139ed4

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139ed4

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Prime factorization	139 (prime)
Step size	17.2662¢
Octave	70\139ed4 (1208.63¢)
Twelfth	110\139ed4 (1899.28¢)
Consistency limit	1
Distinct consistency limit	1

139 equal divisions of the 4th harmonic (abbreviated 139ed4) is a nonoctave tuning system that divides the interval of 4/1 into 139 equal parts of about 17.3 ¢ each. Each step represents a frequency ratio of 4^1/139, or the 139th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	17.266
2	34.532	50/49, 51/50
3	51.799
4	69.065	51/49
5	86.331	41/39
6	103.597
7	120.863
8	138.129
9	155.396	47/43
10	172.662	21/19
11	189.928	29/26
12	207.194
13	224.46	49/43
14	241.727	54/47
15	258.993	43/37
16	276.259	27/23, 34/29
17	293.525
18	310.791
19	328.058
20	345.324
21	362.59	37/30
22	379.856
23	397.122	39/31
24	414.388	47/37
25	431.655	50/39
26	448.921	35/27
27	466.187
28	483.453	41/31
29	500.719
30	517.986	31/23
31	535.252
32	552.518
33	569.784
34	587.05
35	604.317
36	621.583	43/30
37	638.849
38	656.115	19/13, 54/37
39	673.381	31/21
40	690.647
41	707.914
42	725.18	35/23
43	742.446
44	759.712
45	776.978	47/30
46	794.245	49/31
47	811.511
48	828.777	21/13, 50/31
49	846.043	31/19
50	863.309	51/31
51	880.576
52	897.842
53	915.108	39/23
54	932.374
55	949.64
56	966.906
57	984.173	30/17
58	1001.439	41/23
59	1018.705	9/5
60	1035.971
61	1053.237
62	1070.504	13/7
63	1087.77
64	1105.036
65	1122.302
66	1139.568
67	1156.835	41/21
68	1174.101
69	1191.367
70	1208.633
71	1225.899
72	1243.165
73	1260.432	29/14
74	1277.698	23/11
75	1294.964	19/9
76	1312.23
77	1329.496
78	1346.763	37/17
79	1364.029	11/5
80	1381.295
81	1398.561
82	1415.827
83	1433.094
84	1450.36
85	1467.626	7/3
86	1484.892
87	1502.158	50/21
88	1519.424
89	1536.691	17/7
90	1553.957	27/11
91	1571.223
92	1588.489
93	1605.755	43/17
94	1623.022	23/9
95	1640.288	49/19
96	1657.554
97	1674.82	50/19
98	1692.086
99	1709.353	51/19
100	1726.619
101	1743.885
102	1761.151	47/17
103	1778.417
104	1795.683
105	1812.95
106	1830.216
107	1847.482
108	1864.748
109	1882.014
110	1899.281
111	1916.547
112	1933.813
113	1951.079
114	1968.345
115	1985.612
116	2002.878	35/11
117	2020.144
118	2037.41
119	2054.676
120	2071.942	43/13
121	2089.209
122	2106.475
123	2123.741
124	2141.007	31/9
125	2158.273
126	2175.54
127	2192.806	39/11
128	2210.072
129	2227.338
130	2244.604
131	2261.871
132	2279.137	41/11
133	2296.403	49/13
134	2313.669
135	2330.935	50/13
136	2348.201
137	2365.468	51/13
138	2382.734
139	2400

Harmonics

Approximation of harmonics in 139ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.63	-2.67	+0.00	-6.46	+5.96	-1.92	+8.63	-5.35	+2.18	-7.43	-2.67
	Relative (%)	+50.0	-15.5	+0.0	-37.4	+34.5	-11.1	+50.0	-31.0	+12.6	-43.0	-15.5
Steps (reduced)		70 (70)	110 (110)	139 (0)	161 (22)	180 (41)	195 (56)	209 (70)	220 (81)	231 (92)	240 (101)	249 (110)

Approximation of harmonics in 139ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-3.12	+6.71	+8.13	+0.00	-1.36	+3.28	-3.99	-6.46	-4.59	+1.20	-6.69
	Relative (%)	-18.1	+38.9	+47.1	+0.0	-7.9	+19.0	-23.1	-37.4	-26.6	+7.0	-38.8
Steps (reduced)		257 (118)	265 (126)	272 (133)	278 (0)	284 (6)	290 (12)	295 (17)	300 (22)	305 (27)	310 (32)	314 (36)