57-odd-limit: Difference between revisions
Jump to navigation
Jump to search
Adding some links |
No edit summary |
||
| Line 1: | Line 1: | ||
{{Odd-limit navigation}} | {{Odd-limit navigation}}¨The '''57-odd-limit''' is the set of all [[Rational interval|rational intervals]] which can be written as 2<sup>''k''</sup>(''a''/''b'') where ''a'', ''b'' ≤ 57 and ''k'' is an integer. To the 55-odd-limit, it adds 18 pairs of [[octave-reduced]] intervals involving 57. | ||
Below is a list of all octave-reduced intervals in the 57-odd-limit. | Below is a list of all octave-reduced intervals in the 57-odd-limit. | ||
| Line 23: | Line 23: | ||
* [[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]] | ||
* '''57/55, [[110/57]]''' | * '''[[57/55]], [[110/57]]''' | ||
* 28/27, [[27/14]] | * [[28/27]], [[27/14]] | ||
* 55/53, [[106/55]] | * [[55/53]], [[106/55]] | ||
* 27/26, [[52/27]] | * [[27/26]], [[52/27]] | ||
* 53/51, [[102/53]] | * [[53/51]], [[102/53]] | ||
* 26/25, [[25/13]] | * [[26/25]], [[25/13]] | ||
* 51/49, [[98/51]] | * [[51/49]], [[98/51]] | ||
* 25/24, [[48/25]] | * [[25/24]], [[48/25]] | ||
* 49/47, [[94/49]] | * [[49/47]], [[94/49]] | ||
* 24/23, [[23/12]] | * [[24/23]], [[23/12]] | ||
* 47/45, [[90/47]] | * [[47/45]], [[90/47]] | ||
* 23/22, [[44/23]] | * [[23/22]], [[44/23]] | ||
* 45/43, [[86/45]] | * [[45/43]], [[86/45]] | ||
* 22/21, [[21/11]] | * [[22/21]], [[21/11]] | ||
* 43/41, [[82/43]] | * [[43/41]], [[82/43]] | ||
* 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]] | ||
* 58/55, [[55/29]] | * [[58/55]], [[55/29]] | ||
* 19/18, [[36/19]] | * [[19/18]], [[36/19]] | ||
* 56/53, [[53/28]] | * [[56/53]], [[53/28]] | ||
* 37/35, [[70/37]] | * [[37/35]], [[70/37]] | ||
* 55/52, [[104/55]] | * [[55/52]], [[104/55]] | ||
* 18/17, [[17/9]] | * [[18/17]], [[17/9]] | ||
* 53/50, [[100/53]] | * [[53/50]], [[100/53]] | ||
* 35/33, [[66/35]] | * [[35/33]], [[66/35]] | ||
* 52/49, [[49/26]] | * [[52/49]], [[49/26]] | ||
* 17/16, [[32/17]] | * [[17/16]], [[32/17]] | ||
* 50/47, [[47/25]] | * [[50/47]], [[47/25]] | ||
* 33/31, [[62/33]] | * [[33/31]], [[62/33]] | ||
* 49/46, [[92/49]] | * [[49/46]], [[92/49]] | ||
* 16/15, [[15/8]] | * [[16/15]], [[15/8]] | ||
* 47/44, [[88/47]] | * [[47/44]], [[88/47]] | ||
* 31/29, [[58/31]] | * [[31/29]], [[58/31]] | ||
* 46/43, [[43/23]] | * [[46/43]], [[43/23]] | ||
* 15/14, [[28/15]] | * [[15/14]], [[28/15]] | ||
* 44/41, [[41/22]] | * [[44/41]], [[41/22]] | ||
* 29/27, [[54/29]] | * [[29/27]], [[54/29]] | ||
* 43/40, [[80/43]] | * [[43/40]], [[80/43]] | ||
