41-odd-limit

Odd limit

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1-odd-limit  3-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 ≤ 41 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
• 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	Name
42/41	41.719	fowuzo 2nd	quadragintaunimal inframinor second
41/40	42.749	fowogu unison	quadragintaunimal quartertone
41/39	86.58	fowothu unison	quadragintaunimal ultraprime
44/41	122.256	fowulo 2nd	quadragintaunimal lesser minor second
41/38	131.549	fowonu unison	quadragintaunimal hyperprime
41/37	177.718	fowothisu unison	quadragintaunimal neutral second
46/41	199.212	fowutwetho 3rd	quadragintaunimal minor tone
41/36	225.152	fowo 2nd	quadragintaunimal major tone
48/41	272.893	fowu 3rd	quadragintaunimal subminor third
41/35	273.923	foworugu 2nd	quadragintaunimal ultramajor second
41/34	324.107	fowosu 2nd	quadragintaunimal minor third
50/41	343.565	fowuyoyo 3rd	quadragintaunimal neutral third
41/33	375.789	fowolu 3rd	quadragintaunimal submajor third
52/41	411.465	fowutho 4th	quadragintaunimal lesser major third
41/32	429.062	fowo 3rd	quadragintaunimal greater major third
54/41	476.803	fowu 4th	quadragintaunimal lesser minor fourth
41/31	484.027	fowothiwu 4th	quadragintaunimal greater minor fourth
56/41	539.764	fowuzo 5th	quadragintaunimal subdiminished fifth
41/30	540.794	fowogu 4th	quadragintaunimal major fourth
41/29	599.485	fowotwenu 4th	quadragintaunimal lesser tritone
58/41	600.515	fowutweno 5th	quadragintaunimal greater tritone
60/41	659.206	fowuyo 5th	quadragintaunimal lesser minor fifth
41/28	660.236	foworu 4th	quadragintaunimal superaugmented fourth
62/41	715.973	fowuthiwo 5th	quadragintaunimal lesser major fifth
41/27	723.197	fowo 5th	quadragintaunimal greater major fifth
64/41	770.938	fowu 6th	quadragintaunimal lesser minor sixth
41/26	788.535	fowothu 5th	quadragintaunimal augmented fifth
66/41	824.211	fowulo 6th	quadragintaunimal greater minor sixth
41/25	856.435	fowogugu 6th	quadragintaunimal neutral sixth
68/41	875.893	fowuso 7th	quadragintaunimal submajor sixth
70/41	926.077	fowuzoyo 7th	quadragintaunimal lesser major sixth
41/24	927.107	fowo 6th	quadragintaunimal greater major sixth
72/41	974.848	fowu 7th	quadragintaunimal lesser minor seventh
41/23	1000.788	fowotwethu 6th	quadragintaunimal hypermajor sixth
74/41	1022.282	fowuthiso octave	quadragintaunimal greater minor seventh
76/41	1068.451	fowuno octave	quadragintaunimal infraoctave
41/22	1077.744	fowolu 7th	quadragintaunimal lesser major seventh
78/41	1113.42	fowutho octave	quadragintaunimal greater major seventh
80/41	1157.251	fowuyo octave	quadragintaunimal ultramajor seventh
41/21	1158.281	foworu 7th	quadragintaunimal ultramajor seventh

The smallest equal division of the octave which is consistent to the 41-odd-limit is 311edo; The smallest edo that comes closest to being distinct in the 41-odd-limit is 1600edo (misses 50/39, 39/25). that which is truly distinctly consistent to the same is 20567edo (by virtue of it being distinctly consistent through the 57-odd-limit).