User:MisterShafXen/65ed8

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65ed8

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Prime factorization	5 × 13
Step size	55.3846 ¢
Octave	22\65ed8 (1218.46 ¢)
Twelfth	34\65ed8 (1883.08 ¢)
Consistency limit	2
Distinct consistency limit	2

65 equal divisions of the 8th harmonic (abbreviated 65ed8) is a nonoctave tuning system that divides the interval of 8/1 into 65 equal parts of about 55.4 ¢ each. Each step represents a frequency ratio of 8^1/65, or the 65th root of 8.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	55.4	30/29, 31/30
2	110.8	33/31
3	166.2	11/10
4	221.5	33/29
5	276.9
6	332.3	17/14, 23/19
7	387.7
8	443.1	22/17
9	498.5
10	553.8
11	609.2
12	664.6
13	720
14	775.4	36/23
15	830.8	21/13
16	886.2	5/3
17	941.5	31/18
18	996.9
19	1052.3	11/6
20	1107.7	19/10, 36/19
21	1163.1
22	1218.5
23	1273.8	23/11
24	1329.2
25	1384.6
26	1440	23/10
27	1495.4
28	1550.8
29	1606.2
30	1661.5
31	1716.9	35/13
32	1772.3	25/9
33	1827.7
34	1883.1
35	1938.5
36	1993.8	19/6
37	2049.2	36/11
38	2104.6
39	2160
40	2215.4	18/5
41	2270.8	26/7
42	2326.2	23/6
43	2381.5
44	2436.9
45	2492.3
46	2547.7
47	2603.1
48	2658.5
49	2713.8
50	2769.2
51	2824.6
52	2880
53	2935.4
54	2990.8
55	3046.2	29/5
56	3101.5	6/1
57	3156.9	31/5
58	3212.3
59	3267.7	33/5
60	3323.1
61	3378.5
62	3433.8
63	3489.2
64	3544.6
65	3600

Harmonics

Approximation of harmonics in 65ed8

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+18.5	-18.9	-18.5	-17.1	-0.4	+9.6	+0.0	+17.6	+1.4	+2.5	+18.0
	Relative (%)	+33.3	-34.1	-33.3	-30.8	-0.8	+17.4	+0.0	+31.8	+2.5	+4.6	+32.6
Steps (reduced)		22 (22)	34 (34)	43 (43)	50 (50)	56 (56)	61 (61)	65 (0)	69 (4)	72 (7)	75 (10)	78 (13)