57-odd-limit: Difference between revisions

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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.
{{Odd-limit navigation|57}}¨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.
{| class="wikitable mw-collapsible mw-collapsed"
 
|+57-odd-limit intervals
* [[1/1]]
|1
* '''[[58/57]], [[57/29]]'''
|2
* '''[[57/56]], [[112/57]]'''
|-
* [[56/55]], [[55/28]]
|58/57
* [[55/54]], [[108/55]]
|57/29
* [[54/53]], [[53/27]]
|-
* [[53/52]], [[104/53]]
|57/56
* [[52/51]], [[51/26]]
|112/57
* [[51/50]], [[100/51]]
|-
* [[50/49]], [[49/25]]
|56/55
* [[49/48]], [[96/49]]
|55/28
* [[48/47]], [[47/24]]
|-
* [[47/46]], [[92/47]]
|55/54
* [[46/45]], [[45/23]]
|108/55
* [[45/44]], [[88/45]]
|-
* [[44/43]], [[43/22]]
|54/53
* [[43/42]], [[84/43]]
|53/27
* [[42/41]], [[41/21]]
|-
* [[41/40]], [[80/41]]
|53/52
* [[40/39]], [[39/20]]
|104/53
* [[39/38]], [[76/39]]
|-
* [[38/37]], [[37/19]]
|52/51
* [[37/36]], [[72/37]]
|51/26
* [[36/35]], [[35/18]]
|-
* [[35/34]], [[68/35]]
|51/50
* [[34/33]], [[33/17]]
|100/51
* [[33/32]], [[64/33]]
|-
* [[32/31]], [[31/16]]
|50/49
* [[31/30]], [[60/31]]
|49/25
* [[30/29]], [[29/15]]
|-
* [[29/28]], [[56/29]]
|49/48
* '''[[57/55]], [[110/57]]'''
|96/49
* [[28/27]], [[27/14]]
|-
* [[55/53]], [[106/55]]
|48/47
* [[27/26]], [[52/27]]
|47/24
* [[53/51]], [[102/53]]
|-
* [[26/25]], [[25/13]]
|47/46
* [[51/49]], [[98/51]]
|92/47
* [[25/24]], [[48/25]]
|-
* [[49/47]], [[94/49]]
|46/45
* [[24/23]], [[23/12]]
|45/23
* [[47/45]], [[90/47]]
|-
* [[23/22]], [[44/23]]
|45/44
* [[45/43]], [[86/45]]
|88/45
* [[22/21]], [[21/11]]
|-
* [[43/41]], [[82/43]]
|44/43
* [[21/20]], [[40/21]]
|43/22
* [[41/39]], [[78/41]]
|-
* [[20/19]], [[19/10]]
|43/42
* [[39/37]], [[74/39]]
|84/43
* [[58/55]], [[55/29]]
|-
* [[19/18]], [[36/19]]
|42/41
* [[56/53]], [[53/28]]
|41/21
* [[37/35]], [[70/37]]
|-
* [[55/52]], [[104/55]]
|41/40
* [[18/17]], [[17/9]]
|80/41
* [[53/50]], [[100/53]]
|-
* [[35/33]], [[66/35]]
|40/39
* [[52/49]], [[49/26]]
|39/20
* [[17/16]], [[32/17]]
|-
* [[50/47]], [[47/25]]
|39/38
* [[33/31]], [[62/33]]
|76/39
* [[49/46]], [[92/49]]
|-
* [[16/15]], [[15/8]]
|38/37
* [[47/44]], [[88/47]]
|37/19
* [[31/29]], [[58/31]]
|-
* [[46/43]], [[43/23]]
|37/36
* [[15/14]], [[28/15]]
|72/37
* [[44/41]], [[41/22]]
|-
* [[29/27]], [[54/29]]
|36/35
* [[43/40]], [[80/43]]
|35/18
* '''[[57/53]], [[106/57]]'''
|-
* [[14/13]], [[13/7]]
|35/34
* [[55/51]], [[102/55]]
|68/35
* [[41/38]], [[76/41]]
|-
* [[27/25]], [[50/27]]
|34/33