* '''57/53, [[106/57]]''' | * '''[[57/53]], [[106/57]]''' | ||
* 14/13, [[13/7]] | * [[14/13]], [[13/7]] | ||
* 55/51, [[102/55]] | * [[55/51]], [[102/55]] | ||
* 41/38, [[76/41]] | * [[41/38]], [[76/41]] | ||
* 27/25, [[50/27]] | * [[27/25]], [[50/27]] | ||
* 40/37, [[37/20]] | * [[40/37]], [[37/20]] | ||
* 53/49, [[98/53]] | * [[53/49]], [[98/53]] | ||
* 13/12, [[24/13]] | * [[13/12]], [[24/13]] | ||
* 51/47, [[94/51]] | * [[51/47]], [[94/51]] | ||
* 38/35, [[35/19]] | * [[38/35]], [[35/19]] | ||
* 25/23, [[46/25]] | * [[25/23]], [[46/25]] | ||
* '''62/57, [[57/31]]''' | * '''[[62/57]], [[57/31]]''' | ||
* 37/34, [[68/37]] | * [[37/34]], [[68/37]] | ||
* 49/45, [[11/6]] | * [[49/45]], [[11/6]] | ||
* 12/11, [[86/47]] | * [[12/11]], [[86/47]] | ||
* 47/43, [[64/35]] | * [[47/43]], [[64/35]] | ||
* 35/32, [[53/29]] | * [[35/32]], [[53/29]] | ||
* 58/53, [[42/23]] | * [[58/53]], [[42/23]] | ||
* '''23/21, [[104/57]]''' | * '''[[23/21]], [[104/57]]''' | ||
* '''57/52, [[31/17]]''' | * '''[[57/52]], [[31/17]]''' | ||
* 34/31, [[82/45]] | * [[34/31]], [[82/45]] | ||
* [[45/41 | * [[45/41 ]] [[51/28]] | ||
* 56/51, [[20/11]] | * [[56/51]], [[20/11]] | ||
* 11/10, [[49/27]] | * [[11/10]], [[49/27]] | ||
* 54/49, [[78/43]] | * [[54/49]], [[78/43]] | ||
* 43/39, [[29/16]] | * [[43/39]], [[29/16]] | ||
* 32/29, 96/53 | * [[32/29]], [[96/53]] | ||
* 53/48, 38/21 | * [[53/48]], [[38/21]] | ||
* 21/19, 47/26 | * [[21/19]], [[47/26]] | ||
* 52/47, 56/31 | * [[52/47]], [[56/31]] | ||
* 31/28, 74/41 | * [[31/28]], [[74/41]] | ||
* 41/37, 92/51 | * [[41/37]], [[92/51]] | ||
* 51/46, 9/5 | * [[51/46]], [[9/5]] | ||
* 10/9, 88/49 | * [[10/9]], [[88/49]] | ||
* 49/44, 70/39 | * [[49/44]], [[70/39]] | ||
* 39/35, 52/29 | * [[39/35]], [[52/29]] | ||
* 29/26, 43/24 | * [[29/26]], [[43/24]] | ||
* 48/43, 34/19 | * [[48/43]], [[34/19]] | ||
* 19/17, 84/47 | * [[19/17]], [[84/47]] | ||
* 47/42, 25/14 | * [[47/42]], [[25/14]] | ||
* 28/25, 66/37 | * [[28/25]], [[66/37]] | ||
* 37/33, 41/23 | * [[37/33]], [[41/23]] | ||
* 46/41, 98/55 | * [[46/41]], [[98/55]] | ||
* '''55/49, 57/32''' | * '''[[55/49]], [[57/32]]''' | ||
* '''64/57, 16/9''' | * '''[[64/57]], [[16/9]]''' | ||
* 9/8, 55/31 | * [[9/8]], [[55/31]] | ||
* 62/55, 94/53 | * [[62/55]], [[94/53]] | ||
* 53/47, 39/22 | * [[53/47]], [[39/22]] | ||
* 44/39, 62/35 | * [[44/39]], [[62/35]] | ||
* 35/31, 23/13 | * [[35/31]], [[23/13]] | ||
* 26/23, 76/43 | * [[26/23]], [[76/43]] | ||
* 43/38, 53/30 | * [[43/38]], [[53/30]] | ||
