64ed7/3

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64ed7/3

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Prime factorization	26
Step size	22.9199¢
Octave	52\64ed7/3 (1191.83¢) (→13\16ed7/3)
Twelfth	83\64ed7/3 (1902.35¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	3

64 equal divisions of 7/3 (abbreviated 64ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 64 equal parts of about 22.9⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/64, or the 64th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	22.9
2	45.8
3	68.8	27/26
4	91.7	19/18, 20/19
5	114.6	31/29
6	137.5
7	160.4	23/21, 34/31
8	183.4	10/9
9	206.3
10	229.2
11	252.1	22/19
12	275	27/23, 34/29
13	298
14	320.9
15	343.8	11/9
16	366.7	21/17, 26/21
17	389.6
18	412.6	33/26
19	435.5	9/7
20	458.4	30/23
21	481.3	29/22
22	504.2
23	527.2	19/14, 23/17
24	550.1
25	573
26	595.9	31/22
27	618.8	10/7
28	641.8	29/20
29	664.7
30	687.6
31	710.5
32	733.4	26/17, 29/19
33	756.4	17/11, 31/20
34	779.3	11/7
35	802.2	27/17
36	825.1	29/18
37	848	31/19
38	871	33/20
39	893.9
40	916.8	17/10
41	939.7	31/18
42	962.6
43	985.6	23/13, 30/17
44	1008.5	34/19
45	1031.4	20/11
46	1054.3
47	1077.2
48	1100.2	17/9
49	1123.1	21/11
50	1146	33/17
51	1168.9
52	1191.8
53	1214.8
54	1237.7
55	1260.6	29/14
56	1283.5	21/10
57	1306.4
58	1329.4
59	1352.3
60	1375.2	31/14
61	1398.1
62	1421
63	1444	23/10, 30/13
64	1466.9	7/3

Harmonics

Approximation of harmonics in 64ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-8.2	+0.4	+6.6	+9.9	-7.8	+0.4	-1.6	+0.8	+1.7	-2.8	+7.0
	Relative (%)	-35.6	+1.7	+28.7	+43.2	-33.9	+1.7	-6.9	+3.4	+7.6	-12.3	+30.4
Steps (reduced)		52 (52)	83 (19)	105 (41)	122 (58)	135 (7)	147 (19)	157 (29)	166 (38)	174 (46)	181 (53)	188 (60)

Approximation of harmonics in 64ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.9	-7.8	+10.3	-9.7	-0.1	-7.4	-9.3	-6.4	+0.8	-11.0	+3.7
	Relative (%)	+25.8	-33.9	+44.9	-42.5	-0.5	-32.2	-40.6	-28.0	+3.4	-48.0	+16.3
Steps (reduced)		194 (2)	199 (7)	205 (13)	209 (17)	214 (22)	218 (26)	222 (30)	226 (34)	230 (38)	233 (41)	237 (45)