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	14.1
2	28.2
3	42.3	40/39, 41/40, 42/41, 43/42
4	56.4	32/31
5	70.5
6	84.6	21/20, 41/39, 43/41
7	98.7	18/17
8	112.8
9	126.9	14/13, 43/40
10	141
11	155.1	23/21
12	169.3	32/29, 43/39
13	183.4	10/9
14	197.5	37/33, 46/41
15	211.6	26/23
16	225.7	33/29, 41/36
17	239.8	23/20, 39/34
18	253.9	22/19
19	268	7/6
20	282.1	20/17, 33/28
21	296.2	19/16
22	310.3
23	324.4	41/34
24	338.5	28/23
25	352.6	38/31
26	366.7	21/17
27	380.8
28	394.9
29	409
30	423.1	23/18, 37/29
31	437.2	9/7
32	451.3	35/27
33	465.4	17/13
34	479.6	29/22
35	493.7
36	507.8
37	521.9	23/17, 27/20
38	536
39	550.1	11/8
40	564.2	18/13
41	578.3
42	592.4	31/22
43	606.5	44/31
44	620.6
45	634.7	13/9
46	648.8	16/11
47	662.9
48	677	34/23
49	691.1
50	705.2
51	719.3
52	733.4	26/17, 29/19
53	747.5	20/13, 37/24
54	761.6
55	775.7	36/23
56	789.9	41/26
57	804	43/27
58	818.1
59	832.2	21/13, 34/21
60	846.3	31/19
61	860.4	23/14
62	874.5
63	888.6
64	902.7	32/19
65	916.8	17/10
66	930.9	12/7
67	945	19/11
68	959.1	40/23
69	973.2
70	987.3	23/13
71	1001.4	41/23
72	1015.5	9/5
73	1029.6	29/16
74	1043.7	42/23
75	1057.8
76	1071.9	13/7
77	1086
78	1100.2	17/9
79	1114.3	40/21
80	1128.4	23/12
81	1142.5
82	1156.6	39/20, 41/21
83	1170.7
84	1184.8
85	1198.9	2/1
86	1213
87	1227.1
88	1241.2	41/20, 43/21
89	1255.3	33/16
90	1269.4
91	1283.5	21/10
92	1297.6	36/17
93	1311.7
94	1325.8	43/20
95	1339.9	13/6
96	1354
97	1368.1
98	1382.2	20/9
99	1396.3
100	1410.5
101	1424.6	41/18
102	1438.7	39/17
103	1452.8	37/16, 44/19
104	1466.9	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)