103edo: Difference between revisions

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! Degree
! Degree
! Cents
! Cents
! Temperament
! Approximate Ratios
|-
|-
| 1
| 1
| 11.650
| 11.650
| Marvel and Benediction
| 81/80, 126/125
|-
|-
| 2
| 2
| 23.301
| 23.301
| Hemisecordite
| 65/64, 66/65, 78/77
|-
|-
| 3
| 3
| 34.951
| 34.951
| Marvel and Benediction, Hemisecordite
| 49/48, 50/49, 64/63
|-
|-
| 4
| 4
| 46.602
| 46.602
| Marvel and Benediction
| 33/32, 35/34, 36/35
|-
|-
| 5
| 5
| 58.252
| 58.252
| Hemisecordite
| 27/26, 34/33
|-
|-
| 6
| 6
| 69.903
| 69.903
| Marvel and Benediction
| 25/24, 26/25, 28/27
|-
|-
| 7
| 7
| 81.553
| 81.553
| Marvel and Benediction, Hemisecordite
| 21/20, 22/21
|-
|-
| 8
| 8
| 93.204
| 93.204
| Hemisecordite
| 18/17
|-
|-
| 9
| 9
| 104.854
| 104.854
| Marvel and Benediction
| 17/16
|-
|-
| 10
| 10
| 116.505
| 116.505
| Marvel and Benediction, Hemisecordite
| 15/14, 16/15
|-
|-
| 11
| 11
| 128.155
| 128.155
| Marvel and Benediction
| 14/13
|-
|-
| 12
| 12
| 139.806
| 139.806
| Hemisecordite
| 13/12
|-
|-
| 13
| 13
| 151.456
| 151.456
| Marvel and Benediction, Hemisecordite
| 12/11
|-
|-
| 14
| 14
| 163.107
| 163.107
| Marvel and Benediction
| 11/10
|-
|-
| 15
| 15
| 174.757
| 174.757
| Hemisecordite
| 72/65
|-
|-
| 16
| 16
| 186.408
| 186.408
| Marvel and Benediction
| 10/9
|-
|-
| 17
| 17
| 198.058
| 198.058
| Marvel and Benediction, Hemisecordite
| 9/8
|-
|-
| 18
| 18
| 209.708
| 209.708
| Hemisecordite
|  
|-
|-
| 19
| 19
| 221.359
| 221.359
| Marvel and Benediction
| 17/15, 25/22
|-
|-
| 20
| 20
| 233.010
| 233.010
| Marvel and Benediction, Hemisecordite
| 8/7
|-
|-
| 21
| 21
| 244.660
| 244.660
| Marvel and Benediction
| 15/13
|-
|-
| 22
| 22
| 256.311
| 256.311
| Hemisecordite
|  
|-
|-
| 23
| 23
| 267.961
| 267.961
| Marvel and Benediction, Hemisecordite
| 7/6
|-
|-
| 24
| 24
| 279.712
| 279.712
| Marvel and Benediction
| 20/17
|-
|-
| 25
| 25
| 291.262
| 291.262
| Hemisecordite
| 13/11
|-
|-
| 26
| 26
| 303.013
| 303.013
| Marvel and Benediction
| 25/21
|-
|-
| 27
| 27
| 314.563
| 314.563
| Marvel and Benediction, Hemisecordite
| 6/5
|-
|-
| 28
| 28
| 326.214
| 326.214
| Hemisecordite
| 63/52, 65/54
|-
|-
| 29
| 29
| 337.864
| 337.864
| Marvel and Benediction
| 17/14, 39/32
|-
|-
| 30
| 30
| 349.615
| 349.615
| Marvel and Benediction, Hemisecordite
| 11/9, 27/22
|-
|-
| 31
| 31
| 361.165
| 361.165
| Marvel and Benediction
| 16/13, 21/17
|-
|-
| 32
| 32
| 372.816
| 372.816
| Hemisecordite
| 26/21, 81/65
|-
|-
| 33
| 33
| 384.466
| 384.466
| Marvel and Benediction, Hemisecordite
| 5/4
|-
|-
| 34
| 34
| 396.117
| 396.117
| Marvel and Benediction
| 44/35
|-
|-
| 35
| 35
| 407.767
| 407.767
| Hemisecordite
| 33/26
|-
|-
| 36
| 36
| 419.417
| 419.417
| Marvel and Benediction
| 14/11
|-
|-
| 37
| 37
| 431.068
| 431.068
| Marvel and Benediction, Hemisecordite
| 9/7
|-
|-
| 38
| 38
| 442.708
| 442.708
| Hemisecordite
| 22/17
|-
|-
| 39
| 39
| 454.369
| 454.369
| Marvel and Benediction
| 13/10
|-
|-
| 40
| 40
| 466.019
| 466.019
| Marvel and Benediction, Hemisecordite
| 17/13, 21/16
|-
|-
| 41
| 41
| 477.670
| 477.670
| Marvel and Benediction
|  
|-
|-
| 42
| 42
| 489.320
| 489.320
| Hemisecordite
| 65/49
|-
|-
| 43
| 43
| 500.971
| 500.971
| Marvel and Benediction, Hemisecordite
| 4/3
|-
|-
| 44
| 44
| 512.621
| 512.621
| Marvel and Benediction
| 27/20
|-
|-
| 45
| 45
| 524.272
| 524.272
| Hemisecordite
| 65/48
|-
|-
| 46
| 46
| 535.922
| 535.922
| Marvel and Benediction
| 15/11
|-
|-
| 47
| 47
| 547.573
| 547.573
| Marevel and Benediction, Hemisecordite
| 11/8
|-
|-
| 48
| 48
| 559.223
| 559.223
| Hemisecordite
| 18/13
|-
|-
| 49
| 49
| 570.874
| 570.874
| Marvel and Benediction
| 25/18
|-
|-
| 50
| 50
| 582.524
| 582.524
| Marvel and Benediction, Hemisecordite
| 7/5
|-
|-
| 51
| 51
| 594.175
| 594.175
|  
| 24/17
|-
|-
| …
| …

