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37-odd-limit: Difference between revisions

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{{Odd-limit navigation}}The 37'''-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'' ≤ 37 and ''k'' is an integer. To the [[39-odd-limit|37-odd-limit]], it adds 18 pairs of [[octave-reduced]] intervals involving 37.
{{Odd-limit navigation|37}}
 
{{Odd-limit intro|37}}
Below is a list of all octave-reduced intervals in the 37-odd-limit.


* [[1/1]]
* [[1/1]]
* [[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]]
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* [[20/19]], [[19/10]]
* [[20/19]], [[19/10]]
* [[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]]
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* [[14/13]], [[13/7]]
* [[14/13]], [[13/7]]
* [[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]]
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* [[19/17]], [[34/19]]
* [[19/17]], [[34/19]]
* [[28/25]], [[25/14]]
* [[28/25]], [[25/14]]
* [[37/33]], [[66/37]]
* '''[[37/33]], [[66/37]]'''
* [[9/8]], [[16/9]]
* [[9/8]], [[16/9]]
* [[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]]
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* [[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]]
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* [[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]]
* [[35/29]], [[58/35]]
* [[35/29]], [[58/35]]
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* [[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]]
* [[46/37]], [[37/23]]
* '''[[46/37]], [[37/23]]'''
* [[5/4]], [[8/5]]
* [[5/4]], [[8/5]]
* [[44/35]], [[35/22]]
* [[44/35]], [[35/22]]
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* [[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]]
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* [[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]]
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* [[29/22]], [[44/29]]
* [[29/22]], [[44/29]]
* [[33/25]], [[50/33]]
* [[33/25]], [[50/33]]
* [[37/28]], [[56/37]]
* '''[[37/28]], [[56/37]]'''
* [[4/3]], [[3/2]]
* [[4/3]], [[3/2]]
* [[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]]
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* [[15/11]], [[22/15]]
* [[15/11]], [[22/15]]
* [[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]]
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* [[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]]
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{| class="wikitable"
{| class="wikitable"
|'''Ratio'''
! Ratio
|'''Size ('''[[Cents|¢]]''')'''
! Size ([[cents|¢]])
|Color name
! Color name
|Name
! Name
|-
|-
|38/37
| 38/37
|46.169
| 46.169
|
|  
|
|  
|-
|-
|37/36
| 37/36
|47.434
| 47.434
|
|  
|
|  
|-
|-
|37/35
| 37/35
|96.204
| 96.204
|
|  
|
|  
|-
|-
|40/37
| 40/37
|134.97
| 134.97
|
|  
|
|  
|-
|-
|37/34
| 37/34
|146.389
| 146.389
|
|  
|
|  
|-
|-
|37/33
| 37/33
|198.071
| 198.071
|
|  
|
|  
|-
|-
|42/37
| 42/37
|219.437
| 219.437
|
|  
|
|  
|-
|-
|37/32
| 37/32
|251.344
| 251.344
|
|  
|
|  
|-
|-
|44/37
| 44/37
|299.974
| 299.974
|
|  
|
|  
|-
|-
|37/31
| 37/31
|306.308
| 306.308
|
|  
|
|  
|-
|-
|37/30
| 37/30
|363.075
| 363.075
|
|  
|
|  
|-
|-
|46/37
| 46/37
|376.93
| 376.93
|
|  
|
|  
|-
|-
|37/29
| 37/29
|421.767
| 421.767
|
|  
|
|  
|-
|-
|48/37
| 48/37
|450.611
| 450.611
|
|  
|
|  
|-
|-
|37/28
| 37/28
|482.518
| 482.518
|
|  
|
|  
|-
|-
|50/37
| 50/37
|521.283
| 521.283
|
|  
|
|  
|-
|-
|37/27
| 37/27
|545.479
| 545.479
|
|  
|
|  
|-
|-
|52/37
| 52/37
|589.184
| 589.184
|
|  
|
|  
|-
|-
|37/26
| 37/26
|610.816
| 610.816
|
|  
|
|  
|-
|-
|54/37
| 54/37
|654.521
| 654.521
|
|  
|
|  
|-
|-
|37/25
| 37/25
|678.717
| 678.717
|
|  
|
|  
|-
|-
|56/37
| 56/37
|717.482
| 717.482
|
|  
|
|  
|}
|}
The smallest [[equal division of the octave]] which is consistent to the 37-odd-limit is [[311edo]] (by virtue of it being consistent in the [[41-odd-limit]]); that which is distinctly consistent to the same is [[1600edo]].
The smallest [[equal division of the octave]] which is consistent to the 37-odd-limit is [[311edo]] (by virtue of it being consistent in the [[41-odd-limit]]); that which is distinctly consistent to the same is [[1600edo]].
[[Category:37-odd-limit| ]] <!-- main article -->
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