67ed7/3

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Prime factorization	67 (prime)
Step size	21.8936¢
Octave	55\67ed7/3 (1204.15¢)
Twelfth	87\67ed7/3 (1904.74¢)
Consistency limit	4
Distinct consistency limit	4

67 equal divisions of 7/3 (abbreviated 67ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 67 equal parts of about 21.9 ¢ each. Each step represents a frequency ratio of (7/3)^1/67, or the 67th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	21.894
2	43.787
3	65.681	27/26, 28/27
4	87.574	20/19, 21/20
5	109.468	33/31
6	131.362	14/13
7	153.255	12/11
8	175.149	21/19, 31/28
9	197.042
10	218.936	17/15
11	240.83	23/20, 31/27
12	262.723	36/31
13	284.617	20/17, 33/28
14	306.51	31/26
15	328.404	23/19, 35/29
16	350.298	11/9
17	372.191	26/21
18	394.085
19	415.978	14/11, 33/26
20	437.872	9/7
21	459.766	30/23
22	481.659
23	503.553
24	525.446	19/14, 23/17
25	547.34
26	569.233
27	591.127	31/22
28	613.021
29	634.914	13/9
30	656.808	19/13
31	678.701	34/23
32	700.595	3/2
33	722.489
34	744.382	20/13
35	766.276	14/9
36	788.169	30/19
37	810.063
38	831.957	21/13, 34/21
39	853.85	18/11
40	875.744
41	897.637
42	919.531	17/10
43	941.425	31/18
44	963.318
45	985.212	23/13, 30/17
46	1007.105	34/19
47	1028.999
48	1050.893	11/6
49	1072.786	13/7
50	1094.68
51	1116.573	21/11
52	1138.467	27/14, 29/15
53	1160.361
54	1182.254
55	1204.148
56	1226.041
57	1247.935	35/17
58	1269.829
59	1291.722	19/9
60	1313.616
61	1335.509	13/6
62	1357.403
63	1379.297	20/9, 31/14
64	1401.19	9/4
65	1423.084
66	1444.977	23/10, 30/13
67	1466.871	7/3

Harmonics

Approximation of harmonics in 67ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.15	+2.79	+8.30	-5.83	+6.94	+2.79	-9.45	+5.58	-1.68	+8.47	-10.81
	Relative (%)	+18.9	+12.7	+37.9	-26.6	+31.7	+12.7	-43.2	+25.5	-7.7	+38.7	-49.4
Steps (reduced)		55 (55)	87 (20)	110 (43)	127 (60)	142 (8)	154 (20)	164 (30)	174 (40)	182 (48)	190 (56)	196 (62)

Approximation of harmonics in 67ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.87	+6.94	-3.04	-5.30	-0.79	+9.72	+3.69	+2.47	+5.58	-9.28	+1.34
	Relative (%)	+17.7	+31.7	-13.9	-24.2	-3.6	+44.4	+16.9	+11.3	+25.5	-42.4	+6.1
Steps (reduced)		203 (2)	209 (8)	214 (13)	219 (18)	224 (23)	229 (28)	233 (32)	237 (36)	241 (40)	244 (43)	248 (47)