Table of 311edo intervals

Below is a 41-limit transversal of 311et

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

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