275edo
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275edo uses a step size of 4.3636363636364 cents, and is a commatonal and nanotonal EDO. It can be thought of as eleven sets of 25edo, or as 55edo with a five times smaller step size. Divisors are {{#rreplace: 275 55 25 11 5 1|/(\d+)(\D+)?/|\1\2}}. It is consistent and uniquely consistent in the 9-odd-limit.
Step | Five limit | Seven limit | Eleven limit | Thirteen limit |
1 | 78732/78125 | 2400/2401 | 176/175 | 176/175 |
2 | 32805/32768 | 126/125 | 121/120 | 121/120 |
3 | 2048/2025 | 225/224 | 225/224 | 144/143 |
4 | 15625/15552 | 4000/3969 | 99/98 | 91/90 |
5 | 81/80 | 81/80 | 81/80 | 66/65 |
6 | ? | 64/63 | 64/63 | 64/63 |
7 | 20000/19683 | 3125/3087 | 55/54 | 55/54 |
8 | 128/125 | 49/48 | 49/48 | 49/48 |
9 | 3125/3072 | 50/49 | 50/49 | 50/49 |
10 | 6561/6400 | 1029/1000 | 45/44 | 40/39 |
11 | ? | 36/35 | 36/35 | 36/35 |
12 | 250/243 | 250/243 | 33/32 | 33/32 |
13 | 648/625 | 648/625 | 363/350 | 65/63 |
14 | 16875/16384 | 28/27 | 28/27 | 28/27 |
15 | 20480/19683 | 3125/3024 | 125/121 | 26/25 |
16 | 16384/15625 | 392/375 | 80/77 | 80/77 |
17 | 25/24 | 25/24 | 25/24 | 25/24 |
18 | 6561/6250 | 2500/2401 | 22/21 | 22/21 |
19 | ? | 21/20 | 21/20 | 21/20 |
20 | 256/243 | 256/243 | 132/125 | 104/99 |
21 | 82944/78125 | 1323/1250 | 81/77 | 81/77 |
22 | 135/128 | 135/128 | 135/128 | 55/52 |
23 | ? | 200/189 | 128/121 | 128/121 |
24 | 62500/59049 | 1701/1600 | 35/33 | 35/33 |
25 | 16/15 | 16/15 | 16/15 | 16/15 |
26 | 78125/73728 | 625/588 | 77/72 | 77/72 |
27 | 2187/2048 | 343/320 | 242/225 | 125/117 |
28 | 32768/30375 | 15/14 | 15/14 | 15/14 |
29 | 3125/2916 | 3125/2916 | 189/176 | 14/13 |
30 | 27/25 | 27/25 | 27/25 | 27/25 |
31 | ? | 175/162 | 175/162 | 175/162 |
32 | 64000/59049 | 3402/3125 | 88/81 | 13/12 |
33 | 2048/1875 | 49/45 | 49/45 | 49/45 |
34 | 625/576 | 160/147 | 160/147 | 160/147 |
35 | 2187/2000 | 686/625 | 12/11 | 12/11 |
36 | ? | 35/32 | 35/32 | 35/32 |
37 | 800/729 | 375/343 | 11/10 | 11/10 |
38 | 3456/3125 | 441/400 | 441/400 | 100/91 |
39 | 1125/1024 | 54/49 | 54/49 | 54/49 |
40 | 65536/59049 | 625/567 | 243/220 | 72/65 |
41 | ? | 567/512 | 256/231 | 231/208 |
42 | 10/9 | 10/9 | 10/9 | 10/9 |
43 | 17496/15625 | 8000/7203 | 49/44 | 39/35 |
44 | 18225/16384 | 28/25 | 28/25 | 28/25 |
45 | 4096/3645 | 125/112 | 125/112 | 125/112 |
46 | 78125/69984 | 3528/3125 | 55/49 | 55/49 |
47 | 9/8 | 9/8 | 9/8 | 9/8 |
