256edo

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Welcome to 256edo. You might notice this EDO of a step size of 4.6875, aside from being commatonal and nanotonal, is a power of two, and the information about a note in a single octave fits within an 8-bit byte. Divisors are {{#rreplace: 256 128 64 32 16 8 4 2 1|/(\d+)(\D+)?/|\1\2}}. It therefore might not be unusual to see this tuning, or a multiple of it, in applications storing logarithmic frequencies. It is not consistent in the 5-odd-limit. It is contorted in 5-limit.

Step Five limit Seven limit Eleven limit Thirteen limit
1 ? 225/224 225/224 169/168
2 15552/15625 245/243 100/99 100/99
3 ? 875/864 176/175 144/143
4 2048/2025 2048/2025 99/98 78/77
5 ? 64/63 64/63 64/63
6 81/80 50/49 50/49 50/49
7 ? 686/675 56/55 56/55
8 250/243 49/48 45/44 45/44
9 ? 525/512 352/343 40/39
10 128/125 128/125 125/121 65/63
11 ? 36/35 36/35 36/35
12 6561/6400 405/392 33/32 33/32
13 ? 28/27 28/27 28/27
14 25/24 25/24 25/24 25/24
15 ? 1875/1792 126/121 26/25
16 648/625 256/245 256/245 117/112
17 ? 360/343 22/21 22/21
18 256/243 256/243 256/243 256/243
19 ? 21/20 21/20 21/20
20 135/128 135/128 128/121 96/91
21 ? 343/324 35/33 35/33
22 3125/2916 1225/1152 132/125 132/125
23 ? 729/686 297/280 117/110
24 16/15 16/15 16/15 16/15
25 ? 15/14 15/14 15/14
26 2187/2048 784/729 275/256 275/256
27 ? 175/162 175/162 175/162
28 625/576 625/576 242/225 14/13
29 ? 672/625 121/112 13/12
30 27/25 27/25 27/25 27/25
31 ? 243/224 243/224 243/224
32 800/729 49/45 12/11 12/11
33 ? 35/32 35/32 35/32
34 1125/1024 1125/1024 400/363 100/91
35 ? 192/175 192/175 192/175
36 2187/2000 54/49 11/10 11/10
37 ? 448/405 256/231 195/176
38 10/9 10/9 10/9 10/9
39 ? 125/112 125/112 72/65
40 3456/3125 2401/2160 49/44 39/35
41 ? 384/343 352/315 143/128
42 4096/3645 2187/1960 55/49 55/49
43 ? 28/25 28/25 28/25
44 9/8 9/8 9/8 9/8
45 ? 1372/1215 112/99 44/39
46 2500/2187 245/216 25/22 25/22
47 ? 875/768 198/175 147/130
48 256/225 256/225 256/225 91/80
49 ? 8/7 8/7 8/7
50 729/640 225/196 55/48 55/48
51 ? 280/243 63/55 63/55
52 125/108 125/108 125/108 125/108
53 ? 3125/2688 121/105 15/13
54 144/125 144/125 144/125 65/56
55 ? 81/70 81/70 81/70
56 2560/2187 784/675 64/55 64/55
57 ? 7/6 7/6 7/6
58 75/64 75/64 75/64 75/64
59 ? 1024/875 350/297 117/100
60 729/625 288/245 88/75 88/75
61 ? 405/343 33/28 13/11
62 32/27 32/27 32/27 32/27
63 ? 25/21 25/21 25/21
64 1215/1024 1215/1024 144/121 77/65
65 ? 343/288 105/88 105/88
66 3125/2592 1225/1024 176/147 140/117
67 ? 448/375 448/375 65/54
68 6/5 6/5 6/5 6/5
69 ? 135/112 77/64 77/64
70 8000/6561 98/81 40/33 40/33
71 ? 175/144 175/144 175/144
72 625/512 625/512 121/100 63/52
73 ? 128/105 128/105 39/32