* 60/53, 30/17 | * [[60/53]], [[30/17]] | ||
* 17/15, 37/21 | * [[17/15]], [[37/21]] | ||
* 42/37, 44/25 | * [[42/37]], [[44/25]] | ||
* 25/22, 51/29 | * [[25/22]], [[51/29]] | ||
* 58/51, 58/33 | * [[58/51]], [[58/33]] | ||
* 33/29, 72/41 | * [[33/29]], [[72/41]] | ||
* 41/36, 86/49 | * [[41/36]], [[86/49]] | ||
* '''49/43, 100/57''' | * '''[[49/43]], [[100/57]]''' | ||
* '''57/50, 7/4''' | * '''[[57/50]], [[7/4]]''' | ||
* 8/7, 96/55 | * [[8/7]], [[96/55]] | ||
* 55/48, 38/39 | * [[55/48]], [[38/39]] | ||
* 47/41, 82/47 | * [[47/41]], [[82/47]] | ||
* 39/34, 68/39 | * [[39/34]], [[68/39]] | ||
* 31/27, 54/31 | * [[31/27]], [[54/31]] | ||
* 54/47, 47/27 | * [[54/47]], [[47/27]] | ||
* 23/20, 40/23 | * [[23/20]], [[40/23]] | ||
* 38/33, 33/19 | * [[38/33]], [[33/19]] | ||
* 53/46, 92/53 | * [[53/46]], [[92/53]] | ||
* 15/13, 26/15 | * [[15/13]], [[26/15]] | ||
* 52/45, 45/26 | * [[52/45]], [[45/26]] | ||
* 37/32, 64/37 | * [[37/32]], [[64/37]] | ||
* 22/19, 19/11 | * [[22/19]], [[19/11]] | ||
* 51/44, 88/51 | * [[51/44]], [[88/51]] | ||
* 29/25, 50/29 | * [[29/25]], [[50/29]] | ||
* 36/31, 31/18 | * [[36/31]], [[31/18]] | ||
* 43/37, 74/43 | * [[43/37]], [[74/43]] | ||
* 50/43, 43/25 | * [[50/43]], [[43/25]] | ||
* '''57/49, 98/57''' | * '''[[57/49]], [[98/57]]''' | ||
* 64/55, 55/32 | * [[64/55]], [[55/32]] | ||
* 7/6, 12/7 | * [[7/6]], [[12/7]] | ||
* 62/53, 53/31 | * [[62/53]], [[53/31]] | ||
* 55/47, 94/55 | * [[55/47]], [[94/55]] | ||
* 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]] | ||
* 47/40, 80/47 | * [[47/40]], [[80/47]] | ||
* 20/17, 17/10 | * [[20/17]], [[17/10]] | ||
* 53/45, 90/53 | * [[53/45]], [[90/53]] | ||
* 33/28, 56/33 | * [[33/28]], [[56/33]] | ||
* 46/39, 39/23 | * [[46/39]], [[39/23]] | ||
* 13/11, 22/13 | * [[13/11]], [[22/13]] | ||
* 58/49, 49/29 | * [[58/49]], [[49/29]] | ||
* 45/38, 76/45 | * [[45/38]], [[76/45]] | ||
* 32/27, 27/16 | * [[32/27]], [[27/16]] | ||
* 51/43, 86/51 | * [[51/43]], [[86/51]] | ||
* 19/16, 32/19 | * [[19/16]], [[32/19]] | ||
* 44/37, 37/22 | * [[44/37]], [[37/22]] | ||
* 25/21, 42/25 | * [[25/21]], [[42/25]] | ||
* 56/47, 47/28 | * [[56/47]], [[47/28]] | ||
* 31/26, 52/31 | * [[31/26]], [[52/31]] | ||
* '''68/57, 57/34''' | * '''[[68/57]], [[57/34]]''' | ||
* 37/31, 62/37 | * [[37/31]], [[62/37]] | ||
* 43/36, 72/43 | * [[43/36]], [[72/43]] | ||
* 49/41, 82/49 | * [[49/41]], [[82/49]] | ||
* 55/46, 92/55 | * [[55/46]], [[92/55]] | ||
* 6/5, 5/3 | * [[6/5]], [[5/3]] | ||
* 53/44, 88/53 | * [[53/44]], [[88/53]] | ||
