120edt

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120edt

121edt →

Prime factorization	23 × 3 × 5
Step size	15.8496¢
Octave	76\120edt (1204.57¢) (→19\30edt)
Consistency limit	2
Distinct consistency limit	2
Special properties	Highly composite

120 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 120edt or 120ed3), is a nonoctave tuning system that divides the interval of 3/1 into 120 equal parts of about 15.8 ¢ each. Each step represents a frequency ratio of 3^1/120, or the 120th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.85
2	31.699
3	47.549	36/35
4	63.399	27/26
5	79.248	22/21, 45/43
6	95.098	19/18
7	110.947
8	126.797
9	142.647	38/35
10	158.496	34/31
11	174.346	21/19
12	190.196	29/26
13	206.045
14	221.895	25/22, 33/29
15	237.744	31/27, 39/34, 47/41
16	253.594	22/19
17	269.444
18	285.293	46/39
19	301.143	25/21
20	316.993	6/5
21	332.842
22	348.692	11/9
23	364.541
24	380.391
25	396.241	39/31, 44/35
26	412.09	33/26
27	427.94
28	443.79
29	459.639	43/33, 47/36
30	475.489	25/19
31	491.338
32	507.188
33	523.038	23/17
34	538.887	15/11, 41/30
35	554.737
36	570.587	25/18
37	586.436
38	602.286
39	618.135	10/7
40	633.985
41	649.835
42	665.684
43	681.534	43/29, 46/31
44	697.384
45	713.233
46	729.083
47	744.932
48	760.782	45/29
49	776.632	47/30
50	792.481	30/19
51	808.331
52	824.181	29/18, 37/23
53	840.03
54	855.88	41/25
55	871.729	43/26
56	887.579
57	903.429
58	919.278
59	935.128	12/7
60	950.978	26/15, 45/26
61	966.827	7/4
62	982.677
63	998.526
64	1014.376
65	1030.226
66	1046.075
67	1061.925
68	1077.775	41/22
69	1093.624	47/25
70	1109.474	19/10
71	1125.323
72	1141.173	29/15
73	1157.023	41/21
74	1172.872
75	1188.722
76	1204.572
77	1220.421
78	1236.271	49/24
79	1252.12
80	1267.97
81	1283.82	21/10
82	1299.669
83	1315.519	47/22
84	1331.369	41/19
85	1347.218	37/17
86	1363.068	11/5
87	1378.917
88	1394.767	47/21
89	1410.617
90	1426.466	41/18
91	1442.316
92	1458.166
93	1474.015
94	1489.865	26/11
95	1505.714	31/13, 43/18
96	1521.564
97	1537.414
98	1553.263	27/11, 49/20
99	1569.113	47/19
100	1584.963	5/2
101	1600.812
102	1616.662
103	1632.511
104	1648.361
105	1664.211	34/13
106	1680.06	29/11
107	1695.91
108	1711.76
109	1727.609	19/7
110	1743.459
111	1759.308
112	1775.158
113	1791.008
114	1806.857
115	1822.707	43/15
116	1838.557	26/9
117	1854.406	35/12
118	1870.256
119	1886.105
120	1901.955	3/1

Harmonics

Approximation of harmonics in 120edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.57	+0.00	-6.71	+3.22	+4.57	+7.14	-2.14	+0.00	+7.79	+1.28	-6.71
	Relative (%)	+28.8	+0.0	-42.3	+20.3	+28.8	+45.1	-13.5	+0.0	+49.2	+8.1	-42.3
Steps (reduced)		76 (76)	120 (0)	151 (31)	176 (56)	196 (76)	213 (93)	227 (107)	240 (0)	252 (12)	262 (22)	271 (31)

Approximation of harmonics in 120edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-4.13	+3.22	+2.44	-7.42	+4.57	+6.07	-3.49	+7.14	+5.86	-7.70
	Relative (%)	-16.6	-26.1	+20.3	+15.4	-46.8	+28.8	+38.3	-22.0	+45.1	+36.9	-48.6
Steps (reduced)		280 (40)	288 (48)	296 (56)	303 (63)	309 (69)	316 (76)	322 (82)	327 (87)	333 (93)	338 (98)	342 (102)