104ed7/3

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104ed7/3

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Prime factorization	23 × 13
Step size	14.1045¢
Octave	85\104ed7/3 (1198.88¢) (semiconvergent)
Twelfth	135\104ed7/3 (1904.11¢)
Consistency limit	4
Distinct consistency limit	4

104 equal divisions of 7/3 (abbreviated 104ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 104 equal parts of about 14.1 ¢ each. Each step represents a frequency ratio of (7/3)^1/104, or the 104th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	14.105
2	28.209
3	42.314	40/39, 41/40, 42/41, 43/42
4	56.418	32/31
5	70.523
6	84.627	21/20, 41/39, 43/41
7	98.732	18/17
8	112.836
9	126.941	14/13, 43/40
10	141.045
11	155.15	23/21
12	169.254	32/29, 43/39
13	183.359	10/9
14	197.463	37/33, 46/41
15	211.568	26/23
16	225.672	33/29, 41/36
17	239.777	23/20, 39/34
18	253.882	22/19
19	267.986	7/6
20	282.091	20/17, 33/28
21	296.195	19/16
22	310.3
23	324.404	41/34
24	338.509	28/23
25	352.613	38/31
26	366.718	21/17
27	380.822
28	394.927
29	409.031
30	423.136	23/18, 37/29
31	437.24	9/7
32	451.345	35/27
33	465.449	17/13
34	479.554	29/22
35	493.658
36	507.763
37	521.868	23/17, 27/20
38	535.972
39	550.077	11/8
40	564.181	18/13
41	578.286
42	592.39	31/22
43	606.495	44/31
44	620.599
45	634.704	13/9
46	648.808	16/11
47	662.913
48	677.017	34/23
49	691.122
50	705.226
51	719.331
52	733.435	26/17, 29/19
53	747.54	20/13, 37/24
54	761.645
55	775.749	36/23
56	789.854	41/26
57	803.958	43/27
58	818.063
59	832.167	21/13, 34/21
60	846.272	31/19
61	860.376	23/14
62	874.481
63	888.585
64	902.69	32/19
65	916.794	17/10
66	930.899	12/7
67	945.003	19/11
68	959.108	40/23
69	973.212
70	987.317	23/13
71	1001.421	41/23
72	1015.526	9/5
73	1029.631	29/16
74	1043.735	42/23
75	1057.84
76	1071.944	13/7
77	1086.049
78	1100.153	17/9
79	1114.258	40/21
80	1128.362	23/12
81	1142.467
82	1156.571	39/20, 41/21
83	1170.676
84	1184.78
85	1198.885	2/1
86	1212.989
87	1227.094
88	1241.198	41/20, 43/21
89	1255.303	33/16
90	1269.408
91	1283.512	21/10
92	1297.617	36/17
93	1311.721
94	1325.826	43/20
95	1339.93	13/6
96	1354.035
97	1368.139
98	1382.244	20/9
99	1396.348
100	1410.453
101	1424.557	41/18
102	1438.662	39/17
103	1452.766	37/16, 44/19
104	1466.871	7/3

Harmonics

Approximation of harmonics in 104ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.12	+2.16	-2.23	+6.38	+1.04	+2.16	-3.35	+4.31	+5.27	-4.59	-0.07
	Relative (%)	-7.9	+15.3	-15.8	+45.3	+7.4	+15.3	-23.7	+30.6	+37.3	-32.5	-0.5
Steps (reduced)		85 (85)	135 (31)	170 (66)	198 (94)	220 (12)	239 (31)	255 (47)	270 (62)	283 (75)	294 (86)	305 (97)

Approximation of harmonics in 104ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.40	+1.04	-5.57	-4.46	+3.42	+3.20	-5.78	+4.15	+4.31	-5.70	+1.97
	Relative (%)	+17.0	+7.4	-39.5	-31.6	+24.2	+22.7	-41.0	+29.4	+30.6	-40.4	+14.0
Steps (reduced)		315 (3)	324 (12)	332 (20)	340 (28)	348 (36)	355 (43)	361 (49)	368 (56)	374 (62)	379 (67)	385 (73)