* 47/39, 78/47 | * [[47/39]], [[78/47]] | ||
* 41/34, 68/41 | * [[41/34]], [[68/41]] | ||
* 35/29, 58/35 | * [[35/29]], [[58/35]] | ||
* 64/53, 53/32 | * [[64/53]], [[53/32]] | ||
* 29/24, 48/29 | * [[29/24]], [[48/29]] | ||
* 52/43, 43/26 | * [[52/43]], [[43/26]] | ||
* 23/19, 38/23 | * [[23/19]], [[38/23]] | ||
* 40/33, 33/20 | * [[40/33]], [[33/20]] | ||
* '''57/47, 94/57''' | * '''[[57/47]], [[94/57]]''' | ||
* 17/14, 28/17 | * [[17/14]], [[28/17]] | ||
* 62/51, 51/31 | * [[62/51]], [[51/31]] | ||
* 45/37, 74/45 | * [[45/37]], [[74/45]] | ||
* 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]] | ||
* 60/49, 49/30 | * [[60/49]], [[49/30]] | ||
* 49/40, 80/49 | * [[49/40]], [[80/49]] | ||
* 38/31, 31/19 | * [[38/31]], [[31/19]] | ||
* 27/22, 44/27 | * [[27/22]], [[44/27]] | ||
* '''70/57, 57/35''' | * '''[[70/57]], [[57/35]]''' | ||
* 43/35, 70/43 | * [[43/35]], [[70/43]] | ||
* 16/13, 13/8 | * [[16/13]], [[13/8]] | ||
* 53/43, 86/53 | * [[53/43]], [[86/53]] | ||
* 37/30, 60/37 | * [[37/30]], [[60/37]] | ||
* 58/47, 47/29 | * [[58/47]], [[47/29]] | ||
* 21/17, 34/21 | * [[21/17]], [[34/21]] | ||
* 68/55, 55/34 | * [[68/55]], [[55/34]] | ||
* 47/38, 76/47 | * [[47/38]], [[76/47]] | ||
* 26/21, 21/13 | * [[26/21]], [[21/13]] | ||
* '''57/46, 92/57''' | * '''[[57/46]], [[92/57]]''' | ||
* 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]] | ||
* 51/41, 82/51 | * [[51/41]], [[82/51]] | ||
* 56/45, 45/28 | * [[56/45]], [[45/28]] | ||
* 66/53, 53/33 | * [[66/53]], [[53/33]] | ||
* 5/4, 8/5 | * [[5/4]], [[8/5]] | ||
* 64/51, 51/32 | * [[64/51]], [[51/32]] | ||
* 54/43, 43/27 | * [[54/43]], [[43/27]] | ||
* 49/39, 78/49 | * [[49/39]], [[78/49]] | ||
* 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]] | ||
* 53/42, 84/53 | * [[53/42]], [[84/53]] | ||
* 24/19, 19/12 | * [[24/19]], [[19/12]] | ||
* 43/34, 68/43 | * [[43/34]], [[68/43]] | ||
* 62/49, 49/31 | * [[62/49]], [[49/31]] | ||
* 19/15, 30/19 | * [[19/15]], [[30/19]] | ||
* 52/41, 41/26 | * [[52/41]], [[41/26]] | ||
* 33/26, 52/33 | * [[33/26]], [[52/33]] | ||
* 47/37, 74/47 | * [[47/37]], [[74/47]] | ||
* 14/11, 11/7 | * [[14/11]], [[11/7]] | ||
* 51/40, 80/51 | * [[51/40]], [[80/51]] | ||
* 37/29, 58/37 | * [[37/29]], [[58/37]] | ||
* 60/47, 47/30 | * [[60/47]], [[47/30]] | ||
* 23/18, 36/23 | * [[23/18]], [[36/23]] | ||
* 55/43, 86/55 | * [[55/43]], [[86/55]] | ||
* 32/25, 25/16 | * [[32/25]], [[25/16]] | ||
* 41/32, 64/41 | * [[41/32]], [[64/41]] | ||
* 50/39, 39/25 | * [[50/39]], [[39/25]] | ||
* 68/53, 53/34 | * [[68/53]], [[53/34]] | ||
