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	28.387
2	56.775	30/29, 31/30
3	85.162
4	113.55	31/29
5	141.937	13/12, 25/23
6	170.324	21/19
7	198.712	28/25
8	227.099	33/29
9	255.486	29/25, 36/31
10	283.874	33/28
11	312.261	6/5
12	340.649	28/23
13	369.036	21/17, 31/25
14	397.423	29/23, 34/27
15	425.811	23/18
16	454.198	13/10
17	482.586	33/25
18	510.973
19	539.36	15/11
20	567.748	25/18
21	596.135	31/22
22	624.523	33/23
23	652.91
24	681.297
25	709.685
26	738.072	23/15
27	766.459	14/9
28	794.847
29	823.234	29/18
30	851.622	18/11
31	880.009
32	908.396	22/13
33	936.784
34	965.171
35	993.559
36	1021.946
37	1050.333	11/6
38	1078.721	28/15
39	1107.108
40	1135.496	25/13, 27/14
41	1163.883
42	1192.27
43	1220.658
44	1249.045	35/17
45	1277.432	23/11
46	1305.82
47	1334.207
48	1362.595	11/5
49	1390.982	29/13
50	1419.369	25/11, 34/15
51	1447.757	30/13
52	1476.144
53	1504.532	31/13
54	1532.919	17/7
55	1561.306
56	1589.694	5/2
57	1618.081	28/11
58	1646.469	31/12
59	1674.856	29/11
60	1703.243
61	1731.631	19/7
62	1760.018	36/13
63	1788.405
64	1816.793
65	1845.18	29/10
66	1873.568
67	1901.955	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)