213edo

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213edo uses a step size of 5.6338028169014 cents, and is a commatonal EDO. It can be thought of as three sets of 71edo. Divisors are {{#rreplace: 213 71 3 1|/(\d+)(\D+)?/|\1\2}}. It is consistent and uniquely consistent in the 7-odd-limit.

Step Five limit Seven limit Eleven limit Thirteen limit
1 2048/2025 245/243 176/175 169/168
2 15625/15552 126/125 121/120 91/90
3 20000/19683 225/224 100/99 100/99
4 32805/32768 64/63 64/63 64/63
5 81/80 81/80 55/54 55/54
6 128/125 49/48 49/48 49/48
7 3125/3072 50/49 50/49 50/49
8 250/243 250/243 45/44 40/39
9 20480/19683 36/35 36/35 36/35
10 6561/6400 28/27 28/27 28/27
11 648/625 648/625 125/121 26/25
12 16384/15625 392/375 80/77 80/77
13 25/24 25/24 25/24 25/24
14 256/243 256/243 22/21 22/21
15 ? 21/20 21/20 21/20
16 6561/6250 343/324 132/125 132/125
17 82944/78125 200/189 81/77 81/77
18 135/128 135/128 35/33 35/33
19 16/15 16/15 16/15 16/15
20 32768/30375 625/588 77/72 77/72
21 3125/2916 343/320 242/225 125/117
22 64000/59049 15/14 15/14 15/14
23 2187/2048 175/162 175/162 14/13
24 27/25 27/25 27/25 13/12
25 2048/1875 49/45 49/45 49/45
26 625/576 160/147 160/147 160/147
27 800/729 243/224 12/11 12/11
28 65536/59049 35/32 35/32 35/32
29 2187/2000 375/343 11/10 11/10
30 3456/3125 441/400 400/363 100/91
31 1125/1024 54/49 54/49 54/49
32 10/9 10/9 10/9 10/9
33 4096/3645 567/512 49/44 39/35
34 78125/69984 28/25 28/25 28/25
35 17496/15625 125/112 125/112 125/112
36 18225/16384 640/567 55/49 55/49
37 9/8 9/8 9/8 9/8
38 256/225 245/216 198/175 143/126
39 15625/13824 500/441 154/135 91/80
40 2500/2187 343/300 25/22 25/22
41 ? 8/7 8/7 8/7
42 729/640 280/243 55/48 55/48
43 144/125 144/125 121/105 52/45
44 9375/8192 225/196 225/196 225/196
45 125/108 125/108 125/108 15/13
46 2560/2187 81/70 64/55 64/55
47 59049/51200 7/6 7/6 7/6
48 729/625 400/343 88/75 88/75
49 18432/15625 147/125 90/77 90/77
50 75/64 75/64 75/64 75/64
51 32/27 32/27 32/27 13/11
52 65536/54675 189/160 189/160 77/65
53 15625/13122 343/288 297/250 143/120
54 93312/78125 25/21 25/21 25/21
55 1215/1024 875/729 105/88 105/88
56 6/5 6/5 6/5 6/5
57 4096/3375 98/81 77/64 77/64
58 3125/2592 756/625 121/100 91/75
59 8000/6561 135/112 40/33 40/33
60 19683/16384 128/105 128/105 63/52
61 243/200 243/200 11/9 11/9
62 768/625 49/40 49/40 49/40
63 625/512 60/49 60/49 60/49
64 100/81 100/81 27/22 16/13
65 8192/6561 216/175 121/98 26/21
66 19683/16000 56/45 56/45 56/45
67 3888/3125 625/504 150/121 150/121
68 10125/8192 243/196 96/77 96/77
69 5/4 5/4 5/4 5/4
70 512/405 512/405 44/35 44/35
71 78125/62208 63/50 63/50 63/50
72 19683/15625 343/270 125/99 125/99
73 ? 80/63 80/63 80/63
74 81/64 81/64 14/11 14/11
75 32/25 32/25 32/25 32/25
76 15625/12288 125/98 77/60 77/60
77 625/486 625/486 225/176 50/39
78 25600/19683 9/7 9/7 9/7
79 6561/5120 35/27 35/27 35/27
80 162/125 162/125 162/125 13/10
81 4096/3125 98/75 98/75 98/75
82 125/96 64/49 64/49 64/49
83 320/243 320/243 55/42 55/42
84 ? 21/16 21/16 21/16
85 6561/5000 450/343 33/25 33/25
86 20736/15625 250/189 160/121 120/91
87 675/512 324/245 175/132 65/49
88 4/3 4/3 4/3 4/3
89 8192/6075 980/729 147/110 147/110
90 15625/11664 168/125 121/90 121/90
91 80000/59049 75/56 75/56 75/56
92 10935/8192 256/189 66/49 35/26
93 27/20 27/20 27/20 27/20
94 512/375 49/36 49/36 49/36
95 3125/2304 200/147 200/147 200/147
96 1000/729 343/250 15/11 15/11
97 81920/59049 48/35 48/35 48/35
98 2187/1600 112/81 11/8 11/8
99 864/625 441/320 242/175 104/75
100 5625/4096 135/98 135/98 135/98
101 25/18 25/18 25/18 18/13
102 1024/729 243/175 88/63 39/28
103 ? 7/5 7/5 7/5
104 4374/3125 343/243 176/125 169/120
105 91125/65536 800/567 108/77 108/77
106 45/32 45/32 45/32 45/32
107 64/45 64/45 64/45 64/45
108 78125/55296 567/400 77/54 77/54
109 3125/2187 343/240 125/88 125/88
110 ? 10/7 10/7 10/7
111 729/512 350/243 63/44 56/39
112 36/25 36/25 36/25 13/9
113 8192/5625 196/135 196/135 196/135
114 625/432 625/432 175/121 75/52
115 3200/2187 81/56 16/11 16/11
116 59049/40960 35/24 35/24 35/24
117 729/500 500/343 22/15 22/15
118 4608/3125 147/100 147/100 147/100
119 375/256 72/49 72/49 72/49
120 40/27 40/27 40/27 40/27
121 16384/10935 189/128 49/33 49/33
122 59049/40000 112/75 112/75 112/75
123 23328/15625 125/84 125/84 125/84
124 6075/4096 729/490 220/147 175/117
125 3/2 3/2 3/2 3/2
126 1024/675 245/162 245/162 98/65
127 15625/10368 189/125 121/80 91/60
128 10000/6561 343/225 50/33 50/33
129 98415/65536 32/21 32/21 32/21
130 243/160 243/160 55/36 55/36
131 192/125 49/32 49/32 49/32
132 3125/2048 75/49 75/49 75/49
133 125/81 125/81 125/81 20/13
134 10240/6561 54/35 54/35 54/35
135 19683/12800 14/9 14/9 14/9
136 972/625 972/62

