139edo

139edo is the 34th prime EDO. It has a step size of 8.6330935251799 cents. It is a commatonal EDO. It is not consistent in the 5-odd-limit. It is also starling family.

Step	Five limit	Seven limit	Eleven limit	Thirteen limit
1	81/80	81/80	81/80	81/80
2	6561/6400	2430/2401	99/98	78/77
3	2048/2025	245/243	56/55	56/55
4	128/125	49/48	45/44	45/44
5	648/625	36/35	36/35	36/35
6	6561/6250	405/392	33/32	33/32
7	20000/19683	2240/2187	125/121	26/25
8	250/243	28/27	28/27	28/27
9	25/24	21/20	21/20	21/20
10	135/128	135/128	22/21	22/21
11	2187/2048	729/686	128/121	96/91
12	256/243	256/243	35/33	35/33
13	16/15	16/15	16/15	16/15
14	27/25	15/14	15/14	15/14
15	2187/2000	243/224	243/224	14/13
16	32768/30375	784/729	121/112	13/12
17	2048/1875	49/45	12/11	12/11
18	625/576	35/32	35/32	35/32
19	1125/1024	54/49	11/10	11/10
20	18225/16384	2187/1960	400/363	72/65
21	800/729	448/405	49/44	39/35
22	10/9	10/9	10/9	10/9
23	9/8	9/8	9/8	9/8
24	729/640	729/640	55/49	55/49
25	4096/3645	1372/1215	112/99	44/39
26	256/225	245/216	25/22	25/22
27	144/125	8/7	8/7	8/7
28	729/625	81/70	55/48	55/48
29	59049/50000	3645/3136	121/105	15/13
30	2500/2187	280/243	64/55	64/55
31	125/108	7/6	7/6	7/6
32	75/64	75/64	75/64	75/64
33	1215/1024	405/343	33/28	13/11
34	2560/2187	1715/1458	144/121	77/65
35	32/27	32/27	32/27	32/27
36	6/5	6/5	6/5	6/5
37	243/200	135/112	77/64	77/64
38	19683/16000	2187/1792	121/100	63/52
39	4096/3375	98/81	40/33	39/32
40	768/625	49/40	27/22	27/22
41	625/512	60/49	11/9	11/9
42	10125/8192	243/196	99/80	16/13
43	8000/6561	896/729	121/98	26/21
44	100/81	56/45	56/45	56/45
45	5/4	5/4	5/4	5/4
46	81/64	81/64	44/35	44/35
47	6561/5120	2187/1715	121/96	91/72
48	512/405	343/270	14/11	14/11
49	32/25	32/25	32/25	32/25
50	162/125	9/7	9/7	9/7
51	6561/5000	729/560	165/128	50/39
52	25000/19683	1568/1215	128/99	13/10
53	625/486	35/27	35/27	35/27
54	125/96	21/16	21/16	21/16
55	675/512	324/245	33/25	33/25
56	10935/8192	3645/2744	160/121	117/88
57	320/243	320/243	147/110	65/49
58	4/3	4/3	4/3	4/3
59	27/20	27/20	27/20	27/20
60	2187/1600	1215/896	66/49	35/26
61	8192/6075	980/729	224/165	65/48
62	512/375	49/36	15/11	15/11
63	864/625	48/35	48/35	48/35
64	4374/3125	135/98	11/8	11/8
65	80000/59049	2187/1568	168/121	18/13
66	1000/729	112/81	112/81	39/28
67	25/18	7/5	7/5	7/5
68	45/32	45/32	45/32	45/32
69	729/512	486/343	99/70	78/55
70	1024/729	343/243	140/99	55/39
71	64/45	64/45	63/44	63/44
72	36/25	10/7	10/7	10/7
73	729/500	81/56	81/56	56/39