48 | ? | 640/567 | 198/175 | 147/130 |
49 | ? | 567/500 | 112/99 | 112/99 |
50 | 256/225 | 245/216 | 245/216 | 143/126 |
51 | 15625/13824 | 500/441 | 154/135 | 91/80 |
52 | 729/640 | 343/300 | 25/22 | 25/22 |
53 | ? | 8/7 | 8/7 | 8/7 |
54 | 2500/2187 | 2500/2187 | 55/48 | 55/48 |
55 | 144/125 | 144/125 | 121/105 | 121/105 |
56 | 9375/8192 | 225/196 | 225/196 | 169/147 |
57 | 59049/51200 | 9261/8000 | 343/297 | 15/13 |
58 | 32768/28125 | 81/70 | 81/70 | 81/70 |
59 | 125/108 | 125/108 | 125/108 | 121/104 |
60 | 729/625 | 729/625 | 64/55 | 64/55 |
61 | ? | 7/6 | 7/6 | 7/6 |
62 | 2560/2187 | 400/343 | 88/75 | 88/75 |
63 | 18432/15625 | 147/125 | 90/77 | 90/77 |
64 | 75/64 | 75/64 | 75/64 | 75/64 |
65 | 59049/50000 | 2000/1701 | 33/28 | 33/28 |
66 | ? | 189/160 | 189/160 | 77/65 |
67 | 32/27 | 32/27 | 32/27 | 13/11 |
68 | 93312/78125 | 3125/2646 | 196/165 | 108/91 |
69 | 1215/1024 | 343/288 | 343/288 | 143/120 |
70 | 65536/54675 | 25/21 | 25/21 | 25/21 |
71 | 15625/13122 | 2401/2000 | 105/88 | 105/88 |
72 | 6/5 | 6/5 | 6/5 | 6/5 |
73 | 78125/65536 | 875/729 | 77/64 | 77/64 |
74 | 19683/16384 | 756/625 | 121/100 | 65/54 |
75 | 4096/3375 | 98/81 | 98/81 | 98/81 |
76 | 3125/2592 | 1600/1323 | 297/245 | 63/52 |
77 | 243/200 | 243/200 | 40/33 | 40/33 |
78 | ? | 128/105 | 128/105 | 128/105 |
79 | 8000/6561 | 1250/1029 | 11/9 | 11/9 |
80 | 768/625 | 49/40 | 49/40 | 49/40 |
81 | 625/512 | 60/49 | 60/49 | 60/49 |
82 | 19683/16000 | 3087/2500 | 27/22 | 16/13 |
83 | ? | 216/175 | 121/98 | 121/98 |
84 | 100/81 | 100/81 | 99/80 | 99/80 |
85 | 3888/3125 | 3888/3125 | 245/198 | 26/21 |
86 | 10125/8192 | 56/45 | 56/45 | 56/45 |
87 | 8192/6561 | 625/504 | 150/121 | 81/65 |
88 | 98304/78125 | 784/625 | 96/77 | 96/77 |
89 | 5/4 | 5/4 | 5/4 | 5/4 |
90 | 19683/15625 | 3000/2401 | 44/35 | 44/35 |
91 | ? | 63/50 | 63/50 | 63/50 |
92 | 512/405 | 432/343 | 432/343 | 180/143 |
93 | 78125/62208 | 3969/3125 | 308/243 | 91/72 |
94 | 81/64 | 81/64 | 81/64 | 33/26 |
95 | ? | 80/63 | 80/63 | 80/63 |
96 | 25000/19683 | 2401/1875 | 14/11 | 14/11 |
97 | 32/25 | 32/25 | 32/25 | 32/25 |
98 | 15625/12288 | 125/98 | 77/60 | 77/60 |
99 | 6561/5120 | 1029/800 | 225/176 | 50/39 |
100 | 65536/50625 | 9/7 | 9/7 | 9/7 |
101 | 625/486 | 625/486 | 165/128 | 84/65 |
102 | 162/125 | 162/125 | 128/99 | 128/99 |
103 | 84375/65536 | 35/27 | 35/27 | 35/27 |
104 | 25600/19683 | 4000/3087 | 176/135 | 13/10 |