5

343/220 39/25
137 24576/15625 196/125 120/77 120/77
138 25/16 25/16 25/16 25/16
139 128/81 128/81 11/7 11/7
140 ? 63/40 63/40 63/40
141 19683/12500 343/216 198/125 143/90
142 ? 100/63 100/63 100/63
143 405/256 405/256 35/22 35/22
144 8/5 8/5 8/5 8/5
145 16384/10125 392/243 77/48 77/48
146 3125/1944 1008/625 121/75 121/75
147 32000/19683 45/28 45/28 45/28
148 6561/4096 175/108 175/108 21/13
149 81/50 81/50 44/27 13/8
150 1024/625 49/30 49/30 49/30
151 625/384 80/49 80/49 80/49
152 400/243 400/243 18/11 18/11
153 32768/19683 105/64 105/64 104/63
154 6561/4000 224/135 33/20 33/20
155 5184/3125 625/378 200/121 150/91
156 3375/2048 81/49 81/49 81/49
157 5/3 5/3 5/3 5/3
158 2048/1215 1225/729 147/88 117/70
159 78125/46656 42/25 42/25 42/25
160 26244/15625 375/224 375/224 169/100
161 54675/32768 320/189 165/98 130/77
162 27/16 27/16 27/16 22/13
163 128/75 128/75 128/75 128/75
164 15625/9216 250/147 77/45 77/45
165 1250/729 343/200 75/44 75/44
166 ? 12/7 12/7 12/7
167 2187/1280 140/81 55/32 55/32
168 216/125 216/125 121/70 26/15
169 16384/9375 392/225 392/225 392/225
170 125/72 125/72 125/72 45/26
171 1280/729 243/140 96/55 96/55
172 ? 7/4 7/4 7/4
173 2187/1250 600/343 44/25 44/25
174 27648/15625 441/250 135/77 135/77
175 225/128 225/128 175/99 175/99
176 16/9 16/9 16/9 16/9
177 32768/18225 567/320 98/55 98/55
178 15625/8748 224/125 224/125 143/80
179 ? 25/14 25/14 25/14
180 3645/2048 875/486 88/49 70/39
181 9/5 9/5 9/5 9/5
182 2048/1125 49/27 49/27 49/27
183 3125/1728 800/441 363/200 91/50
184 4000/2187 405/224 20/11 20/11
185 59049/32768 64/35 64/35 64/35
186 729/400 448/243 11/6 11/6
187 1152/625 147/80 147/80 147/80
188 1875/1024 90/49 90/49 90/49
189 50/27 50/27 50/27 24/13
190 4096/2187 324/175 245/132 13/7
191 59049/32000 28/15 28/15 28/15
192 5832/3125 625/336 225/121 169/90
193 30375/16384 729/392 144/77 144/77
194 15/8 15/8 15/8 15/8
195 256/135 256/135 66/35 49/26
196 78125/41472 189/100 121/64 91/48
197 12500/6561 343/180 125/66 125/66
198 ? 40/21 40/21 40/21
199 243/128 243/128 21/11 21/11
200 48/25 48/25 48/25 48/25
201 15625/8192 375/196 77/40 77/40
202 625/324 625/324 242/125 25/13
203 12800/6561 27/14 27/14 27/14
204 19683/10240 35/18 35/18 35/18
205 243/125 243/125 88/45 39/20
206 6144/3125 49/25 49/25 49/25
207 125/64 96/49 96/49 96/49
208 160/81 160/81 55/28 55/28
209 65536/32805 63/32 63/32 63/32
210 19683/10000 448/225 99/50 99/50
211 31104/15625 125/63 125/63 125/63
212 2025/1024 486/245 175/88 175/88
213 2/1 2/1 2/1 2/1