74	59049/40000	3136/2187	121/84	13/9
75	3125/2187	196/135	16/11	16/11
76	625/432	35/24	35/24	35/24
77	375/256	72/49	22/15	22/15
78	6075/4096	729/490	165/112	65/44
79	3200/2187	1792/1215	49/33	49/33
80	40/27	40/27	40/27	40/27
81	3/2	3/2	3/2	3/2
82	243/160	243/160	121/81	98/65
83	16384/10935	3645/2401	121/80	91/60
84	1024/675	245/162	50/33	50/33
85	192/125	32/21	32/21	32/21
86	972/625	54/35	54/35	54/35
87	19683/12500	1215/784	99/64	20/13
88	10000/6561	1120/729	189/121	39/25
89	125/81	14/9	14/9	14/9
90	25/16	25/16	25/16	25/16
91	405/256	405/256	11/7	11/7
92	6561/4096	2187/1372	192/121	144/91
93	128/81	128/81	35/22	35/22
94	8/5	8/5	8/5	8/5
95	81/50	45/28	45/28	45/28
96	6561/4000	729/448	121/75	21/13
97	16384/10125	392/243	160/99	13/8
98	1024/625	49/30	18/11	18/11
99	625/384	80/49	44/27	44/27
100	3375/2048	81/49	33/20	33/20
101	32000/19683	2401/1458	200/121	104/63
102	400/243	224/135	128/77	117/70
103	5/3	5/3	5/3	5/3
104	27/16	27/16	27/16	27/16
105	2187/1280	2187/1280	121/72	91/54
106	2048/1215	686/405	56/33	22/13
107	128/75	128/75	75/44	75/44
108	216/125	12/7	12/7	12/7
109	2187/1250	243/140	55/32	55/32
110	?	6272/3645	121/70	26/15
111	1250/729	140/81	96/55	96/55
112	125/72	7/4	7/4	7/4
113	225/128	225/128	44/25	44/25
114	3645/2048	1215/686	99/56	39/22
115	1280/729	1280/729	98/55	98/55
116	16/9	16/9	16/9	16/9
117	9/5	9/5	9/5	9/5
118	729/400	405/224	88/49	70/39
119	32768/18225	3920/2187	363/200	65/36
120	2048/1125	49/27	20/11	20/11
121	1152/625	64/35	64/35	64/35
122	1875/1024	90/49	11/6	11/6
123	30375/16384	729/392	224/121	24/13
124	4000/2187	448/243	225/121	13/7
125	50/27	28/15	28/15	28/15
126	15/8	15/8	15/8	15/8
127	243/128	243/128	66/35	49/26
128	4096/2187	1372/729	121/64	91/48
129	256/135	256/135	21/11	21/11
130	48/25	40/21	40/21	40/21
131	243/125	27/14	27/14	27/14
132	19683/10000	2187/1120	121/63	25/13
133	12500/6561	784/405	64/33	39/20
134	625/324	35/18	35/18	35/18
135	125/64	63/32	63/32	63/32
136	2025/1024	486/245	55/28	55/28
137	12800/6561	2401/1215	196/99	77/39
138	160/81	160/81	160/81	143/72
139	2/1	2/1	2/1	2/1

{| class="wikitable"

|-
| | Step
| | Five limit
| | Seven limit
| | Eleven limit
| | Thirteen limit
|-
| | 1
| | 81/80
| | 81/80
| | 81/80
| | 81/80
|-
| | 2
| | 6561/6400
| | 2430/2401
| | 99/98
| | 78/77
|-
| | 3
| | 2048/2025
| | 245/243
| | 56/55
| | 56/55
|-
| | 4
| | 128/125
| | 49/48
| | 45/44
| | 45/44
|-
| | 5
| | 648/625
| | 36/35
| | 36/35
