66edt

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66edt

67edt →

Prime factorization	2 × 3 × 11
Step size	28.8175¢
Octave	42\66edt (1210.34¢) (→7\11edt)
Consistency limit	2
Distinct consistency limit	2

66 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 66edt or 66ed3), is a nonoctave tuning system that divides the interval of 3/1 into 66 equal parts of about 28.8⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/66, or the 66th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	28.8	19.7
2	57.6	39.4
3	86.5	59.1
4	115.3	78.8	31/29
5	144.1	98.5
6	172.9	118.2	21/19
7	201.7	137.9
8	230.5	157.6
9	259.4	177.3
10	288.2	197	13/11
11	317	216.7	6/5
12	345.8	236.4	11/9
13	374.6	256.1
14	403.4	275.8	29/23
15	432.3	295.5	9/7
16	461.1	315.2	17/13
17	489.9	334.8
18	518.7	354.5	31/23
19	547.5	374.2
20	576.4	393.9
21	605.2	413.6	27/19
22	634	433.3	13/9, 36/25
23	662.8	453	22/15
24	691.6	472.7
25	720.4	492.4
26	749.3	512.1
27	778.1	531.8
28	806.9	551.5	35/22
29	835.7	571.2	34/21
30	864.5	590.9
31	893.3	610.6
32	922.2	630.3	29/17
33	951	650	26/15
34	979.8	669.7
35	1008.6	689.4	34/19
36	1037.4	709.1	31/17
37	1066.2	728.8
38	1095.1	748.5
39	1123.9	768.2
40	1152.7	787.9	35/18
41	1181.5	807.6
42	1210.3	827.3
43	1239.2	847
44	1268	866.7	25/12, 27/13
45	1296.8	886.4	19/9
46	1325.6	906.1
47	1354.4	925.8
48	1383.2	945.5
49	1412.1	965.2
50	1440.9	984.8
51	1469.7	1004.5	7/3
52	1498.5	1024.2
53	1527.3	1043.9
54	1556.1	1063.6	27/11
55	1585	1083.3	5/2
56	1613.8	1103	33/13
57	1642.6	1122.7
58	1671.4	1142.4
59	1700.2	1162.1
60	1729.1	1181.8	19/7
61	1757.9	1201.5
62	1786.7	1221.2
63	1815.5	1240.9
64	1844.3	1260.6
65	1873.1	1280.3
66	1902	1300	3/1

Harmonics

Approximation of harmonics in 66edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+10.3	+0.0	-8.1	+9.0	+10.3	+2.8	+2.2	+0.0	-9.5	-1.6	-8.1
	Relative (%)	+35.9	+0.0	-28.3	+31.2	+35.9	+9.8	+7.6	+0.0	-33.0	-5.5	-28.3
Steps (reduced)		42 (42)	66 (0)	83 (17)	97 (31)	108 (42)	117 (51)	125 (59)	132 (0)	138 (6)	144 (12)	149 (17)

Approximation of harmonics in 66edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	+13.2	+9.0	+12.5	-6.0	+10.3	+3.2	+0.8	+2.8	+8.7	-10.6
	Relative (%)	-9.1	+45.7	+31.2	+43.5	-20.8	+35.9	+11.1	+2.9	+9.8	+30.3	-36.7
Steps (reduced)		154 (22)	159 (27)	163 (31)	167 (35)	170 (38)	174 (42)	177 (45)	180 (48)	183 (51)	186 (54)	188 (56)