64edt

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64edt

65edt →

Prime factorization	26
Step size	29.718¢
Octave	40\64edt (1188.72¢) (→5\8edt)
Consistency limit	2
Distinct consistency limit	2

64 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 64edt or 64ed3), is a nonoctave tuning system that divides the interval of 3/1 into 64 equal parts of about 29.7⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/64, or the 64th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	29.7	20.3
2	59.4	40.6	30/29, 31/30
3	89.2	60.9
4	118.9	81.3	31/29
5	148.6	101.6
6	178.3	121.9	10/9
7	208	142.2	35/31
8	237.7	162.5	31/27
9	267.5	182.8	7/6
10	297.2	203.1
11	326.9	223.4	23/19, 35/29
12	356.6	243.8	27/22
13	386.3	264.1
14	416.1	284.4
15	445.8	304.7	22/17, 35/27
16	475.5	325	25/19, 29/22
17	505.2	345.3
18	534.9	365.6	15/11
19	564.6	385.9	18/13
20	594.4	406.3	31/22
21	624.1	426.6	33/23
22	653.8	446.9
23	683.5	467.2
24	713.2	487.5
25	743	507.8	20/13, 23/15
26	772.7	528.1
27	802.4	548.4	27/17, 35/22
28	832.1	568.8	21/13, 34/21
29	861.8	589.1
30	891.5	609.4
31	921.3	629.7	17/10, 29/17
32	951	650
33	980.7	670.3	30/17
34	1010.4	690.6
35	1040.1	710.9	31/17
36	1069.8	731.3	13/7
37	1099.6	751.6	17/9
38	1129.3	771.9
39	1159	792.2
40	1188.7	812.5
41	1218.4	832.8
42	1248.2	853.1	35/17
43	1277.9	873.4	23/11
44	1307.6	893.8
45	1337.3	914.1	13/6
46	1367	934.4	11/5
47	1396.7	954.7
48	1426.5	975
49	1456.2	995.3
50	1485.9	1015.6
51	1515.6	1035.9
52	1545.3	1056.3	22/9
53	1575.1	1076.6
54	1604.8	1096.9
55	1634.5	1117.2	18/7
56	1664.2	1137.5	34/13
57	1693.9	1157.8
58	1723.6	1178.1	27/10
59	1753.4	1198.4
60	1783.1	1218.8
61	1812.8	1239.1
62	1842.5	1259.4	29/10
63	1872.2	1279.7
64	1902	1300	3/1

Harmonics

Approximation of harmonics in 64edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.3	+0.0	+7.2	+7.2	-11.3	-10.7	-4.1	+0.0	-4.1	+9.2	+7.2
	Relative (%)	-38.0	+0.0	+24.1	+24.2	-38.0	-36.0	-13.9	+0.0	-13.8	+31.0	+24.1
Steps (reduced)		40 (40)	64 (0)	81 (17)	94 (30)	104 (40)	113 (49)	121 (57)	128 (0)	134 (6)	140 (12)	145 (17)

Approximation of harmonics in 64edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-12.5	+7.8	+7.2	+14.3	-1.5	-11.3	+14.0	+14.3	-10.7	-2.1	+10.1
	Relative (%)	-42.2	+26.1	+24.2	+48.2	-5.0	-38.0	+47.1	+48.3	-36.0	-7.0	+34.1
Steps (reduced)		149 (21)	154 (26)	158 (30)	162 (34)	165 (37)	168 (40)	172 (44)	175 (47)	177 (49)	180 (52)	183 (55)