140edt

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140edt

141edt →

Prime factorization	22 × 5 × 7
Step size	13.5854¢
Octave	88\140edt (1195.51¢) (→22\35edt)
Consistency limit	2
Distinct consistency limit	2

140 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 140edt or 140ed3), is a nonoctave tuning system that divides the interval of 3/1 into 140 equal parts of about 13.6⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/140, or the 140th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	13.6	9.3
2	27.2	18.6
3	40.8	27.9	42/41, 43/42, 44/43
4	54.3	37.1
5	67.9	46.4	26/25, 51/49
6	81.5	55.7	22/21, 43/41
7	95.1	65	19/18, 37/35
8	108.7	74.3	33/31, 49/46
9	122.3	83.6	29/27, 44/41
10	135.9	92.9
11	149.4	102.1
12	163	111.4
13	176.6	120.7	41/37
14	190.2	130	29/26
15	203.8	139.3
16	217.4	148.6	17/15
17	231	157.9
18	244.5	167.1
19	258.1	176.4	29/25
20	271.7	185.7	55/47
21	285.3	195	46/39
22	298.9	204.3	44/37
23	312.5	213.6
24	326	222.9	35/29
25	339.6	232.1	45/37
26	353.2	241.4	27/22
27	366.8	250.7	21/17
28	380.4	260
29	394	269.3	49/39, 54/43
30	407.6	278.6	43/34
31	421.1	287.9	37/29
32	434.7	297.1	9/7
33	448.3	306.4	35/27
34	461.9	315.7
35	475.5	325	25/19, 54/41
36	489.1	334.3
37	502.7	343.6
38	516.2	352.9	31/23, 35/26
39	529.8	362.1	19/14
40	543.4	371.4	26/19
41	557	380.7	51/37
42	570.6	390
43	584.2	399.3	7/5
44	597.8	408.6
45	611.3	417.9	37/26, 47/33
46	624.9	427.1	33/23
47	638.5	436.4
48	652.1	445.7	51/35
49	665.7	455
50	679.3	464.3	37/25
51	692.9	473.6
52	706.4	482.9
53	720	492.1	47/31
54	733.6	501.4	29/19
55	747.2	510.7
56	760.8	520	45/29
57	774.4	529.3
58	788	538.6	41/26
59	801.5	547.9	27/17
60	815.1	557.1
61	828.7	566.4	21/13
62	842.3	575.7
63	855.9	585	41/25
64	869.5	594.3	43/26
65	883.1	603.6	5/3
66	896.6	612.9	42/25
67	910.2	622.1	22/13
68	923.8	631.4	29/17, 46/27
69	937.4	640.7	43/25
70	951	650	26/15, 45/26
71	964.6	659.3
72	978.1	668.6	44/25, 51/29
73	991.7	677.9	39/22, 55/31
74	1005.3	687.1	25/14
75	1018.9	696.4	9/5
76	1032.5	705.7	49/27
77	1046.1	715
78	1059.7	724.3
79	1073.2	733.6	13/7
80	1086.8	742.9
81	1100.4	752.1	17/9
82	1114	761.4
83	1127.6	770.7
84	1141.2	780	29/15
85	1154.8	789.3	37/19
86	1168.3	798.6
87	1181.9	807.9
88	1195.5	817.1
89	1209.1	826.4
90	1222.7	835.7
91	1236.3	845	47/23
92	1249.9	854.3	35/17
93	1263.4	863.6
94	1277	872.9	23/11
95	1290.6	882.1
96	1304.2	891.4
97	1317.8	900.7	15/7
98	1331.4	910	41/19
99	1345	919.3	37/17
100	1358.5	928.6	46/21
101	1372.1	937.9	42/19
102	1385.7	947.1	49/22
103	1399.3	956.4
104	1412.9	965.7	43/19
105	1426.5	975	41/18
106	1440.1	984.3
107	1453.6	993.6	44/19
108	1467.2	1002.9	7/3
109	1480.8	1012.1
110	1494.4	1021.4
111	1508	1030.7	43/18, 55/23
112	1521.6	1040
113	1535.1	1049.3	17/7
114	1548.7	1058.6	22/9
115	1562.3	1067.9	37/15
116	1575.9	1077.1
117	1589.5	1086.4
118	1603.1	1095.7
119	1616.7	1105
120	1630.2	1114.3
121	1643.8	1123.6
122	1657.4	1132.9
123	1671	1142.1
124	1684.6	1151.4	45/17
125	1698.2	1160.7
126	1711.8	1170
127	1725.3	1179.3
128	1738.9	1188.6
129	1752.5	1197.9
130	1766.1	1207.1
131	1779.7	1216.4
132	1793.3	1225.7	31/11
133	1806.9	1235	54/19
134	1820.4	1244.3
135	1834	1253.6	49/17
136	1847.6	1262.9
137	1861.2	1272.1	41/14
138	1874.8	1281.4
139	1888.4	1290.7
140	1902	1300	3/1

Harmonics

Approximation of harmonics in 140edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.49	+0.00	+4.61	-1.31	-4.49	+0.35	+0.13	+0.00	-5.79	+5.81	+4.61
	Relative (%)	-33.0	+0.0	+34.0	-9.6	-33.0	+2.6	+1.0	+0.0	-42.6	+42.8	+34.0
Steps (reduced)		88 (88)	140 (0)	177 (37)	205 (65)	228 (88)	248 (108)	265 (125)	280 (0)	293 (13)	306 (26)	317 (37)

Approximation of harmonics in 140edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.90	-4.13	-1.31	-4.36	-0.63	-4.49	-2.99	+3.31	+0.35	+1.33	+5.88
	Relative (%)	+14.0	-30.4	-9.6	-32.1	-4.6	-33.0	-22.0	+24.3	+2.6	+9.8	+43.3
Steps (reduced)		327 (47)	336 (56)	345 (65)	353 (73)	361 (81)	368 (88)	375 (95)	382 (102)	388 (108)	394 (114)	400 (120)