67ed4

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67ed4

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Prime factorization	67 (prime)
Step size	35.8209¢
Octave	34\67ed4 (1217.91¢)
Twelfth	53\67ed4 (1898.51¢)
Consistency limit	1
Distinct consistency limit	1

67 equal divisions of the 4th harmonic (abbreviated 67ed4) is a nonoctave tuning system that divides the interval of 4/1 into 67 equal parts of about 35.8 ¢ each. Each step represents a frequency ratio of 4^1/67, or the 67th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	35.8
2	71.6	26/25
3	107.5	33/31
4	143.3	25/23
5	179.1
6	214.9	17/15, 26/23
7	250.7	15/13
8	286.6	13/11
9	322.4	35/29
10	358.2
11	394
12	429.9
13	465.7	17/13
14	501.5
15	537.3	15/11
16	573.1
17	609	27/19
18	644.8
19	680.6	34/23
20	716.4
21	752.2	17/11
22	788.1
23	823.9	29/18
24	859.7	23/14
25	895.5
26	931.3
27	967.2
28	1003	25/14
29	1038.8	31/17
30	1074.6	13/7
31	1110.4
32	1146.3	33/17
33	1182.1
34	1217.9
35	1253.7	31/15, 35/17
36	1289.6
37	1325.4
38	1361.2	11/5
39	1397
40	1432.8
41	1468.7	7/3
42	1504.5	31/13
43	1540.3
44	1576.1
45	1611.9	33/13
46	1647.8
47	1683.6
48	1719.4
49	1755.2
50	1791	31/11
51	1826.9
52	1862.7
53	1898.5	3/1
54	1934.3
55	1970.1
56	2006	35/11
57	2041.8
58	2077.6
59	2113.4
60	2149.3
61	2185.1
62	2220.9	18/5
63	2256.7
64	2292.5
65	2328.4	23/6
66	2364.2
67	2400

Harmonics

Approximation of harmonics in 67ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+17.9	-3.4	+0.0	+7.7	+14.5	-1.7	+17.9	-6.9	-10.2	+3.9	-3.4
	Relative (%)	+50.0	-9.6	+0.0	+21.5	+40.4	-4.6	+50.0	-19.2	-28.5	+10.9	-9.6
Steps (reduced)		34 (34)	53 (53)	67 (0)	78 (11)	87 (20)	94 (27)	101 (34)	106 (39)	111 (44)	116 (49)	120 (53)

Approximation of harmonics in 67ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.3	+16.2	+4.3	+0.0	+2.5	+11.0	-10.9	+7.7	-5.1	-14.0	+16.5
	Relative (%)	+3.5	+45.4	+11.9	+0.0	+7.0	+30.8	-30.6	+21.5	-14.3	-39.1	+46.1
Steps (reduced)		124 (57)	128 (61)	131 (64)	134 (0)	137 (3)	140 (6)	142 (8)	145 (11)	147 (13)	149 (15)	152 (18)