105 | 4096/3125 | 98/75 | 98/75 | 98/75 |
106 | 125/96 | 64/49 | 64/49 | 64/49 |
107 | 6561/5000 | 3125/2401 | 55/42 | 55/42 |
108 | ? | 21/16 | 21/16 | 21/16 |
109 | 320/243 | 320/243 | 33/25 | 33/25 |
110 | 20736/15625 | 1323/1000 | 392/297 | 120/91 |
111 | 675/512 | 324/245 | 324/245 | 143/108 |
112 | ? | 250/189 | 160/121 | 121/91 |
113 | 78125/59049 | 1701/1280 | 175/132 | 65/49 |
114 | 4/3 | 4/3 | 4/3 | 4/3 |
115 | ? | 3125/2352 | 147/110 | 147/110 |
116 | 10935/8192 | 168/125 | 121/90 | 121/90 |
117 | 8192/6075 | 75/56 | 75/56 | 75/56 |
118 | 15625/11664 | 15625/11664 | 66/49 | 35/26 |
119 | 27/20 | 27/20 | 27/20 | 27/20 |
120 | ? | 256/189 | 256/189 | 104/77 |
121 | 80000/59049 | 1701/1250 | 110/81 | 65/48 |
122 | 512/375 | 49/36 | 49/36 | 49/36 |
123 | 3125/2304 | 200/147 | 200/147 | 200/147 |
124 | 2187/1600 | 343/250 | 15/11 | 15/11 |
125 | ? | 48/35 | 48/35 | 48/35 |
126 | 1000/729 | 1000/729 | 11/8 | 11/8 |
127 | 864/625 | 441/320 | 242/175 | 125/91 |
128 | 5625/4096 | 112/81 | 112/81 | 91/66 |
129 | 81920/59049 | 3125/2268 | 243/176 | 18/13 |
130 | 65536/46875 | 243/175 | 243/175 | 243/175 |
131 | 25/18 | 25/18 | 25/18 | 25/18 |
132 | 4374/3125 | 4374/3125 | 88/63 | 39/28 |
133 | 91125/65536 | 7/5 | 7/5 | 7/5 |
134 | 1024/729 | 480/343 | 176/125 | 169/121 |
135 | ? | 882/625 | 108/77 | 108/77 |
136 | 45/32 | 45/32 | 45/32 | 45/32 |
137 | ? | 800/567 | 99/70 | 99/70 |
138 | ? | 567/400 | 140/99 | 140/99 |
139 | 64/45 | 64/45 | 64/45 | 64/45 |
140 | 78125/55296 | 625/441 | 77/54 | 77/54 |
141 | 729/512 | 343/240 | 125/88 | 125/88 |
142 | ? | 10/7 | 10/7 | 10/7 |
143 | 3125/2187 | 3125/2187 | 63/44 | 56/39 |
144 | 36/25 | 36/25 | 36/25 | 36/25 |
145 | 46875/32768 | 350/243 | 231/160 | 231/160 |
146 | 59049/40960 | 4536/3125 | 352/243 | 13/9 |
147 | 8192/5625 | 81/56 | 81/56 | 81/56 |
148 | 625/432 | 625/432 | 175/121 | 175/121 |
149 | 729/500 | 729/500 | 16/11 | 16/11 |
150 | ? | 35/24 | 35/24 | 35/24 |
151 | 3200/2187 | 500/343 | 22/15 | 22/15 |
152 | 4608/3125 | 147/100 | 147/100 | 147/100 |
153 | 375/256 | 72/49 | 72/49 | 72/49 |
154 | 59049/40000 | 2500/1701 | 81/55 | 81/55 |
155 | ? | 189/128 | 189/128 | 77/52 |
156 | 40/27 | 40/27 | 40/27 | 40/27 |
157 | 23328/15625 | 11907/8000 | 49/33 | 49/33 |
158 | 6075/4096 | 112/75 | 112/75 | 112/75 |
159 | 16384/10935 | 125/84 | 125/84 | 125/84 |
160 | 78125/52488 | 2401/1600 | 220/147 | 175/117 |
161 | 3/2 | 3/2 | 3/2 | 3/2 |
