41-odd-limit

The 41-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 31 and k is an integer. To the 39-odd-limit, it adds 20 pairs of octave-reduced intervals involving 41.

Below is a list of all octave-reduced intervals in the 41-odd-limit.

1/1	2/1
42/41	41/21
41/40	80/41
40/39	39/20
39/38	76/39
38/37	37/19
37/36	72/37
36/35	35/18
35/34	68/35
34/33	33/17
33/32	64/33
32/31	31/16
31/30	60/31
30/29	29/15
29/28	56/29
28/27	27/14
27/26	52/27
26/25	25/13
25/24	48/25
24/23	23/12
23/22	44/23
22/21	21/11
21/20	40/21
41/39	78/41
20/19	19/10
39/37	74/39
19/18	36/19
37/35	70/37
18/17	17/9
35/33	66/35
17/16	32/17
33/31	62/33
16/15	15/8
31/29	58/31
15/14	28/15
44/41	41/22
29/27	54/29
14/13	13/7
41/38	76/41
27/25	50/27
40/37	37/20
13/12	24/13
38/35	35/19
25/23	46/25
37/34	68/37
12/11	11/6
35/32	64/35
23/21	42/23
34/31	31/17
11/10	20/11
32/29	29/16
21/19	38/21
31/28	56/31
41/37	74/41
10/9	9/5
39/35	70/39
29/26	52/29
19/17	34/19
28/25	25/14
37/33	66/37
46/41	41/23
9/8	16/9
44/39	39/22
35/31	62/35
26/23	23/13
17/15	30/17
42/37	37/21
25/22	44/25
33/29	58/33
41/36	72/41
8/7	7/4
39/34	68/39
31/27	54/31
23/20	40/23
38/33	33/19
15/13	26/15
37/32	64/37
22/19	19/11
29/25	50/29
36/31	31/18
7/6	12/7
48/41	41/24
41/35	70/41
34/29	29/17
27/23	46/27
20/17	17/10
33/28	56/33
46/39	39/23
13/11	22/13
32/27	27/16
19/16	32/19
44/37	37/22
25/21	42/25
31/26	52/31
37/31	62/37
6/5	5/3
41/34	68/41
35/29	58/35
29/24	48/29
23/19	38/23
40/33	33/20
17/14	28/17
28/23	23/14
39/32	64/39
50/41	41/25
11/9	18/11
38/31	31/19
27/22	44/27
16/13	13/8
37/30	60/37
21/17	34/21
26/21	21/13
31/25	50/31
36/29	29/18
41/33	66/41
46/37	37/23
5/4	8/5
44/35	35/22
39/31	62/39
34/27	27/17
29/23	46/29
24/19	19/12
19/15	30/19
52/41	41/26
33/26	52/33
14/11	11/7
37/29	58/37
23/18	36/23
32/25	25/16
41/32	64/41
50/39	39/25
9/7	14/9
40/31	31/20
31/24	48/31
22/17	17/11
35/27	54/35
48/37	37/24
13/10	20/13
30/23	23/15
17/13	26/17
38/29	29/19
21/16	32/21
46/35	35/23
25/19	38/25
54/41	41/27
29/22	44/29
33/25	50/33
37/28	56/37
41/31	62/41
4/3	3/2
39/29	58/39
35/26	52/35
31/23	46/31
27/20	40/27
50/37	37/25
23/17	34/23
42/31	31/21
19/14	28/19
34/25	25/17
15/11	22/15
56/41	41/28
41/30	60/41
26/19	19/13
37/27	54/37
48/35	35/24
11/8	16/11
40/29	29/20
29/21	42/29
18/13	13/9
25/18	36/25
32/23	23/16
39/28	56/39
46/33	33/23
7/5	10/7
52/37	37/26
38/27	27/19
31/22	44/31
24/17	17/12
41/29	58/41

Ratio	Size (¢)	Color name
42/41	41.719	fowuzo 2nd
41/40	42.749	fowogu unison
41/39	86.58	fowothu unison
44/41	122.256	fowulo 2nd
41/38	131.549	fowonu unison
41/37	177.718	fowothisu unison
46/41	199.212	fowutwetho 3rd
41/36	225.152	fowo 2nd
48/41	272.893	fowu 3rd
41/35	273.923	foworugu 2nd
41/34	324.107	fowosu 2nd
50/41	343.565	fowuyoyo 3rd
41/33	375.789	fowolu 3rd
52/41	411.465	fowutho 4th
41/32	429.062	fowo 3rd
54/41	476.803	fowu 4th
41/31	484.027	fowothiwu 4th
56/41	539.764	fowuzo 5th
41/30	540.794	fowogu 4th
41/29	599.485	fowotwenu 4th
58/41	600.515	fowutweno 5th
60/41	659.206	fowuyo 5th
41/28	660.236	foworu 4th
62/41	715.973	fowuthiwo 5th
41/27	723.197	fowo 5th
64/41	770.938	fowu 6th
41/26	788.535	fowothu 5th
66/41	824.211	fowulo 6th
41/25	856.435	fowogugu 6th
68/41	875.893	fowuso 7th
70/41	926.077	fowuzoyo 7th
41/24	927.107	fowo 6th
72/41	974.848	fowu 7th
41/23	1000.788	fowotwethu 6th
74/41	1022.282	fowuthiso octave
76/41	1068.451	fowuno octave
41/22	1077.744	fowolu 7th
78/41	1113.42	fowutho octave
80/41	1157.251	fowuyo octave
41/21	1158.281	foworu 7th

The smallest equal division of the octave which is consistent to the 41-odd-limit is 311edo; that which is distinctly consistent to the same is 20567edo (by virtue of it being distinctly consistent through the 57-odd-limit).