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User:CompactStar/Table of 311edo intervals

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Revision as of 02:27, 25 February 2024 by CompactStar (talk | contribs)

This is an archive of table of 311edo intervals

note interval
1 289/288
2 170/169
3 133/132
4 100/99
5 85/84
6 70/69
7 64/63
8 55/54
9 49/48
10 45/44
11 40/39
12 37/36
13 34/33
14 32/31
15 30/29
16 28/27
17 27/26
18 25/24
19 24/23
20 23/22
21 22/21
22 21/20
23 20/19
24 19/18
25 37/35
26 18/17
27 17/16
28 33/31
29 16/15
30 31/29
31 15/14
32 29/27
33 14/13
34 41/38
35 27/25
36 13/12
37 25/23
38 37/34
39 12/11
40 35/32
41 23/21
42 56/51
43 11/10
44 32/29
45 21/19
46 31/28
47 10/9
48 49/44
49 29/26
50 19/17
51 28/25
52 46/41
53 9/8
54 35/31
55 26/23
56 17/15
57 25/22
58 33/29
59 57/50
60 8/7
61 55/48
62 31/27
63 23/20
64 15/13
65 37/32
66 22/19
67 29/25
68 57/49
69 7/6
70 76/65
71 34/29
72 27/23
73 20/17
74 33/28
75 13/11
76 32/27
77 19/16
78 25/21
79 31/26
80 55/46
81 91/76
82 6/5
83 65/54
84 35/29
85 29/24
86 23/19
87 17/14
88 28/23
89 39/32
90 11/9
91 38/31
92 27/22
93 16/13
94 37/30
95 21/17
96 26/21
97 31/25
98 46/37
99 81/65
100 5/4
101 114/91
102 49/39
103 34/27
104 29/23
105 24/19
106 19/15
107 33/26
108 14/11
109 37/29
110 23/18
111 32/25
112 77/60
113 9/7
114 40/31
115 31/24
116 22/17
117 48/37
118 13/10
119 30/23
120 17/13
121 38/29
122 21/16
123 25/19
124 29/22
125 33/25
126 45/34
127 65/49
128 117/88
129 4/3
130 147/110
131 75/56
132 51/38
133 35/26
134 31/23
135 27/20
136 23/17
137 19/14
138 34/25
139 15/11
140 41/30
141 26/19
142 48/35
143 11/8
144 40/29
145 29/21
146 18/13
147 25/18
148 32/23
149 39/28
150 88/63
151 7/5
152 80/57
153 38/27
154 31/22
155 24/17
156 17/12
157 44/31
158 27/19
159 57/40
160 10/7
161 63/44
162 33/23
163 23/16
164 36/25
165 13/9
166 42/29
167 29/20
168 16/11
169 35/24
170 19/13
171 41/28
172 22/15
173 25/17
174 28/19
175 31/21
176 37/25
177 46/31
178 52/35
179 76/51
180 112/75
181 220/147
182 3/2
183 176/117
184 95/63
185 68/45
186 50/33
187 41/27
188 35/23
189 32/21
190 29/19
191 26/17
192 23/15
193 20/13
194 37/24
195 17/11
196 48/31
197 31/20
198 14/9
199 81/52
200 25/16
201 36/23
202 58/37
203 11/7
204 41/26
205 30/19
206 19/12
207 46/29
208 27/17
209 51/32
210 91/57
211 8/5
212 77/48
213 37/23
214 29/18
215 21/13
216 34/21
217 60/37
218 13/8
219 44/27
220 31/19
221 18/11
222 41/25
223 23/14
224 28/17
225 33/20
226 48/29
227 58/35
228 108/65
229 5/3
230 147/88
231 77/46
232 52/31
233 37/22
234 32/19
235 27/16
236 22/13
237 39/23
238 17/10
239 46/27
240 29/17
241 65/38
242 12/7
243 55/32
244 31/18
245 19/11
246 45/26
247 26/15
248 33/19
249 54/31
250 96/55
251 7/4
252 100/57
253 58/33
254 37/21
255 30/17
256 23/13
257 39/22
258 16/9
259 41/23
260 25/14
261 34/19
262 52/29
263 88/49
264 9/5
265 56/31
266 38/21
267 29/16
268 20/11
269 51/28
270 31/17
271 64/35
272 11/6
273 68/37
274 35/19
275 24/13
276 37/20
277 63/34
278 13/7
279 41/22
280 28/15
281 58/31
282 15/8
283 62/33
284 32/17
285 17/9
286 70/37
287 36/19
288 19/10
289 40/21
290 21/11
291 44/23
292 23/12
293 25/13
294 52/27
295 27/14
296 29/15
297 31/16
298 33/17
299 37/19
300 39/20
301 45/23
302 49/25
303 55/28
304 63/32
305 69/35
306 91/46
307 99/50
308 135/68
309 169/85
310 299/150
311 2/1

