134edt

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134edt

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Prime factorization	2 × 67
Step size	14.1937¢
Octave	85\134edt (1206.46¢)
Consistency limit	2
Distinct consistency limit	2

134 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 134edt or 134ed3), is a nonoctave tuning system that divides the interval of 3/1 into 134 equal parts of about 14.2 ¢ each. Each step represents a frequency ratio of 3^1/134, or the 134th root of 3. 134edt is notable for being a close-to-optimal tuning of Mintra temperament in the no-twos 11-limit and supporting its extensions to primes 13 and 37.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.194
2	28.387
3	42.581	42/41
4	56.775	31/30
5	70.968
6	85.162	41/39
7	99.356	18/17
8	113.55	47/44
9	127.743	14/13
10	141.937	51/47
11	156.131	23/21
12	170.324	43/39
13	184.518
14	198.712	37/33, 46/41
15	212.905	43/38
16	227.099
17	241.293
18	255.486	22/19, 51/44
19	269.68
20	283.874
21	298.068
22	312.261
23	326.455
24	340.649
25	354.842	27/22
26	369.036	47/38
27	383.23
28	397.423	39/31
29	411.617
30	425.811
31	440.005
32	454.198	13/10
33	468.392	38/29
34	482.586	41/31
35	496.779
36	510.973	51/38
37	525.167	42/31
38	539.36	41/30
39	553.554
40	567.748	43/31
41	581.941	7/5
42	596.135
43	610.329
44	624.523	33/23, 43/30
45	638.716
46	652.91
47	667.104
48	681.297	43/29
49	695.491
50	709.685
51	723.878	41/27
52	738.072
53	752.266
54	766.459	14/9
55	780.653
56	794.847
57	809.041
58	823.234	37/23
59	837.428	47/29
60	851.622
61	865.815
62	880.009
63	894.203
64	908.396
65	922.59	46/27
66	936.784
67	950.978
68	965.171
69	979.365	37/21
70	993.559
71	1007.752
72	1021.946
73	1036.14
74	1050.333
75	1064.527
76	1078.721	41/22
77	1092.914
78	1107.108
79	1121.302
80	1135.496	27/14
81	1149.689
82	1163.883	49/25
83	1178.077
84	1192.27
85	1206.464
86	1220.658
87	1234.851
88	1249.045
89	1263.239
90	1277.432	23/11
91	1291.626
92	1305.82
93	1320.014	15/7
94	1334.207
95	1348.401
96	1362.595
97	1376.788	31/14
98	1390.982	38/17
99	1405.176
100	1419.369
101	1433.563
102	1447.757	30/13
103	1461.95
104	1476.144
105	1490.338
106	1504.532	31/13
107	1518.725
108	1532.919
109	1547.113	22/9
110	1561.306
111	1575.5
112	1589.694
113	1603.887
114	1618.081
115	1632.275
116	1646.469	44/17
117	1660.662	47/18
118	1674.856	50/19
119	1689.05
120	1703.243
121	1717.437
122	1731.631
123	1745.824
124	1760.018	47/17
125	1774.212	39/14
126	1788.405
127	1802.599	17/6
128	1816.793
129	1830.987
130	1845.18
131	1859.374	41/14
132	1873.568
133	1887.761
134	1901.955	3/1

Harmonics

Approximation of harmonics in 134edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.46	+0.00	-1.27	-4.35	+6.46	-4.92	+5.20	+0.00	+2.11	-6.76	-1.27
	Relative (%)	+45.5	+0.0	-8.9	-30.6	+45.5	-34.7	+36.6	+0.0	+14.9	-47.6	-8.9
Steps (reduced)		85 (85)	134 (0)	169 (35)	196 (62)	219 (85)	237 (103)	254 (120)	268 (0)	281 (13)	292 (24)	303 (35)

Approximation of harmonics in 134edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.10	+1.54	-4.35	-2.53	+6.06	+6.46	-1.98	-5.62	-4.92	-0.30	-6.28
	Relative (%)	+14.8	+10.9	-30.6	-17.8	+42.7	+45.5	-13.9	-39.6	-34.7	-2.1	-44.3
Steps (reduced)		313 (45)	322 (54)	330 (62)	338 (70)	346 (78)	353 (85)	359 (91)	365 (97)	371 (103)	377 (109)	382 (114)