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	Hekts	Approximate ratios
0	0	0	1/1
1	15.8	10.8
2	31.7	21.7
3	47.5	32.5	36/35
4	63.4	43.3	27/26
5	79.2	54.2	22/21, 45/43
6	95.1	65	19/18
7	110.9	75.8
8	126.8	86.7
9	142.6	97.5	38/35
10	158.5	108.3	34/31
11	174.3	119.2	21/19
12	190.2	130	29/26
13	206	140.8
14	221.9	151.7	25/22, 33/29
15	237.7	162.5	31/27, 39/34, 47/41
16	253.6	173.3	22/19
17	269.4	184.2
18	285.3	195	46/39
19	301.1	205.8	25/21
20	317	216.7	6/5
21	332.8	227.5
22	348.7	238.3	11/9
23	364.5	249.2
24	380.4	260
25	396.2	270.8	39/31, 44/35
26	412.1	281.7	33/26
27	427.9	292.5
28	443.8	303.3
29	459.6	314.2	43/33, 47/36
30	475.5	325	25/19
31	491.3	335.8
32	507.2	346.7
33	523	357.5	23/17
34	538.9	368.3	15/11, 41/30
35	554.7	379.2
36	570.6	390	25/18
37	586.4	400.8
38	602.3	411.7
39	618.1	422.5	10/7
40	634	433.3
41	649.8	444.2
42	665.7	455
43	681.5	465.8	43/29, 46/31
44	697.4	476.7
45	713.2	487.5
46	729.1	498.3
47	744.9	509.2
48	760.8	520	45/29
49	776.6	530.8	47/30
50	792.5	541.7	30/19
51	808.3	552.5
52	824.2	563.3	29/18, 37/23
53	840	574.2
54	855.9	585	41/25
55	871.7	595.8	43/26
56	887.6	606.7
57	903.4	617.5
58	919.3	628.3
59	935.1	639.2	12/7
60	951	650	26/15, 45/26
61	966.8	660.8	7/4
62	982.7	671.7
63	998.5	682.5
64	1014.4	693.3
65	1030.2	704.2
66	1046.1	715
67	1061.9	725.8
68	1077.8	736.7	41/22
69	1093.6	747.5	47/25
70	1109.5	758.3	19/10
71	1125.3	769.2
72	1141.2	780	29/15
73	1157	790.8	41/21
74	1172.9	801.7
75	1188.7	812.5
76	1204.6	823.3
77	1220.4	834.2
78	1236.3	845	49/24
79	1252.1	855.8
80	1268	866.7
81	1283.8	877.5	21/10
82	1299.7	888.3
83	1315.5	899.2	47/22
84	1331.4	910	41/19
85	1347.2	920.8	37/17
86	1363.1	931.7	11/5
87	1378.9	942.5
88	1394.8	953.3	47/21
89	1410.6	964.2
90	1426.5	975	41/18
91	1442.3	985.8
92	1458.2	996.7
93	1474	1007.5
94	1489.9	1018.3	26/11
95	1505.7	1029.2	31/13, 43/18
96	1521.6	1040
97	1537.4	1050.8
98	1553.3	1061.7	27/11, 49/20
99	1569.1	1072.5	47/19
100	1585	1083.3	5/2
101	1600.8	1094.2
102	1616.7	1105
103	1632.5	1115.8
104	1648.4	1126.7
105	1664.2	1137.5	34/13
106	1680.1	1148.3	29/11
107	1695.9	1159.2
108	1711.8	1170
109	1727.6	1180.8	19/7
110	1743.5	1191.7
111	1759.3	1202.5
112	1775.2	1213.3
113	1791	1224.2
114	1806.9	1235
115	1822.7	1245.8	43/15
116	1838.6	1256.7	26/9
117	1854.4	1267.5	35/12
118	1870.3	1278.3
119	1886.1	1289.2
120	1902	1300	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)