162 | ? | 2560/1701 | 264/175 | 98/65 |
163 | 98415/65536 | 189/125 | 121/80 | 121/80 |
164 | 1024/675 | 245/162 | 245/162 | 169/112 |
165 | 15625/10368 | 2000/1323 | 297/196 | 91/60 |
166 | 243/160 | 243/160 | 50/33 | 50/33 |
167 | ? | 32/21 | 32/21 | 32/21 |
168 | 10000/6561 | 3125/2058 | 55/36 | 55/36 |
169 | 192/125 | 49/32 | 49/32 | 49/32 |
170 | 3125/2048 | 75/49 | 75/49 | 75/49 |
171 | 19683/12800 | 3087/2000 | 135/88 | 20/13 |
172 | ? | 54/35 | 54/35 | 54/35 |
173 | 125/81 | 125/81 | 99/64 | 99/64 |
174 | 972/625 | 972/625 | 256/165 | 65/42 |
175 | 50625/32768 | 14/9 | 14/9 | 14/9 |
176 | 10240/6561 | 1600/1029 | 343/220 | 39/25 |
177 | 24576/15625 | 196/125 | 120/77 | 120/77 |
178 | 25/16 | 25/16 | 25/16 | 25/16 |
179 | 19683/12500 | 3750/2401 | 11/7 | 11/7 |
180 | ? | 63/40 | 63/40 | 63/40 |
181 | 128/81 | 128/81 | 128/81 | 52/33 |
182 | ? | 3969/2500 | 243/154 | 144/91 |
183 | 405/256 | 343/216 | 343/216 | 143/90 |
184 | ? | 100/63 | 100/63 | 100/63 |
185 | 31250/19683 | 2401/1500 | 35/22 | 35/22 |
186 | 8/5 | 8/5 | 8/5 | 8/5 |
187 | 78125/49152 | 625/392 | 77/48 | 77/48 |
188 | 6561/4096 | 1008/625 | 121/75 | 121/75 |
189 | 16384/10125 | 45/28 | 45/28 | 45/28 |
190 | 3125/1944 | 3125/1944 | 396/245 | 21/13 |
191 | 81/50 | 81/50 | 81/50 | 81/50 |
192 | ? | 175/108 | 175/108 | 175/108 |
193 | 32000/19683 | 5000/3087 | 44/27 | 13/8 |
194 | 1024/625 | 49/30 | 49/30 | 49/30 |
195 | 625/384 | 80/49 | 80/49 | 80/49 |
196 | 6561/4000 | 1029/625 | 18/11 | 18/11 |
197 | ? | 105/64 | 105/64 | 105/64 |
198 | 400/243 | 400/243 | 33/20 | 33/20 |
199 | 5184/3125 | 1323/800 | 490/297 | 104/63 |
200 | 3375/2048 | 81/49 | 81/49 | 81/49 |
201 | 32768/19683 | 625/378 | 200/121 | 108/65 |
202 | ? | 1458/875 | 128/77 | 128/77 |
203 | 5/3 | 5/3 | 5/3 | 5/3 |
204 | 26244/15625 | 4000/2401 | 147/88 | 117/70 |
205 | 54675/32768 | 42/25 | 42/25 | 42/25 |
206 | 2048/1215 | 375/224 | 375/224 | 240/143 |
207 | 78125/46656 | 5292/3125 | 165/98 | 91/54 |
208 | 27/16 | 27/16 | 27/16 | 22/13 |
209 | ? | 320/189 | 297/175 | 130/77 |
210 | ? | 1701/1000 | 56/33 | 56/33 |
211 | 128/75 | 128/75 | 128/75 | 128/75 |
212 | 15625/9216 | 250/147 | 77/45 | 77/45 |
213 | 2187/1280 | 343/200 | 75/44 | 75/44 |
214 | ? | 12/7 | 12/7 | 12/7 |
215 | 1250/729 | 1250/729 | 55/32 | 55/32 |
216 | 216/125 | 216/125 | 121/70 | 121/70 |
217 | 28125/16384 | 140/81 | 140/81 | 140/81 |
218 | ? | 15625/9072 | 343/198 | 26/15 |
