41-odd-limit: Difference between revisions
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Proposed some names for the 41-odd-limit intervals, feel free to change them if they could be improved |
Added all links to intervals |
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Below is a list of all octave-reduced intervals in the 41-odd-limit. | Below is a list of all octave-reduced intervals in the 41-odd-limit. | ||
* 1/1 | * [[1/1]] | ||
* '''42/41, 41/21''' | * '''[[42/41]], [[41/21]]''' | ||
* '''41/40, 80/41''' | * '''[[41/40]], [[80/41]]''' | ||
* 40/39, 39/20 | * [[40/39]], [[39/20]] | ||
* 39/38, 76/39 | * [[39/38]], [[76/39]] | ||
* 38/37, 37/19 | * [[38/37]], [[37/19]] | ||
* 37/36, 72/37 | * [[37/36]], [[72/37]] | ||
* 36/35, 35/18 | * [[36/35]], [[35/18]] | ||
* 35/34, 68/35 | * [[35/34]], [[68/35]] | ||
* 34/33, 33/17 | * [[34/33]], [[33/17]] | ||
* 33/32, 64/33 | * [[33/32]], [[64/33]] | ||
* 32/31, 31/16 | * [[32/31]], [[31/16]] | ||
* 31/30, 60/31 | * [[31/30]], [[60/31]] | ||
* 30/29, 29/15 | * [[30/29]], [[29/15]] | ||
* 29/28, 56/29 | * [[29/28]], [[56/29]] | ||
* 28/27, 27/14 | * [[28/27]], [[27/14]] | ||
* 27/26, 52/27 | * [[27/26]], [[52/27]] | ||
* 26/25, 25/13 | * [[26/25]], [[25/13]] | ||
* 25/24, 48/25 | * [[25/24]], [[48/25]] | ||
* 24/23, 23/12 | * [[24/23]], [[23/12]] | ||
* 23/22, 44/23 | * [[23/22]], [[44/23]] | ||
* 22/21, 21/11 | * [[22/21]], [[21/11]] | ||
* 21/20, 40/21 | * [[21/20]], [[40/21]] | ||
* '''41/39, 78/41''' | * '''[[41/39]], [[78/41]]''' | ||
* 20/19, 19/10 | * [[20/19]], [[19/10]] | ||
* 39/37, 74/39 | * [[39/37]], [[74/39]] | ||
* 19/18, 36/19 | * [[19/18]], [[36/19]] | ||
* 37/35, 70/37 | * [[37/35]], [[70/37]] | ||
* 18/17, 17/9 | * [[18/17]], [[17/9]] | ||
* 35/33, 66/35 | * [[35/33]], [[66/35]] | ||
* 17/16, 32/17 | * [[17/16]], [[32/17]] | ||
* 33/31, 62/33 | * [[33/31]], [[62/33]] | ||
* 16/15, 15/8 | * [[16/15]], [[15/8]] | ||
* 31/29, 58/31 | * [[31/29]], [[58/31]] | ||
* 15/14, 28/15 | * [[15/14]], [[28/15]] | ||
* '''44/41, 41/22''' | * '''[[44/41]], [[41/22]]''' | ||
* 29/27, 54/29 | * [[29/27]], [[54/29]] | ||
* 14/13, 13/7 | * [[14/13]], [[13/7]] | ||
* '''41/38, 76/41''' | * '''[[41/38]], [[76/41]]''' | ||
* 27/25, 50/27 | * [[27/25]], [[50/27]] | ||
* 40/37, 37/20 | * [[40/37]], [[37/20]] | ||
* 13/12, 24/13 | * [[13/12]], [[24/13]] | ||
* 38/35, 35/19 | * [[38/35]], [[35/19]] | ||
* 25/23, 46/25 | * [[25/23]], [[46/25]] | ||
* 37/34, 68/37 | * [[37/34]], [[68/37]] | ||
* 12/11, 11/6 | * [[12/11]], [[11/6]] | ||
* 35/32, 64/35 | * [[35/32]], [[64/35]] | ||
* 23/21, 42/23 | * [[23/21]], [[42/23]] | ||
* 34/31, 31/17 | * [[34/31]], [[31/17]] | ||
* 11/10, 20/11 | * [[11/10]], [[20/11]] | ||
* 32/29, 29/16 | * [[32/29]], [[29/16]] | ||
* 21/19, 38/21 | * [[21/19]], [[38/21]] | ||
* 31/28, 56/31 | * [[31/28]], [[56/31]] | ||
* '''41/37, 74/41''' | * '''[[41/37]], [[74/41]]''' | ||