| | 36/35
|-
| | 6
| | 6561/6250
| | 405/392
| | 33/32
| | 33/32
|-
| | 7
| | 20000/19683
| | 2240/2187
| | 125/121
| | 26/25
|-
| | 8
| | 250/243
| | 28/27
| | 28/27
| | 28/27
|-
| | 9
| | 25/24
| | 21/20
| | 21/20
| | 21/20
|-
| | 10
| | 135/128
| | 135/128
| | 22/21
| | 22/21
|-
| | 11
| | 2187/2048
| | 729/686
| | 128/121
| | 96/91
|-
| | 12
| | 256/243
| | 256/243
| | 35/33
| | 35/33
|-
| | 13
| | 16/15
| | 16/15
| | 16/15
| | 16/15
|-
| | 14
| | 27/25
| | 15/14
| | 15/14
| | 15/14
|-
| | 15
| | 2187/2000
| | 243/224
| | 243/224
| | 14/13
|-
| | 16
| | 32768/30375
| | 784/729
| | 121/112
| | 13/12
|-
| | 17
| | 2048/1875
| | 49/45
| | 12/11
| | 12/11
|-
| | 18
| | 625/576
| | 35/32
| | 35/32
| | 35/32
|-
| | 19
| | 1125/1024
| | 54/49
| | 11/10
| | 11/10
|-
| | 20
| | 18225/16384
| | 2187/1960
| | 400/363
| | 72/65
|-
| | 21
| | 800/729
| | 448/405
| | 49/44
| | 39/35
|-
| | 22
| | 10/9
| | 10/9
| | 10/9
| | 10/9
|-
| | 23
| | 9/8
| | 9/8
| | 9/8
| | 9/8
|-
| | 24
| | 729/640
| | 729/640
| | 55/49
| | 55/49
|-
| | 25
| | 4096/3645
| | 1372/1215
| | 112/99
| | 44/39
|-
| | 26
| | 256/225
| | 245/216
| | 25/22
| | 25/22
|-
| | 27
| | 144/125
| | 8/7
| | 8/7
| | 8/7
|-
| | 28
| | 729/625
| | 81/70
| | 55/48
| | 55/48
|-
| | 29
| | 59049/50000
| | 3645/3136
| | 121/105
| | 15/13
|-
| | 30
| | 2500/2187
| | 280/243
| | 64/55
| | 64/55
|-
| | 31
| | 125/108
| | 7/6
| | 7/6
| | 7/6
|-
| | 32
| | 75/64
| | 75/64
| | 75/64
| | 75/64
|-
| | 33
| | 1215/1024
| | 405/343
| | 33/28
| | 13/11
|-
| | 34
| | 2560/2187
| | 1715/1458
| | 144/121
| | 77/65
|-
| | 35
| | 32/27
| | 32/27
| | 32/27
| | 32/27
|-
| | 36
| | 6/5
| | 6/5
| | 6/5
| | 6/5
|-
| | 37
| | 243/200
| | 135/112
| | 77/64
| | 77/64
|-
| | 38
| | 19683/16000
| | 2187/1792
| | 121/100
| | 63/52
|-
| | 39
| | 4096/3375
| | 98/81
| | 40/33
| | 39/32
|-
| | 40
| | 768/625
| | 49/40
| | 27/22
| | 27/22
|-
| | 41
| | 625/512
| | 60/49
| | 11/9
| | 11/9
|-
| | 42
| | 10125/8192
| | 243/196
| | 99/80
| | 16/13
|-
| | 43
| | 8000/6561
| | 896/729
| | 121/98
| | 26/21
|-
| | 44
| | 100/81
| | 56/45
| | 56/45
| | 56/45
|-
| | 45
| | 5/4
| | 5/4
| | 5/4
| | 5/4
|-
| | 46
| | 81/64
| | 81/64
| | 44/35
| | 44/35
|-
| | 47
| | 6561/5120
| | 2187/1715
| | 121/96
| | 91/72
|-
| | 48
| | 512/405
| | 343/270
| | 14/11
| | 14/11
|-
| | 49
| | 32/25
| | 32/25
| | 32/25
| | 32/25
|-
| | 50
| | 162/125
| | 9/7
| | 9/7
| | 9/7
|-
| | 51
| | 6561/5000