Revision as of 14:17, 4 July 2021

103edo is the equal division of the octave into 103 steps of size 11.6505 cents each.

Theory

103edo is a good miracle tuning, especially for the 7- and 13-limit and benediction and hemisecordite, two of the 13-limit extensions of miracle. It tempers out 78732/78125 in the 5-limit; 225/224, 1029/1024 and 2401/2400 in the 7-limit; 243/242, 441/440 and 540/539 in the 11-limit; 351/350 and 847/845 in the 13-limit. In the 13-limit it provides the optimal patent val for marvel temperament as well as benediction and hemisecordite.

103edo is the 27th prime edo.

Prime harmonics

Script error: No such module "primes_in_edo".

Intervals

Degree Cents Approximate Ratios
1 11.650 81/80, 126/125
2 23.301 65/64, 66/65, 78/77
3 34.951 49/48, 50/49, 64/63
4 46.602 33/32, 35/34, 36/35
5 58.252 27/26, 34/33
6 69.903 25/24, 26/25, 28/27
7 81.553 21/20, 22/21
8 93.204 18/17
9 104.854 17/16
10 116.505 15/14, 16/15
11 128.155 14/13
12 139.806 13/12
13 151.456 12/11
14 163.107 11/10
15 174.757 72/65
16 186.408 10/9
17 198.058 9/8
18 209.708
19 221.359 17/15, 25/22
20 233.010 8/7
21 244.660 15/13
22 256.311
23 267.961 7/6
24 279.712 20/17
25 291.262 13/11
26 303.013 25/21
27 314.563 6/5
28 326.214 63/52, 65/54
29 337.864 17/14, 39/32
30 349.615 11/9, 27/22
31 361.165 16/13, 21/17
32 372.816 26/21, 81/65
33 384.466 5/4
34 396.117 44/35
35 407.767 33/26
36 419.417 14/11
37 431.068 9/7
38 442.708 22/17
39 454.369 13/10
40 466.019 17/13, 21/16
41 477.670
42 489.320 65/49
43 500.971 4/3
44 512.621 27/20
45 524.272 65/48
46 535.922 15/11
47 547.573 11/8
48 559.223 18/13
49 570.874 25/18
50 582.524 7/5
51 594.175 24/17
… … …