74 243/200 60/49 11/9 11/9
75 ? 896/729 275/224 275/224
76 100/81 49/40 27/22 27/22
77 ? 315/256 315/256 16/13
78 768/625 768/625 121/98 26/21
79 ? 216/175 154/125 154/125
80 8192/6561 243/196 99/80 99/80
81 ? 56/45 56/45 56/45
82 5/4 5/4 5/4 5/4
83 ? 1125/896 343/275 81/65
84 3888/3125 1225/972 125/99 125/99
85 ? 432/343 44/35 44/35
86 512/405 512/405 121/96 91/72
87 ? 63/50 63/50 63/50
88 81/64 81/64 81/64 81/64
89 ? 343/270 14/11 14/11
90 625/486 245/192 225/176 143/112
91 ? 2187/1715 242/189 50/39
92 32/25 32/25 32/25 32/25
93 ? 9/7 9/7 9/7
94 6561/5120 1568/1215 128/99 128/99
95 ? 35/27 35/27 35/27
96 125/96 125/96 125/96 84/65
97 ? 2048/1575 315/242 13/10
98 162/125 64/49 64/49 64/49
99 ? 450/343 55/42 55/42
100 320/243 98/75 72/55 72/55
101 ? 21/16 21/16 21/16
102 675/512 675/512 160/121 120/91
103 ? 1152/875 175/132 65/49
104 6561/5000 324/245 33/25 33/25
105 ? 896/675 297/224 117/88
106 4/3 4/3 4/3 4/3
107 ? 75/56 75/56 75/56
108 10935/8192 980/729 147/110 147/110
109 ? 343/256 343/256 192/143
110 3125/2304 3125/2304 66/49 35/26
111 ? 168/125 168/125 65/48
112 27/20 27/20 27/20 27/20
113 ? 1215/896 224/165 88/65
114 1000/729 49/36 15/11 15/11
115 ? 175/128 175/128 160/117
116 512/375 512/375 500/363 125/91
117 ? 48/35 48/35 48/35
118 2187/1600 135/98 11/8 11/8
119 ? 112/81 112/81 112/81
120 25/18 25/18 25/18 25/18
121 ? 625/448 168/121 18/13
122 864/625 864/625 245/176 39/28
123 ? 243/175 88/63 88/63
124 1024/729 1024/729 275/196 275/196
125 ? 7/5 7/5 7/5
126 45/32 45/32 45/32 45/32
127 ? 343/243 140/99 55/39
128 3125/2187 1225/864 125/88 125/88
129 ? 486/343 99/70 78/55
130 64/45 64/45 64/45 64/45
131 ? 10/7 10/7 10/7
132 729/512 729/512 275/192 275/192
133 ? 343/240 63/44 63/44
134 625/432 625/432 352/245 56/39
135 ? 896/625 121/84 13/9
136 36/25 36/25 36/25 36/25
137 ? 81/56 81/56 81/56
138 3200/2187 196/135 16/11 16/11
139 ? 35/24 35/24 35/24
140 375/256 375/256 363/250 182/125
141 ? 256/175 256/175 117/80
142 729/500 72/49 22/15 22/15
143 ? 1792/1215 165/112 65/44
144 40/27 40/27 40/27 40/27
145 ? 125/84 125/84 96/65
146 4608/3125 2401/1620 49/33 49/33
147 ? 512/343 512/343 143/96
148 15625/10368 729/490 121/81 121/81
149 ? 112/75 112/75 112/75
150 3/2 3/2 3/2 3/2
151 ? 675/448 385/256 169/112
152 10000/6561 245/162 50/33 50/33
153 ? 875/576 264/175 98/65
154 1024/675 1024/675 121/80 91/60
155 ? 32/21 32/21 32/21
156 243/160 75/49 55/36 55/36
157 ? 343/225 84/55 84/55
158 125/81 49/32 49/32 49/32
159 ? 1575/1024 484/315 20/13
160 192/125 192/125 192/125 65/42
161 ? 54/35 54/35 54/35
162 10240/6561 1215/784 99/64 99/64
163 ? 14/9 14/9 14/9
164 25/16 25/16 25/16 25/16
165 ? 3430/2187 189/121 39/25
