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	13.394
2	26.788
3	40.182
4	53.576
5	66.97
6	80.364	22/21
7	93.758	19/18
8	107.152	33/31, 50/47
9	120.546
10	133.94	27/25
11	147.335	37/34
12	160.729	34/31, 45/41
13	174.123	21/19
14	187.517	39/35, 49/44
15	200.911
16	214.305
17	227.699
18	241.093	54/47
19	254.487	22/19
20	267.881	7/6
21	281.275
22	294.669	51/43
23	308.063	55/46
24	321.457	47/39
25	334.851
26	348.245	11/9
27	361.639	37/30
28	375.033	41/33
29	388.427
30	401.821	29/23
31	415.216	47/37
32	428.61	50/39
33	442.004
34	455.398	13/10
35	468.792
36	482.186	33/25
37	495.58
38	508.974	47/35, 55/41
39	522.368	23/17, 50/37
40	535.762	15/11
41	549.156
42	562.55	18/13
43	575.944	46/33
44	589.338
45	602.732
46	616.126	10/7
47	629.52
48	642.914
49	656.308	19/13
50	669.702
51	683.097	43/29, 46/31
52	696.491
53	709.885
54	723.279	41/27
55	736.673
56	750.067	54/35
57	763.461
58	776.855	47/30
59	790.249	30/19
60	803.643	35/22
61	817.037
62	830.431	21/13
63	843.825
64	857.219	41/25
65	870.613
66	884.007	5/3
67	897.401
68	910.795	22/13
69	924.189	29/17
70	937.583	43/25
71	950.978
72	964.372
73	977.766	51/29
74	991.16	39/22, 55/31
75	1004.554
76	1017.948	9/5
77	1031.342
78	1044.736
79	1058.13	35/19
80	1071.524	13/7
81	1084.918
82	1098.312	49/26
83	1111.706	19/10
84	1125.1
85	1138.494
86	1151.888	35/18
87	1165.282
88	1178.676
89	1192.07
90	1205.464
91	1218.858
92	1232.253	55/27
93	1245.647	39/19
94	1259.041
95	1272.435
96	1285.829	21/10
97	1299.223
98	1312.617	47/22
99	1326.011
100	1339.405	13/6
101	1352.799
102	1366.193	11/5
103	1379.587	51/23
104	1392.981
105	1406.375
106	1419.769	25/11
107	1433.163
108	1446.557	30/13
109	1459.951
110	1473.345
111	1486.739
112	1500.134
113	1513.528
114	1526.922
115	1540.316
116	1553.71	27/11
117	1567.104	47/19
118	1580.498
119	1593.892
120	1607.286	43/17
121	1620.68
122	1634.074	18/7
123	1647.468
124	1660.862	47/18
125	1674.256	50/19
126	1687.65
127	1701.044
128	1714.438	35/13
129	1727.832	19/7
130	1741.226	41/15
131	1754.62
132	1768.015	25/9
133	1781.409
134	1794.803	31/11
135	1808.197	54/19
136	1821.591
137	1834.985
138	1848.379
139	1861.773
140	1875.167
141	1888.561
142	1901.955	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)