* 10/9, 9/5 | * [[10/9]], [[9/5]] | ||
* 39/35, 70/39 | * [[39/35]], [[70/39]] | ||
* 29/26, 52/29 | * [[29/26]], [[52/29]] | ||
* 19/17, 34/19 | * [[19/17]], [[34/19]] | ||
* 28/25, 25/14 | * [[28/25]], [[25/14]] | ||
* 37/33, 66/37 | * [[37/33]], [[66/37]] | ||
* '''46/41, 41/23''' | * '''[[46/41]], [[41/23]]''' | ||
* 9/8, 16/9 | * [[9/8]], [[16/9]] | ||
* 44/39, 39/22 | * [[44/39]], [[39/22]] | ||
* 35/31, 62/35 | * [[35/31]], [[62/35]] | ||
* 26/23, 23/13 | * [[26/23]], [[23/13]] | ||
* 17/15, 30/17 | * [[17/15]], [[30/17]] | ||
* 42/37, 37/21 | * [[42/37]], [[37/21]] | ||
* 25/22, 44/25 | * [[25/22]], [[44/25]] | ||
* 33/29, 58/33 | * [[33/29]], [[58/33]] | ||
* '''41/36, 72/41''' | * '''[[41/36]], [[72/41]]''' | ||
* 8/7, 7/4 | * [[8/7]], [[7/4]] | ||
* 39/34, 68/39 | * [[39/34]], [[68/39]] | ||
* 31/27, 54/31 | * [[31/27]], [[54/31]] | ||
* 23/20, 40/23 | * [[23/20]], [[40/23]] | ||
* 38/33, 33/19 | * [[38/33]], [[33/19]] | ||
* 15/13, 26/15 | * [[15/13]], [[26/15]] | ||
* 37/32, 64/37 | * [[37/32]], [[64/37]] | ||
* 22/19, 19/11 | * [[22/19]], [[19/11]] | ||
* 29/25, 50/29 | * [[29/25]], [[50/29]] | ||
* 36/31, 31/18 | * [[36/31]], [[31/18]] | ||
* 7/6, 12/7 | * [[7/6]], [[12/7]] | ||
* '''48/41, 41/24''' | * '''[[48/41]], [[41/24]]''' | ||
* '''41/35, 70/41''' | * '''[[41/35]], [[70/41]]''' | ||
* 34/29, 29/17 | * [[34/29]], [[29/17]] | ||
* 27/23, 46/27 | * [[27/23]], [[46/27]] | ||
* 20/17, 17/10 | * [[20/17]], [[17/10]] | ||
* 33/28, 56/33 | * [[33/28]], [[56/33]] | ||
* 46/39, 39/23 | * [[46/39]], [[39/23]] | ||
* 13/11, 22/13 | * [[13/11]], [[22/13]] | ||
* 32/27, 27/16 | * [[32/27]], [[27/16]] | ||
* 19/16, 32/19 | * [[19/16]], [[32/19]] | ||
* 44/37, 37/22 | * [[44/37]], [[37/22]] | ||
* 25/21, 42/25 | * [[25/21]], [[42/25]] | ||
* 31/26, 52/31 | * [[31/26]], [[52/31]] | ||
* 37/31, 62/37 | * [[37/31]], [[62/37]] | ||
* 6/5, 5/3 | * [[6/5]], [[5/3]] | ||
* '''41/34, 68/41''' | * '''[[41/34]], [[68/41]]''' | ||
* 35/29, 58/35 | * [[35/29]], [[58/35]] | ||
* 29/24, 48/29 | * [[29/24]], [[48/29]] | ||
* 23/19, 38/23 | * [[23/19]], [[38/23]] | ||
* 40/33, 33/20 | * [[40/33]], [[33/20]] | ||
* 17/14, 28/17 | * [[17/14]], [[28/17]] | ||
* 28/23, 23/14 | * [[28/23]], [[23/14]] | ||
* 39/32, 64/39 | * [[39/32]], [[64/39]] | ||
* '''50/41, 41/25''' | * '''[[50/41]], [[41/25]]''' | ||
* 11/9, 18/11 | * [[11/9]], [[18/11]] | ||
* 38/31, 31/19 | * [[38/31]], [[31/19]] | ||
* 27/22, 44/27 | * [[27/22]], [[44/27]] | ||
* 16/13, 13/8 | * [[16/13]], [[13/8]] | ||
* 37/30, 60/37 | * [[37/30]], [[60/37]] | ||
* 21/17, 34/21 | * [[21/17]], [[34/21]] | ||
* 26/21, 21/13 | * [[26/21]], [[21/13]] | ||
* 31/25, 50/31 | * [[31/25]], [[50/31]] | ||
* 36/29, 29/18 | * [[36/29]], [[29/18]] | ||
* '''41/33, 66/41''' | * '''[[41/33]], [[66/41]]''' | ||
* 46/37, 37/23 | * [[46/37]], [[37/23]] | ||
* 5/4, 8/5 | * [[5/4]], [[8/5]] | ||
* 44/35, 35/22 | * [[44/35]], [[35/22]] | ||