166 972/625 384/245 352/225 224/143
167 ? 540/343 11/7 11/7
168 128/81 128/81 128/81 128/81
169 ? 63/40 63/40 63/40
170 405/256 405/256 192/121 144/91
171 ? 343/216 35/22 35/22
172 3125/1944 1225/768 198/125 198/125
173 ? 1792/1125 550/343 125/78
174 8/5 8/5 8/5 8/5
175 ? 45/28 45/28 45/28
176 6561/4096 392/243 160/99 160/99
177 ? 175/108 125/77 125/77
178 625/384 625/384 121/75 21/13
179 ? 512/315 363/224 13/8
180 81/50 80/49 44/27 44/27
181 ? 729/448 275/168 275/168
182 400/243 49/30 18/11 18/11
183 ? 105/64 105/64 64/39
184 1024/625 1024/625 200/121 104/63
185 ? 288/175 288/175 288/175
186 6561/4000 81/49 33/20 33/20
187 ? 224/135 128/77 128/77
188 5/3 5/3 5/3 5/3
189 ? 375/224 375/224 108/65
190 5184/3125 1225/729 147/88 117/70
191 ? 576/343 176/105 176/105
192 2048/1215 2048/1215 121/72 91/54
193 ? 42/25 42/25 42/25
194 27/16 27/16 27/16 27/16
195 ? 686/405 56/33 22/13
196 1250/729 245/144 75/44 75/44
197 ? 875/512 297/175 200/117
198 128/75 128/75 128/75 128/75
199 ? 12/7 12/7 12/7
200 2187/1280 675/392 55/32 55/32
201 ? 140/81 140/81 140/81
202 125/72 125/72 125/72 112/65
203 ? 3125/1792 121/70 26/15
204 216/125 216/125 216/125 195/112
205 ? 243/140 110/63 110/63
206 1280/729 392/225 96/55 96/55
207 ? 7/4 7/4 7/4
208 225/128 225/128 225/128 160/91
209 ? 1536/875 175/99 143/81
210 2187/1250 432/245 44/25 44/25
211 ? 1215/686 99/56 39/22
212 16/9 16/9 16/9 16/9
213 ? 25/14 25/14 25/14
214 3645/2048 2401/1350 98/55 98/55
215 ? 343/192 315/176 143/80
216 3125/1728 2187/1225 88/49 70/39
217 ? 224/125 224/125 65/36
218 9/5 9/5 9/5 9/5
219 ? 405/224 231/128 231/128
220 4000/2187 49/27 20/11 20/11
221 ? 175/96 175/96 175/96
222 1875/1024 1875/1024 363/200 91/50
223 ? 64/35 64/35 64/35
224 729/400 90/49 11/6 11/6
225 ? 448/243 448/243 325/176
226 50/27 50/27 50/27 50/27
227 ? 625/336 224/121 24/13
228 1152/625 1152/625 225/121 13/7
229 ? 324/175 231/125 231/125
230 4096/2187 729/392 275/147 275/147
231 ? 28/15 28/15 28/15
232 15/8 15/8 15/8 15/8
233 ? 1372/729 560/297 220/117
234 5832/3125 1225/648 125/66 125/66
235 ? 648/343 66/35 49/26
236 256/135 256/135 121/64 91/48
237 ? 40/21 40/21 40/21
238 243/128 243/128 243/128 243/128
239 ? 343/180 21/11 21/11
240 625/324 245/128 245/128 169/88
241 ? 3584/1875 121/63 25/13
242 48/25 48/25 48/25 48/25
243 ? 27/14 27/14 27/14
244 12800/6561 784/405 64/33 64/33
245 ? 35/18 35/18 35/18
246 125/64 125/64 125/64 125/64
247 ? 1024/525 343/176 39/20
248 243/125 96/49 88/45 88/45
249 ? 675/343 55/28 55/28
250 160/81 49/25 49/25 49/25
251 ? 63/32 63/32 63/32
252 2025/1024 2025/1024 196/99 77/39
253 ? 1715/864 175/88 143/72
254 15625/7776 486/245 99/50 99/50
255 ? 448/225 448/225 325/162
256 2/1 2/1 2/1 2/1