219 | 16384/9375 | 243/140 | 243/140 | 243/140 |
220 | 125/72 | 125/72 | 125/72 | 125/72 |
221 | 2187/1250 | 2187/1250 | 96/55 | 96/55 |
222 | ? | 7/4 | 7/4 | 7/4 |
223 | 1280/729 | 600/343 | 44/25 | 44/25 |
224 | 27648/15625 | 441/250 | 135/77 | 135/77 |
225 | 225/128 | 225/128 | 225/128 | 143/81 |
226 | ? | 1000/567 | 99/56 | 99/56 |
227 | ? | 567/320 | 175/99 | 175/99 |
228 | 16/9 | 16/9 | 16/9 | 16/9 |
229 | ? | 3125/1764 | 98/55 | 98/55 |
230 | 3645/2048 | 224/125 | 224/125 | 143/80 |
231 | 32768/18225 | 25/14 | 25/14 | 25/14 |
232 | 15625/8748 | 7203/4000 | 88/49 | 70/39 |
233 | 9/5 | 9/5 | 9/5 | 9/5 |
234 | ? | 875/486 | 231/128 | 231/128 |
235 | 59049/32768 | 1134/625 | 363/200 | 65/36 |
236 | 2048/1125 | 49/27 | 49/27 | 49/27 |
237 | 3125/1728 | 800/441 | 800/441 | 91/50 |
238 | 729/400 | 686/375 | 20/11 | 20/11 |
239 | ? | 64/35 | 64/35 | 64/35 |
240 | 4000/2187 | 625/343 | 11/6 | 11/6 |
241 | 1152/625 | 147/80 | 147/80 | 147/80 |
242 | 1875/1024 | 90/49 | 90/49 | 90/49 |
243 | 59049/32000 | 3125/1701 | 81/44 | 24/13 |
244 | ? | 324/175 | 324/175 | 324/175 |
245 | 50/27 | 50/27 | 50/27 | 50/27 |
246 | 5832/3125 | 5832/3125 | 245/132 | 13/7 |
247 | 30375/16384 | 28/15 | 28/15 | 28/15 |
248 | 4096/2187 | 625/336 | 225/121 | 225/121 |
249 | ? | 1176/625 | 144/77 | 144/77 |
250 | 15/8 | 15/8 | 15/8 | 15/8 |
251 | 59049/31250 | 3200/1701 | 66/35 | 49/26 |
252 | ? | 189/100 | 121/64 | 121/64 |
253 | 256/135 | 256/135 | 256/135 | 104/55 |
254 | 78125/41472 | 2500/1323 | 154/81 | 91/48 |
255 | 243/128 | 243/128 | 125/66 | 99/52 |
256 | ? | 40/21 | 40/21 | 40/21 |
257 | 12500/6561 | 2401/1250 | 21/11 | 21/11 |
258 | 48/25 | 48/25 | 48/25 | 48/25 |
259 | 15625/8192 | 375/196 | 77/40 | 77/40 |
260 | 19683/10240 | 3087/1600 | 242/125 | 25/13 |
261 | 32768/16875 | 27/14 | 27/14 | 27/14 |
262 | 625/324 | 625/324 | 495/256 | 126/65 |
263 | 243/125 | 243/125 | 64/33 | 64/33 |
264 | ? | 35/18 | 35/18 | 35/18 |
265 | 12800/6561 | 2000/1029 | 88/45 | 39/20 |
266 | 6144/3125 | 49/25 | 49/25 | 49/25 |
267 | 125/64 | 96/49 | 96/49 | 96/49 |
268 | 19683/10000 | 6174/3125 | 55/28 | 55/28 |
269 | ? | 63/32 | 63/32 | 63/32 |
270 | 160/81 | 160/81 | 99/50 | 65/33 |
271 | 31104/15625 | 3969/2000 | 196/99 | 180/9
1 |
272 | 2025/1024 | 448/225 | 448/225 | 143/72 |
273 | 65536/32805 | 125/63 | 125/63 | 125/63 |
274 | 78125/39366 | 2401/1200 | 175/88 | 175/88 |
275 | 2/1 | 2/1 | 2/1 | 2/1 |