75edo: Difference between revisions

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→Intervals: Removed pions column
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{| class="wikitable"
{| class="wikitable"
|-
|-
| rowspan="2"| '''Step'''
| rowspan="2" | '''Step'''
| colspan="3"| '''Size in'''
| colspan="2" | '''Size in'''
|-
|-
|'''Cents'''
|'''Cents'''
|'''pions'''
|'''7mus'''
|'''7mus'''
|-
|-
| colspan="4"| 0
| colspan="3" | 0
|-
|-
| | 1
| | 1
| | 16
| | 16
|16.96
|20.48 (14.7B<sub>16</sub>)
|20.48 (14.7B<sub>16</sub>)
|-
|-
| | 2
| | 2
| | 32
| | 32
|33.92
|40.96 (28.F6<sub>16</sub>)
|40.96 (28.F6<sub>16</sub>)
|-
|-
| | 3
| | 3
| | 48
| | 48
|50.88
|61.44 (3D.71<sub>16</sub>)
|61.44 (3D.71<sub>16</sub>)
|-
|-
| | 4
| | 4
| | 64
| | 64
|67.84
|81.92 (51.EB8<sub>16</sub>)
|81.92 (51.EB8<sub>16</sub>)
|-
|-
| | 5
| | 5
| | 80
| | 80
|84.8
|102.4 (66.66<sub>16</sub>)
|102.4 (66.66<sub>16</sub>)
|-
|-
| | 6
| | 6
| | 96
| | 96
|101.76
|122.88 (7A.E1<sub>16</sub>)
|122.88 (7A.E1<sub>16</sub>)
|-
|-
| | 7
| | 7
| | 112
| | 112
|118.72
|143.36 (8F.5C<sub>16</sub>)
|143.36 (8F.5C<sub>16</sub>)
|-
|-
| | 8
| | 8
| | 128
| | 128
|135.68
|163.84 (A3.D7<sub>16</sub>)
|163.84 (A3.D7<sub>16</sub>)
|-
|-
| | 9
| | 9
| | 144
| | 144
|152.64
|184.32 (B8.52<sub>16</sub>)
|184.32 (B8.52<sub>16</sub>)
|-
|-
| | 10
| | 10
| | 160
| | 160
|169.6
|204.8 (CC.CD<sub>16</sub>)
|204.8 (CC.CD<sub>16</sub>)
|-
|-
| | 11
| | 11
| | 176
| | 176
|186.56
|225.28 (E1.48<sub>16</sub>)
|225.28 (E1.48<sub>16</sub>)
|-
|-
| | 12
| | 12
| | 192
| | 192
|203.52
|245.76 (F5.C3<sub>16</sub>)
|245.76 (F5.C3<sub>16</sub>)
|-
|-
| | 13
| | 13
| | 208
| | 208
|220.48
|266.24 (10A.3D<sub>16</sub>)
|266.24 (10A.3D<sub>16</sub>)
|-
|-
| | 14
| | 14
| | 224
| | 224
|237.44
|286.72 (11E.B8<sub>16</sub>)
|286.72 (11E.B8<sub>16</sub>)
|-
|-
| | 15
| | 15
| | 240
| | 240
|254.4
|307.2 (133.33<sub>16</sub>)
|307.2 (133.33<sub>16</sub>)
|-
|-
| | 16
| | 16
| | 256
| | 256
|271.36
|327.68 (147.AE<sub>16</sub>)
|327.68 (147.AE<sub>16</sub>)
|-
|-
| | 17
| | 17
| | 272
| | 272
|288.32
|348.16 (15C.29<sub>16</sub>)
|348.16 (15C.29<sub>16</sub>)
|-
|-
| | 18
| | 18
| | 288
| | 288
|305.28
|368.64 (170.A4<sub>16</sub>)
|368.64 (170.A4<sub>16</sub>)
|-
|-
| | 19
| | 19
| | 304
| | 304
|322.24
|389.12 (185.1F<sub>16</sub>)
|389.12 (185.1F<sub>16</sub>)
|-
|-
| | 20
| | 20
| | 320
| | 320
|339.2
|409.6 (199.9A<sub>16</sub>)
|409.6 (199.9A<sub>16</sub>)
|-
|-
| | 21
| | 21
| | 336
| | 336
|356.16
|430.08 (1AE.148<sub>16</sub>)
|430.08 (1AE.148<sub>16</sub>)
|-
|-
| | 22
| | 22
| | 352
| | 352
|373.12
|450.56 (1C2.8F<sub>16</sub>)
|450.56 (1C2.8F<sub>16</sub>)
|-
|-
| | 23
| | 23
| | 368
| | 368
|390.08
|471.04 (1D7.0A<sub>16</sub>)
|471.04 (1D7.0A<sub>16</sub>)
|-
|-
| | 24
| | 24
| | 384
| | 384
|407.04
