106ed7/3

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Prime factorization	2 × 53
Step size	13.8384¢
Octave	87\106ed7/3 (1203.94¢)
Twelfth	137\106ed7/3 (1895.86¢)
Consistency limit	2
Distinct consistency limit	2

106 equal divisions of 7/3 (abbreviated 106ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 106 equal parts of about 13.8⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/106, or the 106th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	13.8
2	27.7
3	41.5	41/40, 44/43
4	55.4
5	69.2
6	83	43/41
7	96.9	18/17
8	110.7
9	124.5	43/40, 44/41
10	138.4	13/12
11	152.2	12/11
12	166.1	11/10
13	179.9	41/37
14	193.7	19/17
15	207.6
16	221.4	33/29
17	235.3	39/34
18	249.1
19	262.9
20	276.8	34/29
21	290.6	13/11
22	304.4	31/26, 37/31
23	318.3
24	332.1	23/19
25	346
26	359.8
27	373.6	36/29
28	387.5
29	401.3	29/23
30	415.2
31	429
32	442.8	31/24, 40/31
33	456.7
34	470.5
35	484.3	37/28, 41/31
36	498.2
37	512	39/29
38	525.9
39	539.7
40	553.5
41	567.4	25/18, 43/31
42	581.2	7/5
43	595.1	31/22
44	608.9	37/26
45	622.7	33/23
46	636.6
47	650.4
48	664.2
49	678.1	34/23
50	691.9
51	705.8
52	719.6
53	733.4	29/19
54	747.3	20/13, 37/24
55	761.1
56	775	36/23
57	788.8	30/19, 41/26
58	802.6
59	816.5
60	830.3
61	844.1
62	858	23/14
63	871.8	43/26
64	885.7	5/3
65	899.5	37/22, 42/25
66	913.3	39/23
67	927.2	41/24
68	941
69	954.8	33/19
70	968.7
71	982.5	30/17
72	996.4
73	1010.2	43/24
74	1024
75	1037.9
76	1051.7
77	1065.6	37/20
78	1079.4	41/22
79	1093.2
80	1107.1	36/19
81	1120.9
82	1134.7
83	1148.6	33/17
84	1162.4	43/22
85	1176.3
86	1190.1
87	1203.9
88	1217.8
89	1231.6
90	1245.5	39/19
91	1259.3	29/14
92	1273.1
93	1287
94	1300.8	36/17
95	1314.6
96	1328.5	28/13
97	1342.3
98	1356.2
99	1370
100	1383.8
101	1397.7
102	1411.5
103	1425.4
104	1439.2	39/17
105	1453
106	1466.9	7/3

Harmonics

Approximation of harmonics in 106ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.94	-6.09	-5.96	-4.79	-2.15	-6.09	-2.01	+1.65	-0.85	+0.20	+1.79
	Relative (%)	+28.5	-44.0	-43.0	-34.6	-15.6	-44.0	-14.6	+11.9	-6.2	+1.5	+12.9
Steps (reduced)		87 (87)	137 (31)	173 (67)	201 (95)	224 (12)	243 (31)	260 (48)	275 (63)	288 (76)	300 (88)	311 (99)

Approximation of harmonics in 106ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.60	-2.15	+2.95	+1.93	-6.16	+5.59	-4.98	+3.09	+1.65	+4.14	-3.62
	Relative (%)	+11.6	-15.6	+21.3	+13.9	-44.5	+40.4	-36.0	+22.3	+11.9	+30.0	-26.2
Steps (reduced)		321 (3)	330 (12)	339 (21)	347 (29)	354 (36)	362 (44)	368 (50)	375 (57)	381 (63)	387 (69)	392 (74)