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	17.3
2	34.5	50/49, 51/50
3	51.8
4	69.1	51/49
5	86.3	41/39
6	103.6
7	120.9
8	138.1
9	155.4	47/43
10	172.7	21/19
11	189.9	29/26
12	207.2
13	224.5	49/43
14	241.7	54/47
15	259	43/37
16	276.3	27/23, 34/29
17	293.5
18	310.8
19	328.1
20	345.3
21	362.6	37/30
22	379.9
23	397.1	39/31
24	414.4	47/37
25	431.7	50/39
26	448.9	35/27
27	466.2
28	483.5	41/31
29	500.7
30	518	31/23
31	535.3
32	552.5
33	569.8
34	587.1
35	604.3
36	621.6	43/30
37	638.8
38	656.1	19/13, 54/37
39	673.4	31/21
40	690.6
41	707.9
42	725.2	35/23
43	742.4
44	759.7
45	777	47/30
46	794.2	49/31
47	811.5
48	828.8	21/13, 50/31
49	846	31/19
50	863.3	51/31
51	880.6
52	897.8
53	915.1	39/23
54	932.4
55	949.6
56	966.9
57	984.2	30/17
58	1001.4	41/23
59	1018.7	9/5
60	1036
61	1053.2
62	1070.5	13/7
63	1087.8
64	1105
65	1122.3
66	1139.6
67	1156.8	41/21
68	1174.1
69	1191.4
70	1208.6
71	1225.9
72	1243.2
73	1260.4	29/14
74	1277.7	23/11
75	1295	19/9
76	1312.2
77	1329.5
78	1346.8	37/17
79	1364	11/5
80	1381.3
81	1398.6
82	1415.8
83	1433.1
84	1450.4
85	1467.6	7/3
86	1484.9
87	1502.2	50/21
88	1519.4
89	1536.7	17/7
90	1554	27/11
91	1571.2
92	1588.5
93	1605.8	43/17
94	1623	23/9
95	1640.3	49/19
96	1657.6
97	1674.8	50/19
98	1692.1
99	1709.4	51/19
100	1726.6
101	1743.9
102	1761.2	47/17
103	1778.4
104	1795.7
105	1812.9
106	1830.2
107	1847.5
108	1864.7
109	1882
110	1899.3
111	1916.5
112	1933.8
113	1951.1
114	1968.3
115	1985.6
116	2002.9	35/11
117	2020.1
118	2037.4
119	2054.7
120	2071.9	43/13
121	2089.2
122	2106.5
123	2123.7
124	2141	31/9
125	2158.3
126	2175.5
127	2192.8	39/11
128	2210.1
129	2227.3
130	2244.6
131	2261.9
132	2279.1	41/11
133	2296.4	49/13
134	2313.7
135	2330.9	50/13
136	2348.2
137	2365.5	51/13
138	2382.7
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)