41-odd-limit
The 41-odd-limit is the set of all rational intervals which can be written as 2k(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
- 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; that which is distinctly consistent to the same is 20567edo (by virtue of it being distinctly consistent through the 57-odd-limit).