134edt

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134edt

135edt →

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	Hekts	Approximate ratios
0	0	0	1/1
1	14.2	9.7
2	28.4	19.4
3	42.6	29.1	42/41
4	56.8	38.8	31/30
5	71	48.5
6	85.2	58.2	41/39
7	99.4	67.9	18/17
8	113.5	77.6	47/44
9	127.7	87.3	14/13
10	141.9	97	51/47
11	156.1	106.7	23/21
12	170.3	116.4	43/39
13	184.5	126.1
14	198.7	135.8	37/33, 46/41
15	212.9	145.5	43/38
16	227.1	155.2
17	241.3	164.9
18	255.5	174.6	22/19, 51/44
19	269.7	184.3
20	283.9	194
21	298.1	203.7
22	312.3	213.4
23	326.5	223.1
24	340.6	232.8
25	354.8	242.5	27/22
26	369	252.2	47/38
27	383.2	261.9
28	397.4	271.6	39/31
29	411.6	281.3
30	425.8	291
31	440	300.7
32	454.2	310.4	13/10
33	468.4	320.1	38/29
34	482.6	329.9	41/31
35	496.8	339.6
36	511	349.3	51/38
37	525.2	359	42/31
38	539.4	368.7	41/30
39	553.6	378.4
40	567.7	388.1	43/31
41	581.9	397.8	7/5
42	596.1	407.5
43	610.3	417.2
44	624.5	426.9	33/23, 43/30
45	638.7	436.6
46	652.9	446.3
47	667.1	456
48	681.3	465.7	43/29
49	695.5	475.4
50	709.7	485.1
51	723.9	494.8	41/27
52	738.1	504.5
53	752.3	514.2
54	766.5	523.9	14/9
55	780.7	533.6
56	794.8	543.3
57	809	553
58	823.2	562.7	37/23
59	837.4	572.4	47/29
60	851.6	582.1
61	865.8	591.8
62	880	601.5
63	894.2	611.2
64	908.4	620.9
65	922.6	630.6	46/27
66	936.8	640.3
67	951	650
68	965.2	659.7
69	979.4	669.4	37/21
70	993.6	679.1
71	1007.8	688.8
72	1021.9	698.5
73	1036.1	708.2
74	1050.3	717.9
75	1064.5	727.6
76	1078.7	737.3	41/22
77	1092.9	747
78	1107.1	756.7
79	1121.3	766.4
80	1135.5	776.1	27/14
81	1149.7	785.8
82	1163.9	795.5	49/25
83	1178.1	805.2
84	1192.3	814.9
85	1206.5	824.6
86	1220.7	834.3
87	1234.9	844
88	1249	853.7
89	1263.2	863.4
90	1277.4	873.1	23/11
91	1291.6	882.8
92	1305.8	892.5
93	1320	902.2	15/7
94	1334.2	911.9
95	1348.4	921.6
96	1362.6	931.3
97	1376.8	941	31/14
98	1391	950.7	38/17
99	1405.2	960.4
100	1419.4	970.1
101	1433.6	979.9
102	1447.8	989.6	30/13
103	1462	999.3
104	1476.1	1009
105	1490.3	1018.7
106	1504.5	1028.4	31/13
107	1518.7	1038.1
108	1532.9	1047.8
109	1547.1	1057.5	22/9
110	1561.3	1067.2
111	1575.5	1076.9
112	1589.7	1086.6
113	1603.9	1096.3
114	1618.1	1106
115	1632.3	1115.7
116	1646.5	1125.4	44/17
117	1660.7	1135.1	47/18
118	1674.9	1144.8	50/19
119	1689	1154.5
120	1703.2	1164.2
121	1717.4	1173.9
122	1731.6	1183.6
123	1745.8	1193.3
124	1760	1203	47/17
125	1774.2	1212.7	39/14
126	1788.4	1222.4
127	1802.6	1232.1	17/6
128	1816.8	1241.8
129	1831	1251.5
130	1845.2	1261.2
131	1859.4	1270.9	41/14
132	1873.6	1280.6
133	1887.8	1290.3
134	1902	1300	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)