* [[40/37]], [[37/20]]
|33/17
* [[53/49]], [[98/53]]
|-
* [[13/12]], [[24/13]]
|33/32
* [[51/47]], [[94/51]]
|64/33
* [[38/35]], [[35/19]]
|-
* [[25/23]], [[46/25]]
|32/31
* '''[[62/57]], [[57/31]]'''
|31/16
* [[37/34]], [[68/37]]
|-
* [[49/45]], [[11/6]]
|31/30
* [[12/11]], [[86/47]]
|60/31
* [[47/43]], [[64/35]]
|-
* [[35/32]], [[53/29]]
|30/29
* [[58/53]], [[42/23]]
|29/15
* '''[[23/21]], [[104/57]]'''
|-
* '''[[57/52]], [[31/17]]'''
|29/28
* [[34/31]], [[82/45]]
|56/29
* [[45/41 ]] [[51/28]]
|-
* [[56/51]], [[20/11]]
|57/55
* [[11/10]], [[49/27]]
|110/57
* [[54/49]], [[78/43]]
|-
* [[43/39]], [[29/16]]
|28/27
* [[32/29]], [[96/53]]
|27/14
* [[53/48]], [[38/21]]
|-
* [[21/19]], [[47/26]]
|55/53
* [[52/47]], [[56/31]]
|106/55
* [[31/28]], [[74/41]]
|-
* [[41/37]], [[92/51]]
|27/26
* [[51/46]], [[9/5]]
|52/27
* [[10/9]], [[88/49]]
|-
* [[49/44]], [[70/39]]
|53/51
* [[39/35]], [[52/29]]
|102/53
* [[29/26]], [[43/24]]
|-
* [[48/43]], [[34/19]]
|26/25
* [[19/17]], [[84/47]]
|25/13
* [[47/42]], [[25/14]]
|-
* [[28/25]], [[66/37]]
|51/49
* [[37/33]], [[41/23]]
|98/51
* [[46/41]], [[98/55]]
|-
* '''[[55/49]], [[57/32]]'''
|25/24
* '''[[64/57]], [[16/9]]'''
|48/25
* [[9/8]], [[55/31]]
|-
* [[62/55]], [[94/53]]
|49/47
* [[53/47]], [[39/22]]
|94/49
* [[44/39]], [[62/35]]
|-
* [[35/31]], [[23/13]]
|24/23
* [[26/23]], [[76/43]]
|23/12
* [[43/38]], [[53/30]]
|-
* [[60/53]], [[30/17]]
|47/45
* [[17/15]], [[37/21]]
|90/47
* [[42/37]], [[44/25]]
|-
* [[25/22]], [[51/29]]
|23/22
* [[58/51]], [[58/33]]
|44/23
* [[33/29]], [[72/41]]
|-
* [[41/36]], [[86/49]]
|45/43
* '''[[49/43]], [[100/57]]'''
|86/45
* '''[[57/50]], [[7/4]]'''
|-
* [[8/7]], [[96/55]]
|22/21
* [[55/48]], [[38/39]]
|21/11
* [[47/41]], [[82/47]]
|-
* [[39/34]], [[68/39]]
|43/41
* [[31/27]], [[54/31]]
|82/43
* [[54/47]], [[47/27]]
|-
* [[23/20]], [[40/23]]
|21/20
* [[38/33]], [[33/19]]
|40/21
* [[53/46]], [[92/53]]
|-
* [[15/13]], [[26/15]]
|41/39
* [[52/45]], [[45/26]]
|78/41
* [[37/32]], [[64/37]]
|-
* [[22/19]], [[19/11]]
|20/19
* [[51/44]], [[88/51]]
|19/10
* [[29/25]], [[50/29]]
|-
* [[36/31]], [[31/18]]
|39/37
* [[43/37]], [[74/43]]
|74/39
* [[50/43]], [[43/25]]
|-
* '''[[57/49]], [[98/57]]'''
|58/55
* [[64/55]], [[55/32]]
|55/29
* [[7/6]], [[12/7]]
|-
* [[62/53]], [[53/31]]
|19/18
* [[55/47]], [[94/55]]
|36/19
* [[48/41]], [[41/24]]
|-
* [[41/35]], [[70/41]]
|56/53
* [[34/29]], [[29/17]]
|53/28
* [[27/23]], [[46/27]]
|-
* [[47/40]], [[80/47]]
|37/35
* [[20/17]], [[17/10]]
|70/37
* [[53/45]], [[90/53]]
|-
