | 9v (1b)
| |  
| |  
Line 374: Line 313:
| style="text-align:center;" | 58
| style="text-align:center;" | 58
| style="text-align:right;" | 1122.58065
| style="text-align:right;" | 1122.58065
|1436.9032 (59C.E73A<sub>16</sub>)
| style="text-align:center;" | 9⌐
| style="text-align:center;" | 9⌐
| |  
| |  
Line 380: Line 318:
| style="text-align:center;" | 59
| style="text-align:center;" | 59
| style="text-align:right;" | 1141.9355
| style="text-align:right;" | 1141.9355
|1461.6774 (5B5.AD6B<sub>16</sub>)
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| |  
| |  
Line 386: Line 323:
| style="text-align:center;" | 60
| style="text-align:center;" | 60
| style="text-align:right;" | 1161.2903
| style="text-align:right;" | 1161.2903
|1486.4516 (5C4.739D<sub>16</sub>)
| style="text-align:center;" | 9Ɨ (1v)
| style="text-align:center;" | 9Ɨ (1v)
| |  
| |  
Line 392: Line 328:
| style="text-align:center;" | 61
| style="text-align:center;" | 61
| style="text-align:right;" | 1180.6452
| style="text-align:right;" | 1180.6452
|1411.2258 (5E7.39CD<sub>16</sub>)
| style="text-align:center;" | 1⌐ (9‡)
| style="text-align:center;" | 1⌐ (9‡)
| |  
| |  
Line 398: Line 333:
| style="text-align:center;" | 62
| style="text-align:center;" | 62
| style="text-align:right;" | 1200
| style="text-align:right;" | 1200
|1536 (600<sub>16</sub>)
| style="text-align:center;" | 1
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Revision as of 15:57, 12 December 2019

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
2 38.7097 1‡ (9#)
3 58.0645 2b
4 77.41935 1◊2
5 96.7742 1#
6 116.129 2v
7 135.4839 2⌐
8 154.8387 2
9 174.19355 2Ɨ
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 3Ɨ
18 348.3871 3‡
19 367.7419 4b ·
20 387.0968 3◊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‡)
27 522.58065 5 ·
28 541.9355 5Ɨ
29 561.2903 5‡ (4#)
30 580.6452 6b
31 600 5◊6
32 619.3548 5#
33 638.7097 6v
34 658.0645 6⌐
35 677.41935 6 ·
36 696.7742 6Ɨ
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⌐
43 832.2581 7 ·
44 851.6129 7Ɨ
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 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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