* 9/7, 14/9 | * [[9/7]], [[14/9]] | ||
* 58/45, 45/29 | * [[58/45]], [[45/29]] | ||
* 49/38, 76/49 | * [[49/38]], [[76/49]] | ||
* 40/31, 31/20 | * [[40/31]], [[31/20]] | ||
* 31/24, 48/31 | * [[31/24]], [[48/31]] | ||
* 53/41, 82/53 | * [[53/41]], [[82/53]] | ||
* 22/17, 17/11 | * [[22/17]], [[17/11]] | ||
* '''57/44, 88/57''' | * '''[[57/44]], [[88/57]]''' | ||
* 35/27, 54/35 | * [[35/27]], [[54/35]] | ||
* 48/37, 37/24 | * [[48/37]], [[37/24]] | ||
* '''74/57, 57/37''' | * '''[[74/57]], [[57/37]]''' | ||
* 13/10, 20/13 | * [[13/10]], [[20/13]] | ||
* 56/43, 43/28 | * [[56/43]], [[43/28]] | ||
* 43/33, 66/43 | * [[43/33]], [[66/43]] | ||
* 30/23, 23/15 | * [[30/23]], [[23/15]] | ||
* 47/36, 72/47 | * [[47/36]], [[72/47]] | ||
* 64/49, 49/32 | * [[64/49]], [[49/32]] | ||
* 17/13, 26/17 | * [[17/13]], [[26/17]] | ||
* 72/55, 55/36 | * [[72/55]], [[55/36]] | ||
* 55/42, 84/55 | * [[55/42]], [[84/55]] | ||
* 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]] | ||
* 62/47, 47/31 | * [[62/47]], [[47/31]] | ||
* 33/25, 50/33 | * [[33/25]], [[50/33]] | ||
* 70/53, 53/35 | * [[70/53]], [[53/35]] | ||
* 37/28, 56/37 | * [[37/28]], [[56/37]] | ||
* 41/31, 62/41 | * [[41/31]], [[62/41]] | ||
* 45/34, 68/45 | * [[45/34]], [[68/45]] | ||
* 49/37, 74/49 | * [[49/37]], [[74/49]] | ||
* 53/40, 80/53 | * [[53/40]], [[80/53]] | ||
* '''57/43, 86/57''' | * '''[[57/43]], [[86/57]]''' | ||
* 4/3, 3/2 | * [[4/3]], [[3/2]] | ||
* 55/41, 82/55 | * [[55/41]], [[82/55]] | ||
* 51/38, 76/51 | * [[51/38]], [[76/51]] | ||
* 47/35, 70/47 | * [[47/35]], [[70/47]] | ||
* 43/32, 64/43 | * [[43/32]], [[64/43]] | ||
* 39/29, 58/39 | * [[39/29]], [[58/39]] | ||
* 74/55, 55/37 | * [[74/55]], [[55/37]] | ||
* 35/26, 52/35 | * [[35/26]], [[52/35]] | ||
* 66/49, 49/33 | * [[66/49]], [[49/33]] | ||
* 31/23, 46/31 | * [[31/23]], [[46/31]] | ||
* 58/43, 43/29 | * [[58/43]], [[43/29]] | ||
* 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]] | ||
* 72/53, 53/36 | * [[72/53]], [[53/36]] | ||
* 53/39, 78/53 | * [[53/39]], [[78/53]] | ||
* 34/25, 25/17 | * [[34/25]], [[25/17]] | ||
* 49/36, 72/49 | * [[49/36]], [[72/49]] | ||
* 64/47, 47/32 | * [[64/47]], [[47/32]] | ||
* 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]] | ||
* 70/51, 51/35 | * [[70/51]], [[51/35]] | ||
* 11/8, 16/11 | * [[11/8]], [[16/11]] | ||
* 62/45, 45/31 | * [[62/45]], [[45/31]] | ||
* 51/37, 74/51 | * [[51/37]], [[74/51]] | ||
* 40/29, 29/20 | * [[40/29]], [[29/20]] | ||
* 29/21, 42/29 | * [[29/21]], [[42/29]] | ||