| | 729/560
| | 165/128
| | 50/39
|-
| | 52
| | 25000/19683
| | 1568/1215
| | 128/99
| | 13/10
|-
| | 53
| | 625/486
| | 35/27
| | 35/27
| | 35/27
|-
| | 54
| | 125/96
| | 21/16
| | 21/16
| | 21/16
|-
| | 55
| | 675/512
| | 324/245
| | 33/25
| | 33/25
|-
| | 56
| | 10935/8192
| | 3645/2744
| | 160/121
| | 117/88
|-
| | 57
| | 320/243
| | 320/243
| | 147/110
| | 65/49
|-
| | 58
| | 4/3
| | 4/3
| | 4/3
| | 4/3
|-
| | 59
| | 27/20
| | 27/20
| | 27/20
| | 27/20
|-
| | 60
| | 2187/1600
| | 1215/896
| | 66/49
| | 35/26
|-
| | 61
| | 8192/6075
| | 980/729
| | 224/165
| | 65/48
|-
| | 62
| | 512/375
| | 49/36
| | 15/11
| | 15/11
|-
| | 63
| | 864/625
| | 48/35
| | 48/35
| | 48/35
|-
| | 64
| | 4374/3125
| | 135/98
| | 11/8
| | 11/8
|-
| | 65
| | 80000/59049
| | 2187/1568
| | 168/121
| | 18/13
|-
| | 66
| | 1000/729
| | 112/81
| | 112/81
| | 39/28
|-
| | 67
| | 25/18
| | 7/5
| | 7/5
| | 7/5
|-
| | 68
| | 45/32
| | 45/32
| | 45/32
| | 45/32
|-
| | 69
| | 729/512
| | 486/343
| | 99/70
| | 78/55
|-
| | 70
| | 1024/729
| | 343/243
| | 140/99
| | 55/39
|-
| | 71
| | 64/45
| | 64/45
| | 63/44
| | 63/44
|-
| | 72
| | 36/25
| | 10/7
| | 10/7
| | 10/7
|-
| | 73
| | 729/500
| | 81/56
| | 81/56
| | 56/39
|-
| | 74
| | 59049/40000
| | 3136/2187
| | 121/84
| | 13/9
|-
| | 75
| | 3125/2187
| | 196/135
| | 16/11
| | 16/11
|-
| | 76
| | 625/432
| | 35/24
| | 35/24
| | 35/24
|-
| | 77
| | 375/256
| | 72/49
| | 22/15
| | 22/15
|-
| | 78
| | 6075/4096
| | 729/490
| | 165/112
| | 65/44
|-
| | 79
| | 3200/2187
| | 1792/1215
| | 49/33
| | 49/33
|-
| | 80
| | 40/27
| | 40/27
| | 40/27
| | 40/27
|-
| | 81
| | 3/2
| | 3/2
| | 3/2
| | 3/2
|-
| | 82
| | 243/160
| | 243/160
| | 121/81
| | 98/65
|-
| | 83
| | 16384/10935
| | 3645/2401
| | 121/80
| | 91/60
|-
| | 84
| | 1024/675
| | 245/162
| | 50/33
| | 50/33
|-
| | 85
| | 192/125
| | 32/21
| | 32/21
| | 32/21
|-
| | 86
| | 972/625
| | 54/35
| | 54/35
| | 54/35
|-
| | 87
| | 19683/12500
| | 1215/784
| | 99/64
| | 20/13
|-
| | 88
| | 10000/6561
| | 1120/729
| | 189/121
| | 39/25
|-
| | 89
| | 125/81
| | 14/9
| | 14/9
| | 14/9
|-
| | 90
| | 25/16
| | 25/16
| | 25/16
| | 25/16
|-
| | 91
| | 405/256
| | 405/256
| | 11/7
| | 11/7
|-
| | 92
| | 6561/4096
| | 2187/1372
| | 192/121
| | 144/91
|-
| | 93
| | 128/81
| | 128/81
| | 35/22
| | 35/22
|-
| | 94
| | 8/5
| | 8/5
| | 8/5
| | 8/5
|-
| | 95
| | 81/50
| | 45/28
| | 45/28
| | 45/28
|-
| | 96
| | 6561/4000
| | 729/448