* [[33/28]], [[56/33]]
|55/52
* [[46/39]], [[39/23]]
|104/55
* [[13/11]], [[22/13]]
|-
* [[58/49]], [[49/29]]
|18/17
* [[45/38]], [[76/45]]
|17/9
* [[32/27]], [[27/16]]
|-
* [[51/43]], [[86/51]]
|53/50
* [[19/16]], [[32/19]]
|100/53
* [[44/37]], [[37/22]]
|-
* [[25/21]], [[42/25]]
|35/33
* [[56/47]], [[47/28]]
|66/35
* [[31/26]], [[52/31]]
|-
* '''[[68/57]], [[57/34]]'''
|52/49
* [[37/31]], [[62/37]]
|49/26
* [[43/36]], [[72/43]]
|-
* [[49/41]], [[82/49]]
|17/16
* [[55/46]], [[92/55]]
|32/17
* [[6/5]], [[5/3]]
|-
* [[53/44]], [[88/53]]
|50/47
* [[47/39]], [[78/47]]
|47/25
* [[41/34]], [[68/41]]
|-
* [[35/29]], [[58/35]]
|33/31
* [[64/53]], [[53/32]]
|62/33
* [[29/24]], [[48/29]]
|-
* [[52/43]], [[43/26]]
|49/46
* [[23/19]], [[38/23]]
|92/49
* [[40/33]], [[33/20]]
|-
* '''[[57/47]], [[94/57]]'''
|16/15
* [[17/14]], [[28/17]]
|15/8
* [[62/51]], [[51/31]]
|-
* [[45/37]], [[74/45]]
|47/44
* [[28/23]], [[23/14]]
|88/47
* [[39/32]], [[64/39]]
|-
* [[50/41]], [[41/25]]
|31/29
* [[11/9]], [[18/11]]
|58/31
* [[60/49]], [[49/30]]
|-
* [[49/40]], [[80/49]]
|46/43
* [[38/31]], [[31/19]]
|43/23
* [[27/22]], [[44/27]]
|-
* '''[[70/57]], [[57/35]]'''
|15/14
* [[43/35]], [[70/43]]
|28/15
* [[16/13]], [[13/8]]
|-
* [[53/43]], [[86/53]]
|44/41
* [[37/30]], [[60/37]]
|41/22
* [[58/47]], [[47/29]]
|-
* [[21/17]], [[34/21]]
|29/27
* [[68/55]], [[55/34]]
|54/29
* [[47/38]], [[76/47]]
|-
* [[26/21]], [[21/13]]
|43/40
* '''[[57/46]], [[92/57]]'''
|80/43
* [[31/25]], [[50/31]]
|-
* [[36/29]], [[29/18]]
|57/53
* [[41/33]], [[66/41]]
|106/57
* [[46/37]], [[37/23]]
|-
* [[51/41]], [[82/51]]
|14/13
* [[56/45]], [[45/28]]
|13/7
* [[66/53]], [[53/33]]
|-
* [[5/4]], [[8/5]]
|55/51
* [[64/51]], [[51/32]]
|102/55
* [[54/43]], [[43/27]]
|-
* [[49/39]], [[78/49]]
|41/38
* [[44/35]], [[35/22]]
|76/41
* [[39/31]], [[62/39]]
|-
* [[34/27]], [[27/17]]
|27/25
* [[29/23]], [[46/29]]
|50/27
* [[53/42]], [[84/53]]
|-
* [[24/19]], [[19/12]]
|40/37
* [[43/34]], [[68/43]]
|37/20
* [[62/49]], [[49/31]]
|-
* [[19/15]], [[30/19]]
|53/49
* [[52/41]], [[41/26]]
|98/53
* [[33/26]], [[52/33]]
|-
* [[47/37]], [[74/47]]
|13/12
* [[14/11]], [[11/7]]
|24/13
* [[51/40]], [[80/51]]
|-
* [[37/29]], [[58/37]]
|51/47
* [[60/47]], [[47/30]]
|94/51
* [[23/18]], [[36/23]]
|-
* [[55/43]], [[86/55]]
|38/35
* [[32/25]], [[25/16]]
|35/19
* [[41/32]], [[64/41]]
|-
* [[50/39]], [[39/25]]
|25/23
* [[68/53]], [[53/34]]
|46/25
* [[9/7]], [[14/9]]
|-
* [[58/45]], [[45/29]]
|62/57
* [[49/38]], [[76/49]]
|57/31
* [[40/31]], [[31/20]]
|-
