105ed7/3

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105ed7/3

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Prime factorization	3 × 5 × 7
Step size	13.9702¢
Octave	86\105ed7/3 (1201.44¢)
Twelfth	136\105ed7/3 (1899.95¢)
Consistency limit	4
Distinct consistency limit	4

105 equal divisions of 7/3 (abbreviated 105ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 105 equal parts of about 14 ¢ each. Each step represents a frequency ratio of (7/3)^1/105, or the 105th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	13.97
2	27.94
3	41.911	40/39, 41/40, 42/41, 43/42, 44/43
4	55.881	32/31
5	69.851
6	83.821	21/20, 43/41
7	97.791	18/17, 37/35
8	111.762
9	125.732	29/27, 43/40
10	139.702	13/12
11	153.672
12	167.642	43/39
13	181.613	10/9
14	195.583
15	209.553	44/39
16	223.523	33/29, 41/36
17	237.493	39/34
18	251.464	22/19
19	265.434	7/6
20	279.404	20/17
21	293.374
22	307.344	43/36
23	321.315
24	335.285	17/14, 40/33
25	349.255	11/9
26	363.225	37/30
27	377.195	41/33
28	391.166
29	405.136	24/19, 43/34
30	419.106	14/11
31	433.076	9/7
32	447.046	22/17, 35/27
33	461.017
34	474.987
35	488.957
36	502.927
37	516.897	31/23
38	530.868	19/14
39	544.838	26/19, 37/27
40	558.808	29/21, 40/29
41	572.778	32/23, 39/28
42	586.748
43	600.719	17/12, 41/29
44	614.689
45	628.659	23/16
46	642.629	29/20, 42/29
47	656.599	19/13
48	670.57	28/19
49	684.54	46/31
50	698.51
51	712.48
52	726.45
53	740.421	43/28
54	754.391	17/11
55	768.361
56	782.331	11/7
57	796.301	19/12
58	810.272
59	824.242	29/18
60	838.212	13/8
61	852.182	18/11
62	866.152	28/17, 33/20
63	880.123
64	894.093
65	908.063
66	922.033
67	936.003
68	949.974
69	963.944
70	977.914
71	991.884	39/22
72	1005.854	34/19
73	1019.825	9/5
74	1033.795	20/11
75	1047.765	11/6
76	1061.735	24/13
77	1075.705	41/22
78	1089.676
79	1103.646
80	1117.616	21/11, 40/21
81	1131.586
82	1145.556	31/16
83	1159.527	41/21, 43/22
84	1173.497
85	1187.467
86	1201.437	2/1
87	1215.407
88	1229.378
89	1243.348	39/19, 41/20
90	1257.318
91	1271.288
92	1285.258	21/10
93	1299.229	36/17
94	1313.199
95	1327.169	28/13, 43/20
96	1341.139
97	1355.109
98	1369.08
99	1383.05	20/9
100	1397.02
101	1410.99
102	1424.96	41/18
103	1438.931	39/17
104	1452.901	44/19
105	1466.871	7/3

Harmonics

Approximation of harmonics in 105ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.44	-2.01	+2.87	-6.24	-0.57	-2.01	+4.31	-4.02	-4.81	-2.17	+0.87
	Relative (%)	+10.3	-14.4	+20.6	-44.7	-4.1	-14.4	+30.9	-28.7	-34.4	-15.5	+6.2
Steps (reduced)		86 (86)	136 (31)	172 (67)	199 (94)	222 (12)	241 (31)	258 (48)	272 (62)	285 (75)	297 (87)	308 (98)

Approximation of harmonics in 105ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.00	-0.57	+5.72	+5.75	-1.42	-2.58	+1.61	-3.37	-4.02	-0.73	+6.13
	Relative (%)	+14.3	-4.1	+40.9	+41.1	-10.1	-18.5	+11.5	-24.1	-28.7	-5.2	+43.9
Steps (reduced)		318 (3)	327 (12)	336 (21)	344 (29)	351 (36)	358 (43)	365 (50)	371 (56)	377 (62)	383 (68)	389 (74)