139ed5

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139ed5

140ed5 →

Prime factorization	139 (prime)
Step size	20.0454 ¢
Octave	60\139ed5 (1202.73 ¢)
Twelfth	95\139ed5 (1904.32 ¢)
Consistency limit	10
Distinct consistency limit	10

139 equal divisions of the 5th harmonic (abbreviated 139ed5) is a nonoctave tuning system that divides the interval of 5/1 into 139 equal parts of about 20 ¢ each. Each step represents a frequency ratio of 5^1/139, or the 139th root of 5.

Steps	Cents	Approximate ratios
0	0	1/1
1	20
2	40.1	42/41, 43/42, 44/43, 45/44
3	60.1	29/28, 30/29
4	80.2	22/21, 45/43
5	100.2	18/17, 35/33
6	120.3	15/14
7	140.3	51/47
8	160.4	34/31, 45/41
9	180.4
10	200.5	46/41
11	220.5	25/22, 42/37
12	240.5	23/20, 31/27, 54/47
13	260.6	43/37, 50/43
14	280.6	20/17, 47/40
15	300.7	25/21, 44/37
16	320.7
17	340.8	28/23
18	360.8	16/13
19	380.9
20	400.9	29/23
21	421	37/29, 51/40
22	441	40/31, 49/38
23	461	30/23, 47/36
24	481.1	33/25, 37/28
25	501.1
26	521.2	27/20, 50/37
27	541.2	41/30
28	561.3	47/34
29	581.3	7/5
30	601.4	17/12
31	621.4
32	641.5	42/29
33	661.5	22/15, 41/28
34	681.5	40/27, 43/29
35	701.6	3/2
36	721.6	41/27, 44/29, 47/31
37	741.7	23/15, 43/28
38	761.7	45/29
39	781.8	11/7
40	801.8	27/17
41	821.9	37/23, 45/28
42	841.9	13/8
43	862	51/31
44	882
45	902
46	922.1	46/27
47	942.1	31/18, 50/29
48	962.2	54/31
49	982.2	30/17, 37/21
50	1002.3	25/14, 41/23
51	1022.3
52	1042.4	42/23
53	1062.4	24/13
54	1082.5	43/23
55	1102.5	17/9
56	1122.5	44/23
57	1142.6	29/15
58	1162.6	45/23, 47/24
59	1182.7
60	1202.7
61	1222.8
62	1242.8	41/20
63	1262.9
64	1282.9	21/10
65	1303
66	1323
67	1343	50/23
68	1363.1
69	1383.1	20/9
70	1403.2	9/4
71	1423.2
72	1443.3	23/10
73	1463.3
74	1483.4	33/14
75	1503.4	31/13, 50/21
76	1523.5	41/17
77	1543.5	39/16
78	1563.5	37/15
79	1583.6
80	1603.6
81	1623.7	23/9
82	1643.7	31/12
83	1663.8	34/13
84	1683.8	37/14, 45/17
85	1703.9
86	1723.9	46/17
87	1744
88	1764	36/13
89	1784	14/5
90	1804.1	17/6
91	1824.1	43/15
92	1844.2	29/10
93	1864.2	44/15, 47/16
94	1884.3
95	1904.3
96	1924.4
97	1944.4	40/13
98	1964.5	28/9
99	1984.5
100	2004.5	35/11
101	2024.6	29/9
102	2044.6
103	2064.7
104	2084.7	10/3
105	2104.8	27/8
106	2124.8
107	2144.9	38/11
108	2164.9
109	2185
110	2205	25/7
111	2225	47/13
112	2245.1
113	2265.1	37/10
114	2285.2
115	2305.2
116	2325.3	23/6
117	2345.3	31/8
118	2365.4	51/13
119	2385.4
120	2405.5
121	2425.5
122	2445.5
123	2465.6	54/13
124	2485.6	21/5
125	2505.7	17/4
126	2525.7	43/10
127	2545.8
128	2565.8	22/5
129	2585.9	49/11
130	2605.9
131	2626	41/9
132	2646
133	2666	14/3
134	2686.1	33/7
135	2706.1	43/9
136	2726.2	29/6
137	2746.2	44/9
138	2766.3
139	2786.3	5/1

Odd harmonics

Approximation of harmonics in 139ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.73	+2.36	+5.45	+0.00	+5.09	-1.19	+8.18	+4.72	+2.73	-1.92	+7.81
	Relative (%)	+13.6	+11.8	+27.2	+0.0	+25.4	-6.0	+40.8	+23.5	+13.6	-9.6	+39.0
Steps (reduced)		60 (60)	95 (95)	120 (120)	139 (0)	155 (16)	168 (29)	180 (41)	190 (51)	199 (60)	207 (68)	215 (76)

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