* [[31/24]], [[48/31]]
|37/34
* [[53/41]], [[82/53]]
|68/37
* [[22/17]], [[17/11]]
|-
* '''[[57/44]], [[88/57]]'''
|49/45
* [[35/27]], [[54/35]]
|11/6
* [[48/37]], [[37/24]]
|-
* '''[[74/57]], [[57/37]]'''
|12/11
* [[13/10]], [[20/13]]
|86/47
* [[56/43]], [[43/28]]
|-
* [[43/33]], [[66/43]]
|47/43
* [[30/23]], [[23/15]]
|64/35
* [[47/36]], [[72/47]]
|-
* [[64/49]], [[49/32]]
|35/32
* [[17/13]], [[26/17]]
|53/29
* [[72/55]], [[55/36]]
|-
* [[55/42]], [[84/55]]
|58/53
* [[38/29]], [[29/19]]
|42/23
* [[21/16]], [[32/21]]
|-
* [[46/35]], [[35/23]]
|23/21
* [[25/19]], [[38/25]]
|104/57
* [[54/41]], [[41/27]]
|-
* [[29/22]], [[44/29]]
|57/52
* [[62/47]], [[47/31]]
|31/17
* [[33/25]], [[50/33]]
|-
* [[70/53]], [[53/35]]
|34/31
* [[37/28]], [[56/37]]
|82/45
* [[41/31]], [[62/41]]
|-
* [[45/34]], [[68/45]]
|45/41
* [[49/37]], [[74/49]]
|51/28
* [[53/40]], [[80/53]]
|-
* '''[[57/43]], [[86/57]]'''
|56/51
* [[4/3]], [[3/2]]
|20/11
* [[55/41]], [[82/55]]
|-
* [[51/38]], [[76/51]]
|11/10
* [[47/35]], [[70/47]]
|49/27
* [[43/32]], [[64/43]]
|-
* [[39/29]], [[58/39]]
|54/49
* [[74/55]], [[55/37]]
|78/43
* [[35/26]], [[52/35]]
|-
* [[66/49]], [[49/33]]
|43/39
* [[31/23]], [[46/31]]
|29/16
* [[58/43]], [[43/29]]
|-
* [[27/20]], [[40/27]]
|32/29
* [[50/37]], [[37/25]]
|96/53
* [[23/17]], [[34/23]]
|-
* [[42/31]], [[31/21]]
|53/48
* [[19/14]], [[28/19]]
|38/21
* [[72/53]], [[53/36]]
|-
* [[53/39]], [[78/53]]
|21/19
* [[34/25]], [[25/17]]
|47/26
* [[49/36]], [[72/49]]
|-
* [[64/47]], [[47/32]]
|52/47
* [[15/11]], [[22/15]]
|56/31
* [[56/41]], [[41/28]]
|-
* [[41/30]], [[60/41]]
|31/28
* [[26/19]], [[19/13]]
|74/41
* [[37/27]], [[54/37]]
|-
* [[48/35]], [[35/24]]
|41/37
* [[70/51]], [[51/35]]
|92/51
* [[11/8]], [[16/11]]
|-
* [[62/45]], [[45/31]]
|51/46
* [[51/37]], [[74/51]]
|9/5
* [[40/29]], [[29/20]]
|-
* [[29/21]], [[42/29]]
|10/9
* [[76/55]], [[55/38]]
|88/49
* [[47/34]], [[68/47]]
|-
* [[18/13]], [[13/9]]
|49/44
* [[43/31]], [[62/43]]
|70/39
* [[68/49]], [[49/34]]
|-
* [[25/18]], [[36/25]]
|39/35
* '''[[57/41]], [[82/57]]'''
|52/29
* [[32/23]], [[23/16]]
|-
* [[39/28]], [[56/39]]
|29/26
* [[46/33]], [[33/23]]
|43/24
* [[53/38]], [[76/53]]
|-
* [[60/43]], [[43/30]]
|48/43
* [[74/53]], [[53/37]]
|34/19
* [[7/5]], [[10/7]]
|-
* '''[[80/57]], [[57/40]]'''
|19/17
* [[66/47]], [[47/33]]
|84/47
* [[52/37]], [[37/26]]
|-
* [[45/32]], [[64/45]]
|47/42
* [[38/27]], [[27/19]]
|25/14
* [[31/22]], [[44/31]]
|-
* [[55/39]], [[78/55]]
|28/25
* [[24/17]], [[17/12]]
|66/37
* [[41/29]], [[58/41]]
|-
 
