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