103edo: Difference between revisions

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| | Marvel and Benediction
| | Marvel and Benediction
|}
|}
 
Since 103edo has a step of 11.6505 cents, it also allows one to use its MOS scales as circulating temperaments.
{| class="wikitable"
|+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]]
| rowspan="2" |8:7
|-
|14
|[[3L 11s]]
|-
|15
|[[13L 2s]]
| rowspan="2" |7:6
|-
|16
|[[7L 9s]]
|-
|17
|1L 16s
|equal
|-
|18
|11L 7s
| rowspan="3" |6:5
|-
|19
|8L 11s
|-
|20
|[[3L 17s]]
|-
|21
|19L 2s
| rowspan="5" |5:4
|-
|22
|[[15L 7s]]
|-
|23
|14L 9s
|-
|24
|[[7L 17s]]
|-
|25
|3L 22s
|-
|26
|25L 1s
| rowspan="9" |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
| rowspan="17" |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
| rowspan="31" |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
|}
[[Category:Benediction]]
[[Category:Benediction]]
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]

Revision as of 20:12, 20 April 2021

103edo is the equal division of the octave into 103 steps of size 11.6505 cents each. It is a good miracle tuning, especially for the 7- and 13- limits 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. Script error: No such module "primes_in_edo".

13-limit temperaments

Degree cents temperament
1 11.650 Marvel and Benediction
2 23.301 Hemisecordite
3 34.951 Marvel and Benediction, Hemisecordite
4 46.602 Marvel and Benediction
5 58.252 Hemisecordite
6 69.903 Marvel and Benediction
7 81.553 Marvel and Benediction, Hemisecordite
8 93.204 Hemisecordite
9 104.854 Marvel and Benediction
10 116.505 Marvel and Benediction, Hemisecordite
11 128.155 Marvel and Benediction
12 139.806 Hemisecordite
13 151.456 Marvel and Benediction, Hemisecordite
14 163.107 Marvel and Benediction
15 174.757 Hemisecordite
16 186.408 Marvel and Benediction
17 198.058 Marvel and Benediction, Hemisecordite
18 209.708 Hemisecordite
19 221.359 Marvel and Benediction
20 233.010 Marvel and Benediction, Hemisecordite
21 244.660 Marvel and Benediction
22 256.311 Hemisecordite
23 267.961 Marvel and Benediction, Hemisecordite
24 279.712 Marvel and Benediction
25 291.262 Hemisecordite
26 303.013 Marvel and Benediction
27 314.563 Marvel and Benediction, Hemisecordite
28 326.214 Hemisecordite
29 337.864 Marvel and Benediction
30 349.615 Marvel and Benediction, Hemisecordite
31 361.165 Marvel and Benediction
32 372.816 Hemisecordite
33 384.466 Marvel and Benediction, Hemisecordite
34 396.117 Marvel and Benediction
35 407.767 Hemisecordite
36 419.4175 Marvel and Benediction
37 431.068 Marvel and Benediction, Hemisecordite
38 442.708 Hemisecordite
39 454.369 Marvel and Benediction
40 466.019 Marvel and Benediction, Hemisecordite
41 477.670 Marvel and Benediction
42 489.320 Hemisecordite
43 500.971 Marvel and Benediction, Hemisecordite
44 512.621 Marvel and Benediction
45 524.272 Hemisecordite
46 535.922 Marvel and Benediction
47 547.573 Marevel and Benediction, Hemisecordite
48 559.223 Hemisecordite
49 570.874 Marvel and Benediction
50 582.524 Marvel and Benediction, Hemisecordite
52 605.825 Marvel and Benediction, Hemisecordite
53 617.476 Marvel and Benediction, Hemisecordite
54 629.126 Marvel and Benediction
55 640.777 Hemisecordite
56 652.427 Marvel and Benediction, Hemisecordite
57 664.078 Marvel and Benediction
58 675.728 Hemisecordite
59 687.379 Marvel and Benediction
60 699.029 Marvel and Benediction, Hemisecordite
61 710.677 Hemisecordite
62 722.330 Marvel and Benediction
63 733.981 Marvel and Benediction, Hemisecordite
64 745.631 Marvel and Benediction
65 757.282 Hemisecordite
66 768.932 Marvel and Benediction, Hemisecordite
67 780.583 Marvel and Benediction
68 792.233 Hemisecordite
69 803.883 Marvel and Benediction
70 815.534 Marvel and Benediction, Hemisecordite
71 827.185 Hemisecordite
72 838.835 Marvel and Benediction
73 850.385 Marvel and Benediction. Hemisecordite
74 862.156 Marvel and Benediction
75 873.786 Hemisecordite
76 885.537 Marvel and Benediction, Hemisecordite
77 896.987 Marvel and Benediction
78 908.638 Hemisecordite
79 920.388 Marvel and Benediction, Hemisecordite
80 932.039 Marvel and Benediction
81 943.689 Hemisecordite
82 955.34 Marvel and Benediction
83 966.99 Marvel and Benediction, Hemisecordite
84 978.641 Marvel and Benediction
85 990.291 Hemisecordite
86 1001.942 Marvel and Benediction, Hemisecordite
87 1013.592 Marvel and Benediction
88 1025.243 Hemisecordite
89 1036.893 Marvel and Benediction
90 1048.544 Marvel and Benediction, Hemisecordite
91 1060.194 Hemisecordite
92 1071.845 Marvel and Benediction
93 1083.495 Marvel and Benediction, Hemisecordite
94 1095.146 Marvel and Benediction
95 1106.796 Hemisecordite
96 1118.447 Marvel and Benediction, Hemisecordite
97 1130.097 Marvel and Benediction
98 1141.748 Hemisecordite
99 1153.398 Marvel and Benediction
100 1165.0485 Marvel and Benediction, Hemisecordite
101 1176.609 Hemisecordite
102 1188.3495 Marvel and Benediction

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

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 equal
18 11L 7s 6:5
19 8L 11s
20 3L 17s
21 19L 2s 5:4
22 15L 7s
23 14L 9s
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
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