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	22.92
2	45.84
3	68.76	27/26
4	91.679	19/18, 20/19
5	114.599	31/29
6	137.519
7	160.439	23/21, 34/31
8	183.359	10/9
9	206.279
10	229.199
11	252.118	22/19
12	275.038	27/23, 34/29
13	297.958
14	320.878
15	343.798	11/9
16	366.718	21/17, 26/21
17	389.638
18	412.557	33/26
19	435.477	9/7
20	458.397	30/23
21	481.317	29/22
22	504.237
23	527.157	19/14, 23/17
24	550.077
25	572.996
26	595.916	31/22
27	618.836	10/7
28	641.756	29/20
29	664.676
30	687.596
31	710.516
32	733.435	26/17, 29/19
33	756.355	17/11, 31/20
34	779.275	11/7
35	802.195	27/17
36	825.115	29/18
37	848.035	31/19
38	870.955	33/20
39	893.874
40	916.794	17/10
41	939.714	31/18
42	962.634
43	985.554	23/13, 30/17
44	1008.474	34/19
45	1031.394	20/11
46	1054.313
47	1077.233
48	1100.153	17/9
49	1123.073	21/11
50	1145.993	33/17
51	1168.913
52	1191.833
53	1214.752
54	1237.672
55	1260.592	29/14
56	1283.512	21/10
57	1306.432
58	1329.352
59	1352.272
60	1375.191	31/14
61	1398.111
62	1421.031
63	1443.951	23/10, 30/13
64	1466.871	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)