Regular temperament properties

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per octave 		Generator
(reduced) 		Cents
(reduced) 		Associated
ratio 		Temperaments
1 3\103 34.951 1990656/1953125 Gammic (5-limit)
1 5\103 58.252 27/26 Hemisecordite
1 10\103 116.505 15/14~16/15 Miracle / benediction
1 16\103 186.408 10/9 Mintone
1 20\103 233.010 8/7 Slendric
1 26\103 303.013 25/21 Quinmite
1 31\103 361.165 16/13 Phicordial
1 38\103 442.708 162/125 Sensipent / sensei
1 39\103 454.369 13/10 Fibo
1 42\103 489.320 65/49 Catafourth
1 45\103 524.272 65/48 Widefourth
1 47\103 547.573 11/8 Heinz
1 48\103 559.223 242/175 Tritriple
1 50\103 582.524 7/5 Neptune

Scales

Since 103edo has a step of 11.6505 cents, it also allows one to use its MOS scales as circulating temperaments[clarification needed].

Circulating temperaments in 103edo
Tones Pattern L:s
5 3L 2s 21:20
6 1L 5s 18:17
7 5L 2s 15:14
8 7L 1s 13:12
9 4L 5s 12:11
10 3L 7s 11:10
11 4L 7s 10:9
12 7L 5s 9:8
13 12L 1s 8:7
14 3L 11s
15 13L 2s 7:6
16 7L 9s
17 1L 16s
18 11L 7s 6:5
19 8L 11s
20 3L 17s
21 19L 2s 5:4
22 15L 7s
23 11L 12s
24 7L 17s
25 3L 22s
26 25L 1s 4:3
27 22L 5s
28 19L 9s
29 16L 13s
30 13L 17s
31 10L 21s
32 7L 25s
33 4L 29s
34 1L 33s
35 33L 2s 3:2
36 31L 5s
37 29L 8s
38 27L 11s
39 25L 14s
40 23L 17s
41 21L 20s
42 19L 23s
43 17L 26L
44 15L 29s
45 13L 32s
46 11L 35s
47 9L 38s
48 7L 41s
49 5L 44s
50 3L 47s
51 1L 50s
52 51L 1s 2:1
53 50L 3s
54 49L 5s
55 48L 7s
56 47L 9s
57 46L 11s
58 45L 13s
59 44L 15s
60 43L 17s
61 42L 19s
62 41L 21s
63 40L 23s
64 39L 25s
65 38L 27s
66 37L 29s
67 36L 31s
68 35L 33s
69 34L 35s
70 33L 37s
71 32L 39s
72 31L 41s
73 30L 43s
74 29L 45s
75 28L 47s
76 27L 49s
77 26L 51s
78 25L 53s
79 24L 55s
80 23L 57s
81 22L 59s
82 21L 61s