|491.52 (1E9.85<sub>16</sub>)
|491.52 (1E9.85<sub>16</sub>)
|-
|-
| | 25
| | 25
| | 400
| | 400
|424
|512 (200<sub>16</sub>)
|512 (200<sub>16</sub>)
|-
|-
| | 26
| | 26
| | 416
| | 416
|440.96
|532.48 (214.7B<sub>16</sub>)
|532.48 (214.7B<sub>16</sub>)
|-
|-
| | 27
| | 27
| | 432
| | 432
|457.92
|552.96 (228.F6<sub>16</sub>)
|552.96 (228.F6<sub>16</sub>)
|-
|-
| | 28
| | 28
| | 448
| | 448
|474.88
|573.44 (23D.71<sub>16</sub>)
|573.44 (23D.71<sub>16</sub>)
|-
|-
| | 29
| | 29
| | 464
| | 464
|491.84
|593.92 (251.EB8<sub>16</sub>)
|593.92 (251.EB8<sub>16</sub>)
|-
|-
| | 30
| | 30
| | 480
| | 480
|508.8
|614.4 (266.66<sub>16</sub>)
|614.4 (266.66<sub>16</sub>)
|-
|-
| | 31
| | 31
| | 496
| | 496
|525.76
|634.88 (27A.E1<sub>16</sub>)
|634.88 (27A.E1<sub>16</sub>)
|-
|-
| | 32
| | 32
| | 512
| | 512
|542.72
|655.36 (28F.5C<sub>16</sub>)
|655.36 (28F.5C<sub>16</sub>)
|-
|-
| | 33
| | 33
| | 528
| | 528
|559.68
|675.84 (2A3.D7<sub>16</sub>)
|675.84 (2A3.D7<sub>16</sub>)
|-
|-
| | 34
| | 34
| | 544
| | 544
|576.64
|696.32 (2B8.52<sub>16</sub>)
|696.32 (2B8.52<sub>16</sub>)
|-
|-
| | 35
| | 35
| | 560
| | 560
|593.6
|716.8 (2CC.CD<sub>16</sub>)
|716.8 (2CC.CD<sub>16</sub>)
|-
|-
| | 36
| | 36
| | 576
| | 576
|610.56
|737.28 (2E1.48<sub>16</sub>)
|737.28 (2E1.48<sub>16</sub>)
|-
|-
| | 37
| | 37
| | 592
| | 592
|627.52
|757.76 (2F5.C3<sub>16</sub>)
|757.76 (2F5.C3<sub>16</sub>)
|-
|-
| | 38
| | 38
| | 608
| | 608
|644.48
|778.24 (30A.3D<sub>16</sub>)
|778.24 (30A.3D<sub>16</sub>)
|-
|-
| | 39
| | 39
| | 624
| | 624
|661.44
|798.72 (31E.B8<sub>16</sub>)
|798.72 (31E.B8<sub>16</sub>)
|-
|-
| | 40
| | 40
| | 640
| | 640
|678.4
|819.2 (333.33<sub>16</sub>)
|819.2 (333.33<sub>16</sub>)
|-
|-
| | 41
| | 41
| | 656
| | 656
|695.36
|839.68 (347.AE<sub>16</sub>)
|839.68 (347.AE<sub>16</sub>)
|-
|-
| | 42
| | 42
| | 672
| | 672
|712.32
|860.16 (35C.29<sub>16</sub>)
|860.16 (35C.29<sub>16</sub>)
|-
|-
| | 43
| | 43
| | 688
| | 688
|729.28
|880.64 (370.A4<sub>16</sub>)
|880.64 (370.A4<sub>16</sub>)
|-
|-
| | 44
| | 44
| | 704
| | 704
|746.24
|901.12 (385.1F<sub>16</sub>)
|901.12 (385.1F<sub>16</sub>)
|-
|-
| | 45
| | 45
| | 720
| | 720
|763.2
|921.6 (399.9A<sub>16</sub>)
|921.6 (399.9A<sub>16</sub>)
|-
|-
| | 46
| | 46
| | 736
| | 736
|780.16
|942.08 (3AE.148<sub>16</sub>)
|942.08 (3AE.148<sub>16</sub>)
|-
|-
| | 47
| | 47
| | 752
| | 752
|797.12
|962.56 (3C2.8F<sub>16</sub>)
|962.56 (3C2.8F<sub>16</sub>)
|-
|-
| | 48
| | 48
| | 768
| | 768
|814.08
|983.04 (3D7.0A<sub>16</sub>)
|983.04 (3D7.0A<sub>16</sub>)
|-
|-
| | 49
| | 49
| | 784
| | 784
|831.04
|1003.52 (3E9.85<sub>16</sub>)
|1003.52 (3E9.85<sub>16</sub>)
|-
|-
| | 50
| | 50
| | 800
| | 800
|848
|1024 (400<sub>16</sub>)
|1024 (400<sub>16</sub>)
|-
|-
| | 51
| | 51
| | 816
| | 816
|864.96
|1044.48 (414.7B<sub>16</sub>)
|1044.48 (414.7B<sub>16</sub>)
