103ed7/3

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 102ed7/3

103ed7/3

104ed7/3 →

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	14.2
2	28.5
3	42.7	41/40
4	57
5	71.2
6	85.4
7	99.7
8	113.9	31/29
9	128.2	14/13
10	142.4
11	156.7
12	170.9
13	185.1	39/35
14	199.4	37/33
15	213.6	26/23, 43/38
16	227.9
17	242.1	23/20, 38/33
18	256.3
19	270.6
20	284.8	33/28
21	299.1
22	313.3	6/5
23	327.6	29/24
24	341.8	28/23
25	356
26	370.3
27	384.5
28	398.8
29	413	33/26
30	427.2
31	441.5	31/24, 40/31
32	455.7	13/10
33	470	38/29
34	484.2	37/28, 41/31
35	498.5
36	512.7
37	526.9	19/14
38	541.2	26/19
39	555.4	40/29
40	569.7	25/18
41	583.9	7/5
42	598.1	24/17, 41/29
43	612.4	37/26
44	626.6	33/23
45	640.9
46	655.1	19/13
47	669.3	28/19
48	683.6	43/29
49	697.8
50	712.1
51	726.3
52	740.6	43/28
53	754.8	17/11
54	769	39/25
55	783.3
56	797.5	19/12
57	811.8
58	826
59	840.2
60	854.5
61	868.7	33/20, 38/23, 43/26
62	883	5/3
63	897.2	42/25
64	911.5
65	925.7	29/17, 41/24
66	939.9
67	954.2	33/19
68	968.4
69	982.7
70	996.9
71	1011.1	43/24
72	1025.4
73	1039.6	31/17
74	1053.9
75	1068.1
76	1082.4	43/23
77	1096.6
78	1110.8	19/10
79	1125.1	23/12
80	1139.3
81	1153.6	35/18, 37/19
82	1167.8
83	1182
84	1196.3
85	1210.5
86	1224.8
87	1239
88	1253.2
89	1267.5
90	1281.7
91	1296
92	1310.2
93	1324.5	43/20
94	1338.7	13/6
95	1352.9	24/11
96	1367.2
97	1381.4
98	1395.7
99	1409.9
100	1424.1
101	1438.4
102	1452.6
103	1466.9	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)