13-limit temperaments

Marvel and Benediction Hemisecordite
Degree cents Difference from 72edo Degree cents Difference from 62edo
1 11.6505 -5.016¢ 2 23.301 3.946¢
3 34.9515 1.618¢ 3 34.9515 -3.758¢
4 46.602 -3.398¢ 5 58.252 0.188¢
6 69.903 3.236¢ 7 81.553 4.134¢
7 81.553 -1.78¢ 8 93.204 -3.57¢
9 104.854 4.854¢ 10 116.505 0.376¢
10 116.5045 -0.162¢ 12 139.806 4.322¢
11 128.155 -5.178¢ 13 151.456 -3.382¢
13 151.456¢ 1.456¢ 15 174.757 0.563¢
14 163.107¢ -3.56¢ 17 198.058 4.51¢
16 186.408 3.074¢ 18 209.709 -3.1945¢
17 198.058 -1.942¢ 20 233.01 0.751¢
19 221.359 4.693¢ 22 256.311 4.698¢
20 233.01 -0.324¢ 23 267.961 -3.007¢
21 244.66 -5.34¢ 25 291.262 0.94¢
23 267.961 1.2945¢ 27 314.563 4.886¢
24 279.612 -3.722¢ 28 326.214 -2.819¢
26 302.913 2.913¢ 30 349.515 1.1275¢
27 314.563 -2.104¢ 32 372.8155 5.074¢
29 337.864 4.531¢ 33 384.466 -2.631¢
30 349.515 -0.485¢ 35 407.767 1.315¢
31 361.165 -5.502¢ 37 431.068 5.2615¢
33 384.466 1.133¢ 38 442.718 -2.443¢
34 396.1165 -3.8835¢ 40 466.0190 1.503¢
36 419.4175 2.751¢ 42 489.32 5.449¢
37 431.068 -2.265¢ 43 500.971 -2.255¢
39 454.369 4.369¢ 45 524.272 1.691¢
40 466.019 -0.647¢ 47 547.573 5.637¢
41 477.67 -5.663¢ 48 559.223 -2.067¢
43 500.971 0.971¢ 50 582.524 1.879¢
44 512.621¢ -4.045¢ 52 605.825 5.825¢
46 535.922¢ 2.589¢ 53 617.476 -1.879¢
47 547.573¢ -2.427¢ 55 640.777¢ 2.067
49 570.874¢ 4.207¢ 56 652.427 -5.637¢
50 582.524 -0.809¢ 58 675.728 -1.691
52 605.825 5.825¢ 60 699.029 2.255¢
53 617.475 0.809¢ 61 710.68 -5.449¢
54 629.126¢ -4.207¢ 63 733.981 -1.503¢
56 652.427¢ 2.427¢ 65 757.282 2.443¢
57 664.078 -2.589¢ 66 768.932 -5.2615¢
59 687.379 4.045¢ 68 792.233 -1.315¢
60 699.029 -0.971¢ 70 815.534 2.631¢
62 722.33 5.663¢ 71 827.1845 -5.074¢
63 733.981 0.647¢ 73 850.485 -1.1275¢
64 745.631 -4.369¢ 75 873.786 2.819¢
66 768.932 2.265¢ 76 885.437 -4.886¢
67 780.5825 -2.751¢ 78 908.738 -0.94¢
69 803.8835 3.8835¢ 80 932.039 3.007¢
70 815.534 -1.133¢ 81 943.689 -4.698¢
72 838.835 5.501¢ 83 966.99 -0.752¢
73 850.485 0.485¢ 85 990.291 3.1945¢
74 862.136 -4.531¢ 86 1001.942 -4.51¢
76 885.439 2.104¢ 88 1025.243 -0.564¢
77 897.087 -2.913¢ 90 1048.544 3.382¢
79 920.388 3.722¢ 91 1060.194 -4.322¢
80 932.039 -1.2945¢ 93 1083.495 -0.376¢
82 955.34 5.34¢ 95 1106.796 3.57¢
83 966.99 0.324¢ 96 1118.447¢ -4.134¢
84 978.641 -4.693¢ 98 1141.748 -0.188¢
86 1001.942 1.942¢ 100 1165.0485 3.758¢
87 1013.592 -3.074¢ 101 1176.699 -3.946¢
89 1036.893 3.56¢
90 1048.544 -1.456¢
92 1071.845 5.178¢
93 1083.495 0.162¢
94 1095.146 -4.854¢
96 1118.447 1.78¢
97 1130.097 -3.236¢
99 1153.398 3.398¢
100 1165.0485 -1.618¢
102 1188.3495 5.016¢
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