Alternatively, here is only the intervals of the 41-prime-limited 77-odd-limit add-73, with others left blank.

The content of this table was generated with a small amount of Python 3 code, shown first: 

import math
h = [39,40,41,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,73,74,75,76,77,78]
m311 = {}
for i in range(311+1):
  m311[i] = []
for i in range(len(h)):
  for j in range(i,len(h)):
    f = math.gcd(h[i],h[j])
    numer = h[j] // f
    denom = h[i] // f
    interval = str(numer) + '/' + str(denom)
    complement = ''
    if math.gcd(2*denom,numer)==1:
      complement = str(2*denom) + '/' + str(numer)
    else:
      complement = str(denom) + '/' + str(numer//2)
    steps = round(311*math.log(h[j]/h[i],2))
    if interval not in m311[steps]:
      m311[steps].append(interval)
    if complement not in m311[311-steps]:
      m311[311-steps].append(complement)
for i in range(311+1):
  m311[i] = '|-\n| | '+str(i)+'\n| | '+ (', '.join(m311[i]) if len(m311[i])>0 else '')
print( '\n'.join([s for s in m311.values()]) )

Note that the intervals listed for each interval of 311 EDO are in no particular order, so read carefully.

Also note that the blankness of intervals 1\311 to 5\311 and 306\311 to 310\311 show how 311 EDO is a sixth-comma system, with a generic 'comma' being 6\311, which is also what 81/80 is mapped to consistently, although the 81st harmonic is the first in the 41-limit to cause inconsistency.