| | 121/75
| | 21/13
|-
| | 97
| | 16384/10125
| | 392/243
| | 160/99
| | 13/8
|-
| | 98
| | 1024/625
| | 49/30
| | 18/11
| | 18/11
|-
| | 99
| | 625/384
| | 80/49
| | 44/27
| | 44/27
|-
| | 100
| | 3375/2048
| | 81/49
| | 33/20
| | 33/20
|-
| | 101
| | 32000/19683
| | 2401/1458
| | 200/121
| | 104/63
|-
| | 102
| | 400/243
| | 224/135
| | 128/77
| | 117/70
|-
| | 103
| | 5/3
| | 5/3
| | 5/3
| | 5/3
|-
| | 104
| | 27/16
| | 27/16
| | 27/16
| | 27/16
|-
| | 105
| | 2187/1280
| | 2187/1280
| | 121/72
| | 91/54
|-
| | 106
| | 2048/1215
| | 686/405
| | 56/33
| | 22/13
|-
| | 107
| | 128/75
| | 128/75
| | 75/44
| | 75/44
|-
| | 108
| | 216/125
| | 12/7
| | 12/7
| | 12/7
|-
| | 109
| | 2187/1250
| | 243/140
| | 55/32
| | 55/32
|-
| | 110
| | ?
| | 6272/3645
| | 121/70
| | 26/15
|-
| | 111
| | 1250/729
| | 140/81
| | 96/55
| | 96/55
|-
| | 112
| | 125/72
| | 7/4
| | 7/4
| | 7/4
|-
| | 113
| | 225/128
| | 225/128
| | 44/25
| | 44/25
|-
| | 114
| | 3645/2048
| | 1215/686
| | 99/56
| | 39/22
|-
| | 115
| | 1280/729
| | 1280/729
| | 98/55
| | 98/55
|-
| | 116
| | 16/9
| | 16/9
| | 16/9
| | 16/9
|-
| | 117
| | 9/5
| | 9/5
| | 9/5
| | 9/5
|-
| | 118
| | 729/400
| | 405/224
| | 88/49
| | 70/39
|-
| | 119
| | 32768/18225
| | 3920/2187
| | 363/200
| | 65/36
|-
| | 120
| | 2048/1125
| | 49/27
| | 20/11
| | 20/11
|-
| | 121
| | 1152/625
| | 64/35
| | 64/35
| | 64/35
|-
| | 122
| | 1875/1024
| | 90/49
| | 11/6
| | 11/6
|-
| | 123
| | 30375/16384
| | 729/392
| | 224/121
| | 24/13
|-
| | 124
| | 4000/2187
| | 448/243
| | 225/121
| | 13/7
|-
| | 125
| | 50/27
| | 28/15
| | 28/15
| | 28/15
|-
| | 126
| | 15/8
| | 15/8
| | 15/8
| | 15/8
|-
| | 127
| | 243/128
| | 243/128
| | 66/35
| | 49/26
|-
| | 128
| | 4096/2187
| | 1372/729
| | 121/64
| | 91/48
|-
| | 129
| | 256/135
| | 256/135
| | 21/11
| | 21/11
|-
| | 130
| | 48/25
| | 40/21
| | 40/21
| | 40/21
|-
| | 131
| | 243/125
| | 27/14
| | 27/14
| | 27/14
|-
| | 132
| | 19683/10000
| | 2187/1120
| | 121/63
| | 25/13
|-
| | 133
| | 12500/6561
| | 784/405
| | 64/33
| | 39/20
|-
| | 134
| | 625/324
| | 35/18
| | 35/18
| | 35/18
|-
| | 135
| | 125/64
| | 63/32
| | 63/32
| | 63/32
|-
| | 136
| | 2025/1024
| | 486/245
| | 55/28
| | 55/28
|-
| | 137
| | 12800/6561
| | 2401/1215
| | 196/99
| | 77/39
|-
| | 138
| | 160/81
| | 160/81
| | 160/81
| | 143/72
|-
| | 139
| | 2/1
| | 2/1
| | 2/1
| | 2/1
|}

139edo

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