70ed6

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70ed6

71ed6 →

Prime factorization	2 × 5 × 7
Step size	44.3136 ¢
Octave	27\70ed6 (1196.47 ¢)
Twelfth	43\70ed6 (1905.49 ¢)
Consistency limit	10
Distinct consistency limit	8

70 equal divisions of the 6th harmonic (abbreviated 70ed6) is a nonoctave tuning system that divides the interval of 6/1 into 70 equal parts of about 44.3⁠ ⁠¢ each. Each step represents a frequency ratio of 6^1/70, or the 70th root of 6.

70ed6 is very nearly identical to 27 EDO, but with the 6/1 rather than the 2/1 being just, which compresses the octave by 3.5316 ¢. The local zeta peak around 27 is located at 27.086614, which has a step size of 44.3023 ¢, making 70ed6 very close to optimal for 27edo.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	44.3	37/36
2	88.6	20/19
3	132.9	27/25
4	177.3	31/28
5	221.6	25/22, 33/29
6	265.9	7/6
7	310.2
8	354.5	27/22
9	398.8	34/27
10	443.1	22/17, 31/24
11	487.5
12	531.8	19/14, 34/25
13	576.1
14	620.4	10/7
15	664.7	22/15, 25/17
16	709
17	753.3	17/11
18	797.6	19/12, 27/17
19	842	13/8
20	886.3	5/3
21	930.6	12/7
22	974.9
23	1019.2	9/5
24	1063.5	24/13, 37/20
25	1107.8	19/10, 36/19
26	1152.2	35/18, 37/19
27	1196.5	2/1
28	1240.8
29	1285.1	21/10
30	1329.4	28/13
31	1373.7	31/14
32	1418	25/11, 34/15
33	1462.4
34	1506.7	31/13
35	1551	22/9, 27/11
36	1595.3
37	1639.6	31/12
38	1683.9	37/14
39	1728.2	19/7
40	1772.5
41	1816.9	20/7
42	1861.2
43	1905.5	3/1
44	1949.8	37/12
45	1994.1	19/6
46	2038.4	13/4
47	2082.7	10/3
48	2127.1
49	2171.4	7/2
50	2215.7	18/5
51	2260
52	2304.3	34/9
53	2348.6	31/8, 35/9
54	2392.9
55	2437.3
56	2481.6	21/5
57	2525.9
58	2570.2
59	2614.5
60	2658.8
61	2703.1
62	2747.4
63	2791.8
64	2836.1	36/7
65	2880.4	37/7
66	2924.7
67	2969
68	3013.3
69	3057.6
70	3102	6/1

Harmonics

Approximation of harmonics in 70ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-3.53	+3.53	-7.06	+5.45	+0.00	-0.99	-10.59	+7.06	+1.91	+14.16	-3.53
	Relative (%)	-8.0	+8.0	-15.9	+12.3	+0.0	-2.2	-23.9	+15.9	+4.3	+32.0	-8.0
Steps (reduced)		27 (27)	43 (43)	54 (54)	63 (63)	70 (0)	76 (6)	81 (11)	86 (16)	90 (20)	94 (24)	97 (27)

Approximation of prime harmonics in 70ed6

Harmonic		13	17	19	23	29	31	37	41	43	47	53
Error	Absolute (¢)	-9.16	+13.86	-1.44	-22.01	+19.82	-7.01	-3.12	-3.58	+2.59	-18.46	-4.89
	Relative (%)	-20.7	+31.3	-3.3	-49.7	+44.7	-15.8	-7.0	-8.1	+5.8	-41.7	-11.0
Steps (reduced)		100 (30)	111 (41)	115 (45)	122 (52)	132 (62)	134 (64)	141 (1)	145 (5)	147 (7)	150 (10)	155 (15)