steps intervals
0 1/1
1
2
3
4
5
6 78/77, 70/69, 73/72, 74/73, 75/74, 76/75, 77/76
7 63/62, 64/63, 65/64, 66/65, 69/68
8 55/54, 56/55, 57/56, 58/57
9 49/48, 50/49, 51/50, 52/51
10 45/44, 46/45
11 40/39, 41/40, 42/41
12 39/38, 37/36, 75/73, 38/37, 77/75
13 34/33, 35/34, 36/35
14 32/31, 65/63, 33/32
15 30/29, 31/30
16 28/27, 57/55, 29/28
17 80/77, 27/26
18 26/25, 25/24, 51/49, 76/73, 77/74
19 24/23, 73/70
20 23/22, 68/65
21 22/21, 65/62
22 41/39, 21/20
23 20/19
24 39/37, 19/18, 58/55, 77/73
25 55/52, 73/69, 37/35
26 18/17, 35/33
27 17/16, 52/49, 69/65
28 82/77, 49/46, 33/31
29 16/15
30 78/73, 31/29, 77/72
31 15/14, 74/69
32 44/41, 29/27, 73/68
33 14/13
34 41/38, 55/51, 68/63, 69/64
35 40/37, 27/25
36 13/12
37 25/23, 63/58, 38/35
38 49/45, 62/57, 37/34
39 12/11
40 82/75, 35/32
41 80/73, 23/21, 57/52, 34/31
42 45/41, 56/51
43 11/10, 76/69
44 54/49, 32/29, 75/68
45 21/19, 73/66
46 41/37, 51/46, 31/28, 72/65
47 10/9
48 49/44, 69/62
49 39/35, 29/26, 77/69
50 19/17
51 28/25, 65/58, 37/33
52 46/41, 82/73, 55/49, 64/57, 73/65
53 9/8
54 44/39, 62/55, 35/31
55 26/23
56 17/15, 77/68
57 42/37, 25/22
58 41/36, 58/51, 33/29, 74/65
59 57/50, 65/57, 73/64
60 8/7
61 55/48, 63/55
62 39/34, 31/27
63 23/20, 84/73, 38/33
64 15/13
65 52/45, 37/32
66 80/69, 51/44, 22/19, 73/63
67 29/25, 65/56, 36/31
68 57/49, 64/55
69 7/6
70 90/77, 76/65
71 48/41, 41/35, 34/29, 75/64
72 88/75, 27/23, 74/63
73 20/17, 73/62
74 46/39, 33/28
75 13/11
76 45/38, 58/49, 32/27, 77/65
77 82/69, 19/16
78 25/21, 44/37, 69/58
79 31/26, 68/57, 37/31
80 49/41, 55/46, 92/77
81
82 6/5
83 65/54, 77/64
84 41/34, 88/73, 35/29, 76/63
85 29/24, 75/62
86 40/33, 23/19, 63/52
87 17/14
88 28/23, 45/37, 62/51, 73/60
89 39/32, 50/41
90 11/9
91 49/40, 60/49, 38/31
92 27/22, 92/75, 70/57
93 16/13
94 90/73, 69/56, 37/30
95 21/17, 68/55
96 26/21, 57/46
97 41/33, 31/25, 36/29, 77/62
98 51/41, 56/45, 46/37
99 96/77
100 5/4
101
102 49/39, 64/51, 69/55
103 39/31, 44/35, 34/27, 73/58
104 82/65, 29/23, 92/73, 63/50
105 24/19
106 19/15, 62/49
107 80/63, 52/41, 33/26
108 14/11
109 51/40, 88/69, 65/51, 37/29
110 23/18
111 50/39, 41/32, 32/25, 73/57
112 77/60
113 9/7
114 40/31, 58/45, 49/38
115 84/65, 31/24, 75/58
116 57/44, 22/17, 35/27
117 48/37, 100/77, 74/57
118 13/10, 82/63
119 30/23, 73/56
120 17/13, 64/49, 98/75
121 55/42, 72/55, 38/29
122 21/16
123 46/35, 96/73, 25/19
124 54/41, 29/22
125 41/31, 33/25, 37/28
126 45/34, 49/37, 102/77
127 65/49, 69/52, 73/55, 77/58
128
129 4/3
130
131 75/56
132 55/41, 98/73, 51/38
133 39/29, 35/26, 74/55
134 31/23, 66/49
135 27/20, 50/37, 104/77, 73/54, 77/57
136 42/31, 88/65, 23/17, 65/48
137 19/14
138 49/36, 34/25
139 15/11
140 56/41, 41/30
141 26/19, 63/46, 100/73, 37/27
142 48/35, 70/51
143 11/8
144 40/29, 62/45, 51/37
145 29/21, 69/50, 76/55
146 18/13
147 68/49, 25/18, 104/75
148 57/41, 32/23
149 39/28, 46/33
150 88/63, 102/73
151 7/5
152 80/57, 73/52, 108/77
153 45/32, 52/37, 38/27
154 55/39, 31/22, 69/49
155 41/29, 65/46, 24/17
156 58/41, 92/65, 17/12
157 78/55, 44/31, 98/69
158 64/45, 37/26, 27/19
159 57/40, 104/73, 77/54
160 10/7
