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	Approximate ratios
0	0	1/1
1	13.585
2	27.171
3	40.756	42/41, 43/42, 44/43
4	54.342
5	67.927	26/25, 51/49
6	81.512	22/21, 43/41
7	95.098	19/18, 37/35
8	108.683	33/31, 49/46
9	122.269	29/27, 44/41
10	135.854
11	149.439
12	163.025
13	176.61	41/37
14	190.196	29/26
15	203.781
16	217.366	17/15
17	230.952
18	244.537
19	258.122	29/25
20	271.708	55/47
21	285.293	46/39
22	298.879	44/37
23	312.464
24	326.049	35/29
25	339.635	45/37
26	353.22	27/22
27	366.806	21/17
28	380.391
29	393.976	49/39, 54/43
30	407.562	43/34
31	421.147	37/29
32	434.733	9/7
33	448.318	35/27
34	461.903
35	475.489	25/19, 54/41
36	489.074
37	502.66
38	516.245	31/23, 35/26
39	529.83	19/14
40	543.416	26/19
41	557.001	51/37
42	570.587
43	584.172	7/5
44	597.757
45	611.343	37/26, 47/33
46	624.928	33/23
47	638.513
48	652.099	51/35
49	665.684
50	679.27	37/25
51	692.855
52	706.44
53	720.026	47/31
54	733.611	29/19
55	747.197
56	760.782	45/29
57	774.367
58	787.953	41/26
59	801.538	27/17
60	815.124
61	828.709	21/13
62	842.294
63	855.88	41/25
64	869.465	43/26
65	883.051	5/3
66	896.636	42/25
67	910.221	22/13
68	923.807	29/17, 46/27
69	937.392	43/25
70	950.978	26/15, 45/26
71	964.563
72	978.148	44/25, 51/29
73	991.734	39/22, 55/31
74	1005.319	25/14
75	1018.904	9/5
76	1032.49	49/27
77	1046.075
78	1059.661
79	1073.246	13/7
80	1086.831
81	1100.417	17/9
82	1114.002
83	1127.588
84	1141.173	29/15
85	1154.758	37/19
86	1168.344
87	1181.929
88	1195.515
89	1209.1
90	1222.685
91	1236.271	47/23
92	1249.856	35/17
93	1263.442
94	1277.027	23/11
95	1290.612
96	1304.198
97	1317.783	15/7
98	1331.369	41/19
99	1344.954	37/17
100	1358.539	46/21
101	1372.125	42/19
102	1385.71	49/22
103	1399.295
104	1412.881	43/19
105	1426.466	41/18
106	1440.052
107	1453.637	44/19
108	1467.222	7/3
109	1480.808
110	1494.393
111	1507.979	43/18, 55/23
112	1521.564
113	1535.149	17/7
114	1548.735	22/9
115	1562.32	37/15
116	1575.906
117	1589.491
118	1603.076
119	1616.662
120	1630.247
121	1643.833
122	1657.418
123	1671.003
124	1684.589	45/17
125	1698.174
126	1711.76
127	1725.345
128	1738.93
129	1752.516
130	1766.101
131	1779.686
132	1793.272	31/11
133	1806.857	54/19
134	1820.443
135	1834.028	49/17
136	1847.613
137	1861.199	41/14
138	1874.784
139	1888.37
140	1901.955	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)