* 76/55, 55/38 | * [[76/55]], [[55/38]] | ||
* 47/34, 68/47 | * [[47/34]], [[68/47]] | ||
* 18/13, 13/9 | * [[18/13]], [[13/9]] | ||
* 43/31, 62/43 | * [[43/31]], [[62/43]] | ||
* 68/49, 49/34 | * [[68/49]], [[49/34]] | ||
* 25/18, 36/25 | * [[25/18]], [[36/25]] | ||
* '''57/41, 82/57''' | * '''[[57/41]], [[82/57]]''' | ||
* 32/23, 23/16 | * [[32/23]], [[23/16]] | ||
* 39/28, 56/39 | * [[39/28]], [[56/39]] | ||
* 46/33, 33/23 | * [[46/33]], [[33/23]] | ||
* 53/38, 76/53 | * [[53/38]], [[76/53]] | ||
* 60/43, 43/30 | * [[60/43]], [[43/30]] | ||
* 74/53, 53/37 | * [[74/53]], [[53/37]] | ||
* 7/5, 10/7 | * [[7/5]], [[10/7]] | ||
* '''80/57, 57/40''' | * '''[[80/57]], [[57/40]]''' | ||
* 66/47, 47/33 | * [[66/47]], [[47/33]] | ||
* 52/37, 37/26 | * [[52/37]], [[37/26]] | ||
* 45/32, 64/45 | * [[45/32]], [[64/45]] | ||
* 38/27, 27/19 | * [[38/27]], [[27/19]] | ||
* 31/22, 44/31 | * [[31/22]], [[44/31]] | ||
* 55/39, 78/55 | * [[55/39]], [[78/55]] | ||
* 24/17, 17/12 | * [[24/17]], [[17/12]] | ||
* 41/29, 58/41 | * [[41/29]], [[58/41]] | ||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 20:48, 18 September 2025
¨The 57-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 57 and k is an integer. To the 55-odd-limit, it adds 18 pairs of octave-reduced intervals involving 57.
Below is a list of all octave-reduced intervals in the 57-odd-limit.
- 1/1
- 58/57, 57/29
- 57/56, 112/57
- 56/55, 55/28
- 55/54, 108/55
- 54/53, 53/27
- 53/52, 104/53
- 52/51, 51/26
- 51/50, 100/51
- 50/49, 49/25
- 49/48, 96/49
- 48/47, 47/24
- 47/46, 92/47
- 46/45, 45/23
- 45/44, 88/45
- 44/43, 43/22
- 43/42, 84/43
- 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
- 57/55, 110/57
- 28/27, 27/14
- 55/53, 106/55
- 27/26, 52/27
- 53/51, 102/53
- 26/25, 25/13
- 51/49, 98/51
- 25/24, 48/25
- 49/47, 94/49
- 24/23, 23/12
- 47/45, 90/47
- 23/22, 44/23
- 45/43, 86/45
- 22/21, 21/11
- 43/41, 82/43
- 21/20, 40/21
- 41/39, 78/41
- 20/19, 19/10
- 39/37, 74/39
- 58/55, 55/29
- 19/18, 36/19
- 56/53, 53/28
- 37/35, 70/37
- 55/52, 104/55
- 18/17, 17/9
- 53/50, 100/53
- 35/33, 66/35
- 52/49, 49/26
- 17/16, 32/17
- 50/47, 47/25
- 33/31, 62/33
- 49/46, 92/49
- 16/15, 15/8
- 47/44, 88/47
- 31/29, 58/31
- 46/43, 43/23
- 15/14, 28/15
- 44/41, 41/22
- 29/27, 54/29
- 43/40, 80/43
- 57/53, 106/57
- 14/13, 13/7
- 55/51, 102/55
- 41/38, 76/41
- 27/25, 50/27
- 40/37, 37/20
- 53/49, 98/53
- 13/12, 24/13
- 51/47, 94/51
- 38/35, 35/19
- 25/23, 46/25
- 62/57, 57/31
- 37/34, 68/37
- 49/45, 11/6
- 12/11, 86/47
- 47/43, 64/35
- 35/32, 53/29
- 58/53, 42/23
