106ed7/3

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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	13.838
2	27.677
3	41.515	41/40, 44/43
4	55.354
5	69.192
6	83.03	43/41
7	96.869	18/17
8	110.707
9	124.546	43/40, 44/41
10	138.384	13/12
11	152.222	12/11
12	166.061	11/10
13	179.899	41/37
14	193.738	19/17
15	207.576
16	221.414	33/29
17	235.253	39/34
18	249.091
19	262.93
20	276.768	34/29
21	290.607	13/11
22	304.445	31/26, 37/31
23	318.283
24	332.122	23/19
25	345.96
26	359.799
27	373.637	36/29
28	387.475
29	401.314	29/23
30	415.152
31	428.991
32	442.829	31/24, 40/31
33	456.667
34	470.506
35	484.344	37/28, 41/31
36	498.183
37	512.021	39/29
38	525.859
39	539.698
40	553.536
41	567.375	25/18, 43/31
42	581.213	7/5
43	595.051	31/22
44	608.89	37/26
45	622.728	33/23
46	636.567
47	650.405
48	664.243
49	678.082	34/23
50	691.92
51	705.759
52	719.597
53	733.435	29/19
54	747.274	20/13, 37/24
55	761.112
56	774.951	36/23
57	788.789	30/19, 41/26
58	802.627
59	816.466
60	830.304
61	844.143
62	857.981	23/14
63	871.82	43/26
64	885.658	5/3
65	899.496	37/22, 42/25
66	913.335	39/23
67	927.173	41/24
68	941.012
69	954.85	33/19
70	968.688
71	982.527	30/17
72	996.365
73	1010.204	43/24
74	1024.042
75	1037.88
76	1051.719
77	1065.557	37/20
78	1079.396	41/22
79	1093.234
80	1107.072	36/19
81	1120.911
82	1134.749
83	1148.588	33/17
84	1162.426	43/22
85	1176.264
86	1190.103
87	1203.941
88	1217.78
89	1231.618
90	1245.456	39/19
91	1259.295	29/14
92	1273.133
93	1286.972
94	1300.81	36/17
95	1314.648
96	1328.487	28/13
97	1342.325
98	1356.164
99	1370.002
100	1383.84
101	1397.679
102	1411.517
103	1425.356
104	1439.194	39/17
105	1453.033
106	1466.871	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)