103ed7/3

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103ed7/3

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Prime factorization	103 (prime)
Step size	14.2415¢
Octave	84\103ed7/3 (1196.28¢)
Twelfth	134\103ed7/3 (1908.36¢)
Consistency limit	2
Distinct consistency limit	2

103 equal divisions of 7/3 (abbreviated 103ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 103 equal parts of about 14.2 ¢ each. Each step represents a frequency ratio of (7/3)^1/103, or the 103rd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	14.241
2	28.483
3	42.724	41/40
4	56.966
5	71.207
6	85.449
7	99.69
8	113.932	31/29
9	128.173	14/13
10	142.415
11	156.656
12	170.898
13	185.139	39/35
14	199.381	37/33
15	213.622	26/23, 43/38
16	227.863
17	242.105	23/20, 38/33
18	256.346
19	270.588
20	284.829	33/28
21	299.071
22	313.312	6/5
23	327.554	29/24
24	341.795	28/23
25	356.037
26	370.278
27	384.52
28	398.761
29	413.002	33/26
30	427.244
31	441.485	31/24, 40/31
32	455.727	13/10
33	469.968	38/29
34	484.21	37/28, 41/31
35	498.451
36	512.693
37	526.934	19/14
38	541.176	26/19
39	555.417	40/29
40	569.659	25/18
41	583.9	7/5
42	598.142	24/17, 41/29
43	612.383	37/26
44	626.624	33/23
45	640.866
46	655.107	19/13
47	669.349	28/19
48	683.59	43/29
49	697.832
50	712.073
51	726.315
52	740.556	43/28
53	754.798	17/11
54	769.039	39/25
55	783.281
56	797.522	19/12
57	811.764
58	826.005
59	840.246
60	854.488
61	868.729	33/20, 38/23, 43/26
62	882.971	5/3
63	897.212	42/25
64	911.454
65	925.695	29/17, 41/24
66	939.937
67	954.178	33/19
68	968.42
69	982.661
70	996.903
71	1011.144	43/24
72	1025.385
73	1039.627	31/17
74	1053.868
75	1068.11
76	1082.351	43/23
77	1096.593
78	1110.834	19/10
79	1125.076	23/12
80	1139.317
81	1153.559	35/18, 37/19
82	1167.8
83	1182.042
84	1196.283
85	1210.525
86	1224.766
87	1239.007
88	1253.249
89	1267.49
90	1281.732
91	1295.973
92	1310.215
93	1324.456	43/20
94	1338.698	13/6
95	1352.939	24/11
96	1367.181
97	1381.422
98	1395.664
99	1409.905
100	1424.147
101	1438.388
102	1452.629
103	1466.871	7/3

Harmonics

Approximation of harmonics in 103ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-3.72	+6.40	+6.81	+5.01	+2.68	+6.40	+3.09	-1.44	+1.30	-7.05	-1.03
	Relative (%)	-26.1	+44.9	+47.8	+35.2	+18.8	+44.9	+21.7	-10.1	+9.1	-49.5	-7.3
Steps (reduced)		84 (84)	134 (31)	169 (66)	196 (93)	218 (12)	237 (31)	253 (47)	267 (61)	280 (74)	291 (85)	302 (96)

Approximation of harmonics in 103ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.81	+2.68	-2.83	-0.63	-5.89	-5.16	+0.93	-2.42	-1.44	+3.47	-2.28
	Relative (%)	+19.7	+18.8	-19.8	-4.4	-41.4	-36.2	+6.5	-17.0	-10.1	+24.4	-16.0
Steps (reduced)		312 (3)	321 (12)	329 (20)	337 (28)	344 (35)	351 (42)	358 (49)	364 (55)	370 (61)	376 (67)	381 (72)