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	Hekts	Approximate ratios
0	0	0	1/1
1	13.4	9.2
2	26.8	18.3
3	40.2	27.5
4	53.6	36.6
5	67	45.8
6	80.4	54.9	22/21
7	93.8	64.1	19/18
8	107.2	73.2	33/31, 50/47
9	120.5	82.4
10	133.9	91.5	27/25
11	147.3	100.7	37/34
12	160.7	109.9	34/31, 45/41
13	174.1	119	21/19
14	187.5	128.2	39/35, 49/44
15	200.9	137.3
16	214.3	146.5
17	227.7	155.6
18	241.1	164.8	54/47
19	254.5	173.9	22/19
20	267.9	183.1	7/6
21	281.3	192.3
22	294.7	201.4	51/43
23	308.1	210.6	55/46
24	321.5	219.7	47/39
25	334.9	228.9
26	348.2	238	11/9
27	361.6	247.2	37/30
28	375	256.3	41/33
29	388.4	265.5
30	401.8	274.6	29/23
31	415.2	283.8	47/37
32	428.6	293	50/39
33	442	302.1
34	455.4	311.3	13/10
35	468.8	320.4
36	482.2	329.6	33/25
37	495.6	338.7
38	509	347.9	47/35, 55/41
39	522.4	357	23/17, 50/37
40	535.8	366.2	15/11
41	549.2	375.4
42	562.6	384.5	18/13
43	575.9	393.7	46/33
44	589.3	402.8
45	602.7	412
46	616.1	421.1	10/7
47	629.5	430.3
48	642.9	439.4
49	656.3	448.6	19/13
50	669.7	457.7
51	683.1	466.9	43/29, 46/31
52	696.5	476.1
53	709.9	485.2
54	723.3	494.4	41/27
55	736.7	503.5
56	750.1	512.7	54/35
57	763.5	521.8
58	776.9	531	47/30
59	790.2	540.1	30/19
60	803.6	549.3	35/22
61	817	558.5
62	830.4	567.6	21/13
63	843.8	576.8
64	857.2	585.9	41/25
65	870.6	595.1
66	884	604.2	5/3
67	897.4	613.4
68	910.8	622.5	22/13
69	924.2	631.7	29/17
70	937.6	640.8	43/25
71	951	650
72	964.4	659.2
73	977.8	668.3	51/29
74	991.2	677.5	39/22, 55/31
75	1004.6	686.6
76	1017.9	695.8	9/5
77	1031.3	704.9
78	1044.7	714.1
79	1058.1	723.2	35/19
80	1071.5	732.4	13/7
81	1084.9	741.5
82	1098.3	750.7	49/26
83	1111.7	759.9	19/10
84	1125.1	769
85	1138.5	778.2
86	1151.9	787.3	35/18
87	1165.3	796.5
88	1178.7	805.6
89	1192.1	814.8
90	1205.5	823.9
91	1218.9	833.1
92	1232.3	842.3	55/27
93	1245.6	851.4	39/19
94	1259	860.6
95	1272.4	869.7
96	1285.8	878.9	21/10
97	1299.2	888
98	1312.6	897.2	47/22
99	1326	906.3
100	1339.4	915.5	13/6
101	1352.8	924.6
102	1366.2	933.8	11/5
103	1379.6	943	51/23
104	1393	952.1
105	1406.4	961.3
106	1419.8	970.4	25/11
107	1433.2	979.6
108	1446.6	988.7	30/13
109	1460	997.9
110	1473.3	1007
111	1486.7	1016.2
112	1500.1	1025.4
113	1513.5	1034.5
114	1526.9	1043.7
115	1540.3	1052.8
116	1553.7	1062	27/11
117	1567.1	1071.1	47/19
118	1580.5	1080.3
119	1593.9	1089.4
120	1607.3	1098.6	43/17
121	1620.7	1107.7
122	1634.1	1116.9	18/7
123	1647.5	1126.1
124	1660.9	1135.2	47/18
125	1674.3	1144.4	50/19
126	1687.7	1153.5
127	1701	1162.7
128	1714.4	1171.8	35/13
129	1727.8	1181	19/7
130	1741.2	1190.1	41/15
131	1754.6	1199.3
132	1768	1208.5	25/9
133	1781.4	1217.6
134	1794.8	1226.8	31/11
135	1808.2	1235.9	54/19
136	1821.6	1245.1
137	1835	1254.2
138	1848.4	1263.4
139	1861.8	1272.5
140	1875.2	1281.7
141	1888.6	1290.8
142	1902	1300	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)