126edt

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126edt

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Prime factorization	2 × 32 × 7
Step size	15.0949¢
Octave	79\126edt (1192.5¢)
Consistency limit	2
Distinct consistency limit	2

126 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 126edt or 126ed3), is a nonoctave tuning system that divides the interval of 3/1 into 126 equal parts of about 15.1 ¢ each. Each step represents a frequency ratio of 3^1/126, or the 126th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	15.095
2	30.19
3	45.285	38/37, 39/38
4	60.38	30/29
5	75.474	47/45
6	90.569	39/37
7	105.664	50/47
8	120.759
9	135.854
10	150.949
11	166.044	11/10
12	181.139	10/9
13	196.233	37/33
14	211.328	35/31
15	226.423	49/43
16	241.518
17	256.613
18	271.708
19	286.803	46/39
20	301.898
21	316.993
22	332.087	23/19
23	347.182	11/9
24	362.277	37/30
25	377.372	41/33, 46/37, 51/41
26	392.467
27	407.562	19/15, 43/34
28	422.657	37/29
29	437.752
30	452.846	13/10
31	467.941	38/29
32	483.036	41/31
33	498.131
34	513.226	39/29
35	528.321
36	543.416
37	558.511	29/21
38	573.605	46/33
39	588.7
40	603.795
41	618.89	10/7
42	633.985	49/34
43	649.08
44	664.175
45	679.27
46	694.365
47	709.459
48	724.554	41/27
49	739.649	23/15
50	754.744	17/11
51	769.839
52	784.934
53	800.029	27/17, 46/29
54	815.124
55	830.218	21/13
56	845.313
57	860.408	51/31
58	875.503
59	890.598
60	905.693
61	920.788	46/27
62	935.883
63	950.978
64	966.072
65	981.167	37/21
66	996.262
67	1011.357
68	1026.452	38/21
69	1041.547	31/17
70	1056.642	35/19
71	1071.737	13/7
72	1086.831
73	1101.926	17/9
74	1117.021
75	1132.116
76	1147.211	33/17
77	1162.306	45/23
78	1177.401
79	1192.496
80	1207.59
81	1222.685
82	1237.78	47/23
83	1252.875
84	1267.97
85	1283.065	21/10
86	1298.16
87	1313.255
88	1328.35
89	1343.444	50/23
90	1358.539	46/21
91	1373.634
92	1388.729	29/13
93	1403.824
94	1418.919
95	1434.014
96	1449.109	30/13
97	1464.203
98	1479.298
99	1494.393	45/19
100	1509.488	43/18
101	1524.583	41/17
102	1539.678
103	1554.773	27/11
104	1569.868	47/19
105	1584.963
106	1600.057
107	1615.152
108	1630.247
109	1645.342
110	1660.437
111	1675.532	50/19
112	1690.627
113	1705.722
114	1720.816	27/10
115	1735.911	30/11
116	1751.006
117	1766.101
118	1781.196
119	1796.291
120	1811.386	37/13
121	1826.481
122	1841.575	29/10
123	1856.67	38/13
124	1871.765
125	1886.86
126	1901.955	3/1

Harmonics

Approximation of harmonics in 126edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-7.50	+0.00	+0.09	+6.24	-7.50	-2.67	-7.42	+0.00	-1.27	-0.23	+0.09
	Relative (%)	-49.7	+0.0	+0.6	+41.3	-49.7	-17.7	-49.1	+0.0	-8.4	-1.5	+0.6
Steps (reduced)		79 (79)	126 (0)	159 (33)	185 (59)	205 (79)	223 (97)	238 (112)	252 (0)	264 (12)	275 (23)	285 (33)

Approximation of harmonics in 126edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+4.92	+6.24	+0.17	+0.88	-7.50	+4.56	+6.33	-2.67	+7.36	+5.88
	Relative (%)	-17.4	+32.6	+41.3	+1.1	+5.8	-49.7	+30.2	+41.9	-17.7	+48.8	+39.0
Steps (reduced)		294 (42)	303 (51)	311 (59)	318 (66)	325 (73)	331 (79)	338 (86)	344 (92)	349 (97)	355 (103)	360 (108)