142edt

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142edt

143edt →

Prime factorization	2 × 71
Step size	13.394¢
Octave	90\142edt (1205.46¢) (→45\71edt)
Consistency limit	2
Distinct consistency limit	2

142 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 142edt or 142ed3), is a nonoctave tuning system that divides the interval of 3/1 into 142 equal parts of about 13.4 ¢ each. Each step represents a frequency ratio of 3^1/142, or the 142nd root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	13.4
2	26.8
3	40.2
4	53.6
5	67
6	80.4	22/21
7	93.8	19/18
8	107.2	33/31, 50/47
9	120.5
10	133.9	27/25
11	147.3	37/34
12	160.7	34/31, 45/41
13	174.1	21/19
14	187.5	39/35, 49/44
15	200.9
16	214.3
17	227.7
18	241.1	54/47
19	254.5	22/19
20	267.9	7/6
21	281.3
22	294.7	51/43
23	308.1	55/46
24	321.5	47/39
25	334.9
26	348.2	11/9
27	361.6	37/30
28	375	41/33
29	388.4
30	401.8	29/23
31	415.2	47/37
32	428.6	50/39
33	442
34	455.4	13/10
35	468.8
36	482.2	33/25
37	495.6
38	509	47/35, 55/41
39	522.4	23/17, 50/37
40	535.8	15/11
41	549.2
42	562.6	18/13
43	575.9	46/33
44	589.3
45	602.7
46	616.1	10/7
47	629.5
48	642.9
49	656.3	19/13
50	669.7
51	683.1	43/29, 46/31
52	696.5
53	709.9
54	723.3	41/27
55	736.7
56	750.1	54/35
57	763.5
58	776.9	47/30
59	790.2	30/19
60	803.6	35/22
61	817
62	830.4	21/13
63	843.8
64	857.2	41/25
65	870.6
66	884	5/3
67	897.4
68	910.8	22/13
69	924.2	29/17
70	937.6	43/25
71	951
72	964.4
73	977.8	51/29
74	991.2	39/22, 55/31
75	1004.6
76	1017.9	9/5
77	1031.3
78	1044.7
79	1058.1	35/19
80	1071.5	13/7
81	1084.9
82	1098.3	49/26
83	1111.7	19/10
84	1125.1
85	1138.5
86	1151.9	35/18
87	1165.3
88	1178.7
89	1192.1
90	1205.5
91	1218.9
92	1232.3	55/27
93	1245.6	39/19
94	1259
95	1272.4
96	1285.8	21/10
97	1299.2
98	1312.6	47/22
99	1326
100	1339.4	13/6
101	1352.8
102	1366.2	11/5
103	1379.6	51/23
104	1393
105	1406.4
106	1419.8	25/11
107	1433.2
108	1446.6	30/13
109	1460
110	1473.3
111	1486.7
112	1500.1
113	1513.5
114	1526.9
115	1540.3
116	1553.7	27/11
117	1567.1	47/19
118	1580.5
119	1593.9
120	1607.3	43/17
121	1620.7
122	1634.1	18/7
123	1647.5
124	1660.9	47/18
125	1674.3	50/19
126	1687.7
127	1701
128	1714.4	35/13
129	1727.8	19/7
130	1741.2	41/15
131	1754.6
132	1768	25/9
133	1781.4
134	1794.8	31/11
135	1808.2	54/19
136	1821.6
137	1835
138	1848.4
139	1861.8
140	1875.2
141	1888.6
142	1902	3/1

Harmonics

Approximation of harmonics in 142edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+5.46	+0.00	-2.47	-0.35	+5.46	+6.47	+3.00	+0.00	+5.11	+0.84	-2.47
	Relative (%)	+40.8	+0.0	-18.4	-2.6	+40.8	+48.3	+22.4	+0.0	+38.2	+6.3	-18.4
Steps (reduced)		90 (90)	142 (0)	179 (37)	208 (66)	232 (90)	252 (110)	269 (127)	284 (0)	298 (14)	310 (26)	321 (37)

Approximation of harmonics in 142edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.30	-1.46	-0.35	-4.93	-2.73	+5.46	+5.62	-2.82	+6.47	+6.30	-3.68
	Relative (%)	+47.0	-10.9	-2.6	-36.8	-20.4	+40.8	+42.0	-21.0	+48.3	+47.0	-27.5
Steps (reduced)		332 (48)	341 (57)	350 (66)	358 (74)	366 (82)	374 (90)	381 (97)	387 (103)	394 (110)	400 (116)	405 (121)