|-
|-
| | 52
| | 52
| | 832
| | 832
|881.92
|1064.96 (428.F6<sub>16</sub>)
|1064.96 (428.F6<sub>16</sub>)
|-
|-
| | 53
| | 53
| | 848
| | 848
|898.88
|1085.44 (43D.71<sub>16</sub>)
|1085.44 (43D.71<sub>16</sub>)
|-
|-
| | 54
| | 54
| | 864
| | 864
|915.84
|1105.92 (551.EB8<sub>16</sub>)
|1105.92 (551.EB8<sub>16</sub>)
|-
|-
| | 55
| | 55
| | 880
| | 880
|932.8
|1126.4 (466.66<sub>16</sub>)
|1126.4 (466.66<sub>16</sub>)
|-
|-
| | 56
| | 56
| | 896
| | 896
|949.76
|1146.88 (47A.E1<sub>16</sub>)
|1146.88 (47A.E1<sub>16</sub>)
|-
|-
| | 57
| | 57
| | 912
| | 912
|966.72
|1167.36 (48F.5C<sub>16</sub>)
|1167.36 (48F.5C<sub>16</sub>)
|-
|-
| | 58
| | 58
| | 928
| | 928
|983.68
|1187.84 (4A3.D7<sub>16</sub>)
|1187.84 (4A3.D7<sub>16</sub>)
|-
|-
| | 59
| | 59
| | 944
| | 944
|1000.64
|1208.32 (4B8.52<sub>16</sub>)
|1208.32 (4B8.52<sub>16</sub>)
|-
|-
| | 60
| | 60
| | 960
| | 960
|1017.6
|1228.8 (4CC.CD<sub>16</sub>)
|1228.8 (4CC.CD<sub>16</sub>)
|-
|-
| | 61
| | 61
| | 976
| | 976
|1034.56
|1249.28 (4E1.48<sub>16</sub>)
|1249.28 (4E1.48<sub>16</sub>)
|-
|-
| | 62
| | 62
| | 992
| | 992
|1051.52
|1269.76 (4F5.C3<sub>16</sub>)
|1269.76 (4F5.C3<sub>16</sub>)
|-
|-
| | 63
| | 63
| | 1008
| | 1008
|1068.48
|1290.24 (50A.3D<sub>16</sub>)
|1290.24 (50A.3D<sub>16</sub>)
|-
|-
| | 64
| | 64
| | 1024
| | 1024
|1085.44
|1310.72 (51E.B8<sub>16</sub>)
|1310.72 (51E.B8<sub>16</sub>)
|-
|-
| | 65
| | 65
| | 1040
| | 1040
|1102.4
|1331.2 (533.33<sub>16</sub>)
|1331.2 (533.33<sub>16</sub>)
|-
|-
| | 66
| | 66
| | 1056
| | 1056
|1119.36
|1351.68 (547.AE<sub>16</sub>)
|1351.68 (547.AE<sub>16</sub>)
|-
|-
| | 67
| | 67
| | 1072
| | 1072
|1136.32
|1372.16 (55C.29<sub>16</sub>)
|1372.16 (55C.29<sub>16</sub>)
|-
|-
| | 68
| | 68
| | 1088
| | 1088
|1153.28
|1392.64 (570.A4<sub>16</sub>)
|1392.64 (570.A4<sub>16</sub>)
|-
|-
| | 69
| | 69
| | 1104
| | 1104
|1170.24
|1413.12 (585.1F<sub>16</sub>)
|1413.12 (585.1F<sub>16</sub>)
|-
|-
| | 70
| | 70
| | 1120
| | 1120
|1187.2
|1433.6 (599.9A<sub>16</sub>)
|1433.6 (599.9A<sub>16</sub>)
|-
|-
| | 71
| | 71
| | 1136
| | 1136
|1204.16
|1454.08 (5AE.148<sub>16</sub>)
|1454.08 (5AE.148<sub>16</sub>)
|-
|-
| | 72
| | 72
| | 1152
| | 1152
|1221.12
|1474.56 (5C2.8F<sub>16</sub>)
|1474.56 (5C2.8F<sub>16</sub>)
|-
|-
| | 73
| | 73
| | 1168
| | 1168
|1238.08
|1495.04 (5D7.0A<sub>16</sub>)
|1495.04 (5D7.0A<sub>16</sub>)
|-
|-
| | 74
| | 74
| | 1184
| | 1184
|1255.04
|1515.52 (5E9.85<sub>16</sub>)
|1515.52 (5E9.85<sub>16</sub>)
|-
|-
|75
|75
|1200
|1200
|1272
|1536 (600<sub>16</sub>)
|1536 (600<sub>16</sub>)
|}
|}

Revision as of 12:37, 12 December 2019

75edo divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for tetracot temperament. It provides the optimal patent val for the 12&51 temperament in the 7-limit and the 31&75 temperament in the 13-limit.

