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	Hekts	Approximate ratios
0	0	0	1/1
1	15.1	10.3
2	30.2	20.6
3	45.3	31	38/37, 39/38
4	60.4	41.3	30/29
5	75.5	51.6	47/45
6	90.6	61.9	39/37
7	105.7	72.2	50/47
8	120.8	82.5
9	135.9	92.9
10	150.9	103.2
11	166	113.5	11/10
12	181.1	123.8	10/9
13	196.2	134.1	37/33
14	211.3	144.4	35/31
15	226.4	154.8	49/43
16	241.5	165.1
17	256.6	175.4
18	271.7	185.7
19	286.8	196	46/39
20	301.9	206.3
21	317	216.7
22	332.1	227	23/19
23	347.2	237.3	11/9
24	362.3	247.6	37/30
25	377.4	257.9	41/33, 46/37, 51/41
26	392.5	268.3
27	407.6	278.6	19/15, 43/34
28	422.7	288.9	37/29
29	437.8	299.2
30	452.8	309.5	13/10
31	467.9	319.8	38/29
32	483	330.2	41/31
33	498.1	340.5
34	513.2	350.8	39/29
35	528.3	361.1
36	543.4	371.4
37	558.5	381.7	29/21
38	573.6	392.1	46/33
39	588.7	402.4
40	603.8	412.7
41	618.9	423	10/7
42	634	433.3	49/34
43	649.1	443.7
44	664.2	454
45	679.3	464.3
46	694.4	474.6
47	709.5	484.9
48	724.6	495.2	41/27
49	739.6	505.6	23/15
50	754.7	515.9	17/11
51	769.8	526.2
52	784.9	536.5
53	800	546.8	27/17, 46/29
54	815.1	557.1
55	830.2	567.5	21/13
56	845.3	577.8
57	860.4	588.1	51/31
58	875.5	598.4
59	890.6	608.7
60	905.7	619
61	920.8	629.4	46/27
62	935.9	639.7
63	951	650
64	966.1	660.3
65	981.2	670.6	37/21
66	996.3	681
67	1011.4	691.3
68	1026.5	701.6	38/21
69	1041.5	711.9	31/17
70	1056.6	722.2	35/19
71	1071.7	732.5	13/7
72	1086.8	742.9
73	1101.9	753.2	17/9
74	1117	763.5
75	1132.1	773.8
76	1147.2	784.1	33/17
77	1162.3	794.4	45/23
78	1177.4	804.8
79	1192.5	815.1
80	1207.6	825.4
81	1222.7	835.7
82	1237.8	846	47/23
83	1252.9	856.3
84	1268	866.7
85	1283.1	877	21/10
86	1298.2	887.3
87	1313.3	897.6
88	1328.3	907.9
89	1343.4	918.3	50/23
90	1358.5	928.6	46/21
91	1373.6	938.9
92	1388.7	949.2	29/13
93	1403.8	959.5
94	1418.9	969.8
95	1434	980.2
96	1449.1	990.5	30/13
97	1464.2	1000.8
98	1479.3	1011.1
99	1494.4	1021.4	45/19
100	1509.5	1031.7	43/18
101	1524.6	1042.1	41/17
102	1539.7	1052.4
103	1554.8	1062.7	27/11
104	1569.9	1073	47/19
105	1585	1083.3
106	1600.1	1093.7
107	1615.2	1104
108	1630.2	1114.3
109	1645.3	1124.6
110	1660.4	1134.9
111	1675.5	1145.2	50/19
112	1690.6	1155.6
113	1705.7	1165.9
114	1720.8	1176.2	27/10
115	1735.9	1186.5	30/11
116	1751	1196.8
117	1766.1	1207.1
118	1781.2	1217.5
119	1796.3	1227.8
120	1811.4	1238.1	37/13
121	1826.5	1248.4
122	1841.6	1258.7	29/10
123	1856.7	1269	38/13
124	1871.8	1279.4
125	1886.9	1289.7
126	1902	1300	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)