103edo

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.

Intervals

Degree	Cents	Temperament
1	11.6505	Marvel and Benediction
2	23.301	Hemisecordite
3	34.9515	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	116.5045	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
…	…	…

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¢