Intervals

Step Size in
Cents 7mus
0
1 16 20.48 (14.7B16)
2 32 40.96 (28.F616)
3 48 61.44 (3D.7116)
4 64 81.92 (51.EB816)
5 80 102.4 (66.6616)
6 96 122.88 (7A.E116)
7 112 143.36 (8F.5C16)
8 128 163.84 (A3.D716)
9 144 184.32 (B8.5216)
10 160 204.8 (CC.CD16)
11 176 225.28 (E1.4816)
12 192 245.76 (F5.C316)
13 208 266.24 (10A.3D16)
14 224 286.72 (11E.B816)
15 240 307.2 (133.3316)
16 256 327.68 (147.AE16)
17 272 348.16 (15C.2916)
18 288 368.64 (170.A416)
19 304 389.12 (185.1F16)
20 320 409.6 (199.9A16)
21 336 430.08 (1AE.14816)
22 352 450.56 (1C2.8F16)
23 368 471.04 (1D7.0A16)
24 384 491.52 (1E9.8516)
25 400 512 (20016)
26 416 532.48 (214.7B16)
27 432 552.96 (228.F616)
28 448 573.44 (23D.7116)
29 464 593.92 (251.EB816)
30 480 614.4 (266.6616)
31 496 634.88 (27A.E116)
32 512 655.36 (28F.5C16)
33 528 675.84 (2A3.D716)
34 544 696.32 (2B8.5216)
35 560 716.8 (2CC.CD16)
36 576 737.28 (2E1.4816)
37 592 757.76 (2F5.C316)
38 608 778.24 (30A.3D16)
39 624 798.72 (31E.B816)
40 640 819.2 (333.3316)
41 656 839.68 (347.AE16)
42 672 860.16 (35C.2916)
43 688 880.64 (370.A416)
44 704 901.12 (385.1F16)
45 720 921.6 (399.9A16)
46 736 942.08 (3AE.14816)
47 752 962.56 (3C2.8F16)
48 768 983.04 (3D7.0A16)
49 784 1003.52 (3E9.8516)
50 800 1024 (40016)
51 816 1044.48 (414.7B16)
52 832 1064.96 (428.F616)
53 848 1085.44 (43D.7116)
54 864 1105.92 (551.EB816)
55 880 1126.4 (466.6616)
56 896 1146.88 (47A.E116)
57 912 1167.36 (48F.5C16)
58 928 1187.84 (4A3.D716)
59 944 1208.32 (4B8.5216)
60 960 1228.8 (4CC.CD16)
61 976 1249.28 (4E1.4816)
62 992 1269.76 (4F5.C316)
63 1008 1290.24 (50A.3D16)
64 1024 1310.72 (51E.B816)
65 1040 1331.2 (533.3316)
66 1056 1351.68 (547.AE16)
67 1072 1372.16 (55C.2916)
68 1088 1392.64 (570.A416)
69 1104 1413.12 (585.1F16)
70 1120 1433.6 (599.9A16)
71 1136 1454.08 (5AE.14816)
72 1152 1474.56 (5C2.8F16)
73 1168 1495.04 (5D7.0A16)
74 1184 1515.52 (5E9.8516)
75 1200 1536 (60016)
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