- 23/21, 104/57
- 57/52, 31/17
- 34/31, 82/45
- 45/41 51/28
- 56/51, 20/11
- 11/10, 49/27
- 54/49, 78/43
- 43/39, 29/16
- 32/29, 96/53
- 53/48, 38/21
- 21/19, 47/26
- 52/47, 56/31
- 31/28, 74/41
- 41/37, 92/51
- 51/46, 9/5
- 10/9, 88/49
- 49/44, 70/39
- 39/35, 52/29
- 29/26, 43/24
- 48/43, 34/19
- 19/17, 84/47
- 47/42, 25/14
- 28/25, 66/37
- 37/33, 41/23
- 46/41, 98/55
- 55/49, 57/32
- 64/57, 16/9
- 9/8, 55/31
- 62/55, 94/53
- 53/47, 39/22
- 44/39, 62/35
- 35/31, 23/13
- 26/23, 76/43
- 43/38, 53/30
- 60/53, 30/17
- 17/15, 37/21
- 42/37, 44/25
- 25/22, 51/29
- 58/51, 58/33
- 33/29, 72/41
- 41/36, 86/49
- 49/43, 100/57
- 57/50, 7/4
- 8/7, 96/55
- 55/48, 38/39
- 47/41, 82/47
- 39/34, 68/39
- 31/27, 54/31
- 54/47, 47/27
- 23/20, 40/23
- 38/33, 33/19
- 53/46, 92/53
- 15/13, 26/15
- 52/45, 45/26
- 37/32, 64/37
- 22/19, 19/11
- 51/44, 88/51
- 29/25, 50/29
- 36/31, 31/18
- 43/37, 74/43
- 50/43, 43/25
- 57/49, 98/57
- 64/55, 55/32
- 7/6, 12/7
- 62/53, 53/31
- 55/47, 94/55
- 48/41, 41/24
- 41/35, 70/41
- 34/29, 29/17
- 27/23, 46/27
- 47/40, 80/47
- 20/17, 17/10
- 53/45, 90/53
- 33/28, 56/33
- 46/39, 39/23
- 13/11, 22/13
- 58/49, 49/29
- 45/38, 76/45
- 32/27, 27/16
- 51/43, 86/51
- 19/16, 32/19
- 44/37, 37/22
- 25/21, 42/25
- 56/47, 47/28
- 31/26, 52/31
- 68/57, 57/34
- 37/31, 62/37
- 43/36, 72/43
- 49/41, 82/49
- 55/46, 92/55
- 6/5, 5/3
- 53/44, 88/53
- 47/39, 78/47
- 41/34, 68/41
- 35/29, 58/35
- 64/53, 53/32
- 29/24, 48/29
- 52/43, 43/26
- 23/19, 38/23
- 40/33, 33/20
- 57/47, 94/57
- 17/14, 28/17
- 62/51, 51/31
- 45/37, 74/45
- 28/23, 23/14
- 39/32, 64/39
- 50/41, 41/25
- 11/9, 18/11
- 60/49, 49/30
- 49/40, 80/49
- 38/31, 31/19
- 27/22, 44/27
- 70/57, 57/35
- 43/35, 70/43
- 16/13, 13/8
- 53/43, 86/53
- 37/30, 60/37
- 58/47, 47/29
- 21/17, 34/21
- 68/55, 55/34
- 47/38, 76/47
- 26/21, 21/13
- 57/46, 92/57
- 31/25, 50/31
- 36/29, 29/18
- 41/33, 66/41
- 46/37, 37/23
- 51/41, 82/51
- 56/45, 45/28
- 66/53, 53/33
- 5/4, 8/5
- 64/51, 51/32
- 54/43, 43/27
- 49/39, 78/49
- 44/35, 35/22
- 39/31, 62/39
- 34/27, 27/17
- 29/23, 46/29
- 53/42, 84/53
- 24/19, 19/12
- 43/34, 68/43
- 62/49, 49/31
- 19/15, 30/19
- 52/41, 41/26
- 33/26, 52/33
- 47/37, 74/47
- 14/11, 11/7
- 51/40, 80/51
- 37/29, 58/37
- 60/47, 47/30
- 23/18, 36/23
- 55/43, 86/55
- 32/25, 25/16
- 41/32, 64/41
- 50/39, 39/25
- 68/53, 53/34
- 9/7, 14/9
- 58/45, 45/29
- 49/38, 76/49
- 40/31, 31/20
- 31/24, 48/31
- 53/41, 82/53
- 22/17, 17/11
- 57/44, 88/57
- 35/27, 54/35
- 48/37, 37/24
- 74/57, 57/37
- 13/10, 20/13
- 56/43, 43/28
- 43/33, 66/43
