139edt

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139edt

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Prime factorization	139 (prime)
Step size	13.6831¢
Octave	88\139edt (1204.12¢)
Consistency limit	2
Distinct consistency limit	2

139 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 139edt or 139ed3), is a nonoctave tuning system that divides the interval of 3/1 into 139 equal parts of about 13.7 ¢ each. Each step represents a frequency ratio of 3^1/139, or the 139th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	13.683
2	27.366
3	41.049	42/41, 43/42, 44/43
4	54.733
5	68.416	26/25, 51/49
6	82.099	22/21, 43/41
7	95.782	37/35
8	109.465	33/31
9	123.148	29/27, 44/41
10	136.831
11	150.514
12	164.198
13	177.881	41/37
14	191.564
15	205.247
16	218.93	42/37
17	232.613
18	246.296	15/13
19	259.979	43/37
20	273.663	41/35
21	287.346	46/39
22	301.029	44/37
23	314.712	6/5
24	328.395
25	342.078	28/23
26	355.761	27/22, 43/35
27	369.444
28	383.128
29	396.811	44/35
30	410.494	19/15
31	424.177	23/18
32	437.86
33	451.543
34	465.226
35	478.91	29/22
36	492.593
37	506.276
38	519.959
39	533.642
40	547.325
41	561.008	47/34
42	574.691	39/28
43	588.375
44	602.058
45	615.741
46	629.424
47	643.107
48	656.79	19/13
49	670.473	28/19
50	684.156	49/33
51	697.84
52	711.523
53	725.206	35/23, 38/25
54	738.889	23/15
55	752.572	17/11
56	766.255	14/9
57	779.938
58	793.622	49/31
59	807.305	43/27
60	820.988	45/28
61	834.671	34/21, 47/29
62	848.354
63	862.037	51/31
64	875.72
65	889.403
66	903.087
67	916.77
68	930.453
69	944.136
70	957.819
71	971.502
72	985.185
73	998.868
74	1012.552
75	1026.235
76	1039.918	31/17
77	1053.601
78	1067.284
79	1080.967	28/15
80	1094.65
81	1108.333
82	1122.017	44/23
83	1135.7	27/14
84	1149.383	33/17
85	1163.066	45/23
86	1176.749
87	1190.432
88	1204.115
89	1217.799
90	1231.482
91	1245.165	39/19
92	1258.848
93	1272.531
94	1286.214
95	1299.897
96	1313.58	47/22
97	1327.264	28/13
98	1340.947
99	1354.63
100	1368.313
101	1381.996
102	1395.679	47/21
103	1409.362
104	1423.045
105	1436.729
106	1450.412
107	1464.095
108	1477.778	54/23
109	1491.461	45/19
110	1505.144
111	1518.827
112	1532.511
113	1546.194	22/9
114	1559.877
115	1573.56
116	1587.243	5/2
117	1600.926
118	1614.609
119	1628.292
120	1641.976
121	1655.659	13/5
122	1669.342
123	1683.025	37/14
124	1696.708
125	1710.391
126	1724.074
127	1737.757
128	1751.441
129	1765.124
130	1778.807
131	1792.49	31/11
132	1806.173
133	1819.856
134	1833.539	49/17
135	1847.222
136	1860.906	41/14
137	1874.589
138	1888.272
139	1901.955	3/1

Harmonics

Approximation of harmonics in 139edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.12	+0.00	-5.45	+5.04	+4.12	-2.78	-1.34	+0.00	-4.52	-5.33	-5.45
	Relative (%)	+30.1	+0.0	-39.8	+36.9	+30.1	-20.3	-9.8	+0.0	-33.1	-39.0	-39.8
Steps (reduced)		88 (88)	139 (0)	175 (36)	204 (65)	227 (88)	246 (107)	263 (124)	278 (0)	291 (13)	303 (25)	314 (36)

Approximation of harmonics in 139edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.49	+1.34	+5.04	+2.78	-6.40	+4.12	+6.29	-0.41	-2.78	-1.21	+3.93
	Relative (%)	+47.4	+9.8	+36.9	+20.3	-46.7	+30.1	+46.0	-3.0	-20.3	-8.9	+28.7
Steps (reduced)		325 (47)	334 (56)	343 (65)	351 (73)	358 (80)	366 (88)	373 (95)	379 (101)	385 (107)	391 (113)	397 (119)