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	14
2	27.9
3	41.9	40/39, 41/40, 42/41, 43/42, 44/43
4	55.9	32/31
5	69.9
6	83.8	21/20, 43/41
7	97.8	18/17, 37/35
8	111.8
9	125.7	29/27, 43/40
10	139.7	13/12
11	153.7
12	167.6	43/39
13	181.6	10/9
14	195.6
15	209.6	44/39
16	223.5	33/29, 41/36
17	237.5	39/34
18	251.5	22/19
19	265.4	7/6
20	279.4	20/17
21	293.4
22	307.3	43/36
23	321.3
24	335.3	17/14, 40/33
25	349.3	11/9
26	363.2	37/30
27	377.2	41/33
28	391.2
29	405.1	24/19, 43/34
30	419.1	14/11
31	433.1	9/7
32	447	22/17, 35/27
33	461
34	475
35	489
36	502.9
37	516.9	31/23
38	530.9	19/14
39	544.8	26/19, 37/27
40	558.8	29/21, 40/29
41	572.8	32/23, 39/28
42	586.7
43	600.7	17/12, 41/29
44	614.7
45	628.7	23/16
46	642.6	29/20, 42/29
47	656.6	19/13
48	670.6	28/19
49	684.5	46/31
50	698.5
51	712.5
52	726.5
53	740.4	43/28
54	754.4	17/11
55	768.4
56	782.3	11/7
57	796.3	19/12
58	810.3
59	824.2	29/18
60	838.2	13/8
61	852.2	18/11
62	866.2	28/17, 33/20
63	880.1
64	894.1
65	908.1
66	922
67	936
68	950
69	963.9
70	977.9
71	991.9	39/22
72	1005.9	34/19
73	1019.8	9/5
74	1033.8	20/11
75	1047.8	11/6
76	1061.7	24/13
77	1075.7	41/22
78	1089.7
79	1103.6
80	1117.6	21/11, 40/21
81	1131.6
82	1145.6	31/16
83	1159.5	41/21, 43/22
84	1173.5
85	1187.5
86	1201.4	2/1
87	1215.4
88	1229.4
89	1243.3	39/19, 41/20
90	1257.3
91	1271.3
92	1285.3	21/10
93	1299.2	36/17
94	1313.2
95	1327.2	28/13, 43/20
96	1341.1
97	1355.1
98	1369.1
99	1383	20/9
100	1397
101	1411
102	1425	41/18
103	1438.9	39/17
104	1452.9	44/19
105	1466.9	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)