* 39/31, 62/39 | * [[39/31]], [[62/39]] | ||
* 34/27, 27/17 | * [[34/27]], [[27/17]] | ||
* 29/23, 46/29 | * [[29/23]], [[46/29]] | ||
* 24/19, 19/12 | * [[24/19]], [[19/12]] | ||
* 19/15, 30/19 | * [[19/15]], [[30/19]] | ||
* '''52/41, 41/26''' | * '''[[52/41]], [[41/26]]''' | ||
* 33/26, 52/33 | * [[33/26]], [[52/33]] | ||
* 14/11, 11/7 | * [[14/11]], [[11/7]] | ||
* 37/29, 58/37 | * [[37/29]], [[58/37]] | ||
* 23/18, 36/23 | * [[23/18]], [[36/23]] | ||
* 32/25, 25/16 | * [[32/25]], [[25/16]] | ||
* '''41/32, 64/41''' | * '''[[41/32]], [[64/41]]''' | ||
* 50/39, 39/25 | * [[50/39]], [[39/25]] | ||
* 9/7, 14/9 | * [[9/7]], [[14/9]] | ||
* 40/31, 31/20 | * [[40/31]], [[31/20]] | ||
* 31/24, 48/31 | * [[31/24]], [[48/31]] | ||
* 22/17, 17/11 | * [[22/17]], [[17/11]] | ||
* 35/27, 54/35 | * [[35/27]], [[54/35]] | ||
* 48/37, 37/24 | * [[48/37]], [[37/24]] | ||
* 13/10, 20/13 | * [[13/10]], [[20/13]] | ||
* 30/23, 23/15 | * [[30/23]], [[23/15]] | ||
* 17/13, 26/17 | * [[17/13]], [[26/17]] | ||
* 38/29, 29/19 | * [[38/29]], [[29/19]] | ||
* 21/16, 32/21 | * [[21/16]], [[32/21]] | ||
* 46/35, 35/23 | * [[46/35]], [[35/23]] | ||
* 25/19, 38/25 | * [[25/19]], [[38/25]] | ||
* '''54/41, 41/27''' | * '''[[54/41]], [[41/27]]''' | ||
* 29/22, 44/29 | * [[29/22]], [[44/29]] | ||
* 33/25, 50/33 | * [[33/25]], [[50/33]] | ||
* 37/28, 56/37 | * [[37/28]], [[56/37]] | ||
* '''41/31, 62/41''' | * '''[[41/31]], [[62/41]]''' | ||
* 4/3, 3/2 | * [[4/3]], [[3/2]] | ||
* 39/29, 58/39 | * [[39/29]], [[58/39]] | ||
* 35/26, 52/35 | * [[35/26]], [[52/35]] | ||
* 31/23, 46/31 | * [[31/23]], [[46/31]] | ||
* 27/20, 40/27 | * [[27/20]], [[40/27]] | ||
* 50/37, 37/25 | * [[50/37]], [[37/25]] | ||
* 23/17, 34/23 | * [[23/17]], [[34/23]] | ||
* 42/31, 31/21 | * [[42/31]], [[31/21]] | ||
* 19/14, 28/19 | * [[19/14]], [[28/19]] | ||
* 34/25, 25/17 | * [[34/25]], [[25/17]] | ||
* 15/11, 22/15 | * [[15/11]], [[22/15]] | ||
* '''56/41, 41/28''' | * '''[[56/41]], [[41/28]]''' | ||
* '''41/30, 60/41''' | * '''[[41/30]], [[60/41]]''' | ||
* 26/19, 19/13 | * [[26/19]], [[19/13]] | ||
* 37/27, 54/37 | * [[37/27]], [[54/37]] | ||
* 48/35, 35/24 | * [[48/35]], [[35/24]] | ||
* 11/8, 16/11 | * [[11/8]], [[16/11]] | ||
* 40/29, 29/20 | * [[40/29]], [[29/20]] | ||
* 29/21, 42/29 | * [[29/21]], [[42/29]] | ||
* 18/13, 13/9 | * [[18/13]], [[13/9]] | ||
* 25/18, 36/25 | * [[25/18]], [[36/25]] | ||
* 32/23, 23/16 | * [[32/23]], [[23/16]] | ||
* 39/28, 56/39 | * [[39/28]], [[56/39]] | ||
* 46/33, 33/23 | * [[46/33]], [[33/23]] | ||
* 7/5, 10/7 | * [[7/5]], [[10/7]] | ||
* 52/37, 37/26 | * [[52/37]], [[37/26]] | ||
* 38/27, 27/19 | * [[38/27]], [[27/19]] | ||
* 31/22, 44/31 | * [[31/22]], [[44/31]] | ||
* 24/17, 17/12 | * [[24/17]], [[17/12]] | ||
* '''41/29, 58/41''' | * '''[[41/29]], [[58/41]]''' | ||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 20:54, 18 September 2025
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).