- 30/23, 23/15
- 47/36, 72/47
- 64/49, 49/32
- 17/13, 26/17
- 72/55, 55/36
- 55/42, 84/55
- 38/29, 29/19
- 21/16, 32/21
- 46/35, 35/23
- 25/19, 38/25
- 54/41, 41/27
- 29/22, 44/29
- 62/47, 47/31
- 33/25, 50/33
- 70/53, 53/35
- 37/28, 56/37
- 41/31, 62/41
- 45/34, 68/45
- 49/37, 74/49
- 53/40, 80/53
- 57/43, 86/57
- 4/3, 3/2
- 55/41, 82/55
- 51/38, 76/51
- 47/35, 70/47
- 43/32, 64/43
- 39/29, 58/39
- 74/55, 55/37
- 35/26, 52/35
- 66/49, 49/33
- 31/23, 46/31
- 58/43, 43/29
- 27/20, 40/27
- 50/37, 37/25
- 23/17, 34/23
- 42/31, 31/21
- 19/14, 28/19
- 72/53, 53/36
- 53/39, 78/53
- 34/25, 25/17
- 49/36, 72/49
- 64/47, 47/32
- 15/11, 22/15
- 56/41, 41/28
- 41/30, 60/41
- 26/19, 19/13
- 37/27, 54/37
- 48/35, 35/24
- 70/51, 51/35
- 11/8, 16/11
- 62/45, 45/31
- 51/37, 74/51
- 40/29, 29/20
- 29/21, 42/29
- 76/55, 55/38
- 47/34, 68/47
- 18/13, 13/9
- 43/31, 62/43
- 68/49, 49/34
- 25/18, 36/25
- 57/41, 82/57
- 32/23, 23/16
- 39/28, 56/39
- 46/33, 33/23
- 53/38, 76/53
- 60/43, 43/30
- 74/53, 53/37
- 7/5, 10/7
- 80/57, 57/40
- 66/47, 47/33
- 52/37, 37/26
- 45/32, 64/45
- 38/27, 27/19
- 31/22, 44/31
- 55/39, 78/55
- 24/17, 17/12
- 41/29, 58/41
| Ratio | Size (¢) | Color name |
| 58/57 | 30.109 | twenonu unison |
| 57/56 | 30.642 | noru unison |
| 57/55 | 61.836 | nolugu 2nd |
| 57/53 | 125.963 | fithuno 2nd |
| 62/57 | 145.568 | thiwonu unison |
| 57/52 | 158.94 | nothu 2nd |
| 64/57 | 200.532 | inu 2nd |
| 57/50 | 226.841 | nogugu 3rd |
| 57/49 | 261.816 | noruru 2nd |
| 68/57 | 305.487 | nuso 3rd |
| 57/47 | 333.961 | fosuno 3rd |
| 70/57 | 355.672 | nuzoyo 3rd |
| 57/46 | 371.194 | twethuno 3rd |
| 57/44 | 448.15 | nolu 4th |
| 74/57 | 451.876 | thisonu 4th |
| 57/43 | 487.95 | fothuno 4th |
| 57/41 | 570.406 | fowuno 4th |
| 80/57 | 586.846 | nuyo 4th |
| 57/40 | 613.154 | nogu 5th |
| 82/57 | 629.594 | fowunu 4th |
| 86/57 | 712.05 | fothonu 5th |
| 57/37 | 748.124 | thisuno 5th |
| 88/57 | 751.85 | nulo 5th |
| 92/57 | 828.806 | twethonu 6th |
| 57/35 | 844.328 | norugu 6th |
| 94/57 | 866.039 | fosonu 6th |
| 57/34 | 894.513 | nosu 6th |
| 98/57 | 938.184 | nuzozo 7th |
| 100/57 | 973.159 | nuyoyo 6th |
| 57/32 | 999.468 | ino 7th |
| 104/57 | 1041.06 | nutho 7th |
| 57/31 | 1054.432 | thiwuno octave |
| 106/57 | 1074.037 | fithonu 7th |
| 110/57 | 1138.164 | nuloyo 7th |
| 112/57 | 1169.358 | nuzo octave |
| 57/29 | 1169.891 | twenuno octave |
The smallest EDO to be consistent in the 57-odd-limit is 20567edo. It is also distinctly consistent and almost purely consistent in the 57-odd-limit.