161 63/44, 73/51
162 56/39, 33/23
163 82/57, 23/16
164 49/34, 36/25, 75/52
165 13/9
166 42/29, 100/69, 55/38
167 29/20, 45/31, 74/51
168 16/11
169 35/24, 51/35
170 19/13, 92/63, 73/50, 54/37
171 41/28, 60/41
172 22/15
173 72/49, 25/17
174 28/19
175 31/21, 65/44, 34/23, 96/65
176 40/27, 37/25, 77/52, 108/73, 114/77
177 46/31, 49/33
178 58/39, 52/35, 55/37
179 82/55, 73/49, 76/51
180 112/75
181
182 3/2
183
184 98/65, 104/69, 110/73, 116/77
185 68/45, 74/49, 77/51
186 62/41, 50/33, 56/37
187 41/27, 44/29
188 35/23, 73/48, 38/25
189 32/21
190 84/55, 55/36, 29/19
191 26/17, 49/32, 75/49
192 23/15, 112/73
193 20/13, 63/41
194 37/24, 77/50, 57/37
195 88/57, 17/11, 54/35
196 65/42, 48/31, 116/75
197 31/20, 45/29, 76/49
198 14/9
199 120/77
200 39/25, 64/41, 25/16, 114/73
201 36/23
202 80/51, 69/44, 102/65, 58/37
203 11/7
204 63/40, 41/26, 52/33
205 30/19, 49/31
206 19/12
207 65/41, 46/29, 73/46, 100/63
208 62/39, 35/22, 27/17, 116/73
209 78/49, 51/32, 110/69
210
211 8/5
212 77/48
213 82/51, 45/28, 37/23
214 66/41, 50/31, 29/18, 124/77
215 21/13, 92/57
216 34/21, 55/34
217 73/45, 112/69, 60/37
218 13/8
219 44/27, 75/46, 57/35
220 80/49, 49/30, 31/19
221 18/11
222 64/39, 41/25
223 23/14, 74/45, 51/31, 120/73
224 28/17
225 33/20, 38/23, 104/63
226 48/29, 124/75
227 68/41, 73/44, 58/35, 63/38
228 108/65, 128/77
229 5/3
230
231 82/49, 92/55, 77/46
232 52/31, 57/34, 62/37
233 42/25, 37/22, 116/69
234 69/41, 32/19
235 76/45, 49/29, 27/16, 130/77
236 22/13
237 39/23, 56/33
238 17/10, 124/73
239 75/44, 46/27, 63/37
240 41/24, 70/41, 29/17, 128/75
241 77/45, 65/38
242 12/7
243 98/57, 55/32
244 50/29, 112/65, 31/18
245 69/40, 88/51, 19/11, 126/73
246 45/26, 64/37
247 26/15
248 40/23, 73/42, 33/19
249 68/39, 54/31
250 96/55, 110/63
251 7/4
252 100/57, 114/65, 128/73
253 72/41, 51/29, 58/33, 65/37
254 37/21, 44/25
255 30/17, 136/77
256 23/13
257 39/22, 55/31, 62/35
258 16/9
259 41/23, 73/41, 98/55, 57/32, 130/73
260 25/14, 116/65, 66/37
261 34/19
262 70/39, 52/29, 138/77
263 88/49, 124/69
264 9/5
265 74/41, 92/51, 56/31, 65/36
266 38/21, 132/73
267 49/27, 29/16, 136/75
268 20/11, 69/38
269 82/45, 51/28
270 73/40, 42/23, 104/57, 31/17
271 75/41, 64/35
272 11/6
273 90/49, 57/31, 68/37
274 46/25, 116/63, 35/19
275 24/13
276 37/20, 50/27
277 76/41, 102/55, 63/34, 128/69
278 13/7
279 41/22, 54/29, 136/73
280 28/15, 69/37
281 73/39, 58/31, 144/77
282 15/8
283 77/41, 92/49, 62/33
284 32/17, 49/26, 130/69
285 17/9, 66/35
286 104/55, 138/73, 70/37
287 74/39, 36/19, 55/29, 146/77
288 19/10
289 78/41, 40/21
290 21/11, 124/65
291 44/23, 65/34
292 23/12, 140/73
293 25/13, 48/25, 98/51, 73/38, 148/77
294 77/40, 52/27
295 27/14, 110/57, 56/29
296 29/15, 60/31
297 31/16, 126/65, 64/33
298 33/17, 68/35, 35/18
299 76/39, 72/37, 146/75, 37/19, 150/77
300 39/20, 80/41, 41/21
301 88/45, 45/23
302 96/49, 49/25, 100/51, 51/26
303 108/55, 55/28, 112/57, 57/29
304 124/63, 63/32, 128/65, 65/33, 136/69
305 77/39, 69/35, 144/73, 73/37, 148/75, 75/38, 152/77
306
307
308
309
310
311 2/1
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