67edt

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67edt

68edt →

Prime factorization	67 (prime)
Step size	28.3874¢
Octave	42\67edt (1192.27¢)
Consistency limit	2
Distinct consistency limit	2

67EDT is the equal division of the third harmonic into 67 parts of 28.3874 cents each, corresponding to 42.2723 edo. It is related to the regular temperament which tempers out 2100875/2097152 and |-36 45 -14 -1> in the 7-limit, which is supported by 296, 465, 761, and 1057 EDOs among others.

Related regular temperaments

296&465 temperament

7-limit

Commas: 2100875/2097152, |-36 45 -14 -1>

POTE generator: ~64/63 = 28.3825

Mapping: [<1 0 -3 6|, <0 67 225 -135|]

EDOs: 296, 465, 761, 1057

11-limit

Commas: 46656/46585, 2100875/2097152, 21437500/21434787

POTE generator: ~64/63 = 28.3824

Mapping: [<1 0 -3 6 1|, <0 67 225 -135 104|]

EDOs: 296, 465, 761, 1057

13-limit

Commas: 1575/1573, 46656/46585, 199927/199650, 216513/216320

POTE generator: ~64/63 = 28.3825

Mapping: [<1 0 -3 6 1 -2|, <0 67 225 -135 104 241|]

EDOs: 296, 465, 761, 1057

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	28.4
2	56.8	30/29, 31/30
3	85.2
4	113.5	31/29
5	141.9	13/12, 25/23
6	170.3	21/19
7	198.7	28/25
8	227.1	33/29
9	255.5	29/25, 36/31
10	283.9	33/28
11	312.3	6/5
12	340.6	28/23
13	369	21/17, 31/25
14	397.4	29/23, 34/27
15	425.8	23/18
16	454.2	13/10
17	482.6	33/25
18	511
19	539.4	15/11
20	567.7	25/18
21	596.1	31/22
22	624.5	33/23
23	652.9
24	681.3
25	709.7
26	738.1	23/15
27	766.5	14/9
28	794.8
29	823.2	29/18
30	851.6	18/11
31	880
32	908.4	22/13
33	936.8
34	965.2
35	993.6
36	1021.9
37	1050.3	11/6
38	1078.7	28/15
39	1107.1
40	1135.5	25/13, 27/14
41	1163.9
42	1192.3
43	1220.7
44	1249	35/17
45	1277.4	23/11
46	1305.8
47	1334.2
48	1362.6	11/5
49	1391	29/13
50	1419.4	25/11, 34/15
51	1447.8	30/13
52	1476.1
53	1504.5	31/13
54	1532.9	17/7
55	1561.3
56	1589.7	5/2
57	1618.1	28/11
58	1646.5	31/12
59	1674.9	29/11
60	1703.2
61	1731.6	19/7
62	1760	36/13
63	1788.4
64	1816.8
65	1845.2	29/10
66	1873.6
67	1902	3/1

Harmonics

Approximation of harmonics in 67edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-7.7	+0.0	+12.9	-4.3	-7.7	+9.3	+5.2	+0.0	-12.1	-6.8	+12.9
	Relative (%)	-27.2	+0.0	+45.5	-15.3	-27.2	+32.7	+18.3	+0.0	-42.6	-23.8	+45.5
Steps (reduced)		42 (42)	67 (0)	85 (18)	98 (31)	109 (42)	119 (52)	127 (60)	134 (0)	140 (6)	146 (12)	152 (18)

Approximation of harmonics in 67edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-12.1	+1.5	-4.3	-2.5	+6.1	-7.7	+12.2	+8.6	+9.3	+13.9	-6.3
	Relative (%)	-42.6	+5.4	-15.3	-8.9	+21.4	-27.2	+43.0	+30.2	+32.7	+49.0	-22.1
Steps (reduced)		156 (22)	161 (27)	165 (31)	169 (35)	173 (39)	176 (42)	180 (46)	183 (49)	186 (52)	189 (55)	191 (57)