|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
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|43/34
|68/43
|-
|62/49
|49/31
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|19/15
|30/19
|-
|52/41
|41/26
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|33/26
|52/33
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|47/37
|74/47
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|14/11
|11/7
|-
|51/40
|80/51
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|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
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|25/19
|38/25
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|54/41
|41/27
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|29/22
|44/29
|-
|62/47
|47/31
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|33/25
|50/33
|-
|70/53
|53/35
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|37/28
|56/37
|-
|41/31
|62/41
|-
|45/34
|68/45
|-
|49/37
|74/49
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|53/40
|80/53
|-
|57/43
|86/57
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|4/3
|3/2
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|55/41
|82/55
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|51/38
|76/51
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|47/35
|70/47
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|43/32
|64/43
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|39/29
|58/39
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|74/55
|55/37
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|35/26
|52/35
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|66/49
|49/33
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|31/23
|46/31
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|58/43
|43/29
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|27/20
|40/27
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|50/37
|37/25
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|23/17
|34/23
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|42/31
|31/21
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|19/14
|28/19
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|72/53
|53/36
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|53/39
|78/53
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|34/25
|25/17
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|49/36
|72/49
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|64/47
|47/32
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|15/11
|22/15
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|56/41
|41/28
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|41/30
|60/41
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|26/19
|19/13
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|37/27
|54/37
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|48/35
|35/24
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|70/51
|51/35
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|11/8
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|74/51
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|29/20
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|29/21
|42/29
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|76/55
|55/38
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|18/13
|13/9
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|43/31
|62/43
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|49/34
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|36/25
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{| class="wikitable"
{| class="wikitable"
|Ratio
|Ratio
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|twenuno octave
|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.
The smallest EDO to be consistent in the 57-odd-limit is [[20567edo]], on which it is also distinctly consistent and ''almost'' purely consistent (harmonic 49 is off by 26.3%).
 
[[Category:Odd limits]]

Latest revision as of 09:34, 1 October 2025

← 55-odd-limit  57-odd-limit  59-odd-limit →

¨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.

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, on which it is also distinctly consistent and almost purely consistent (harmonic 49 is off by 26.3%).

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