37-odd-limit - Revision history

FloraC: + category

2025-09-23T15:35:17Z

+ category

← Older revision		Revision as of 15:35, 23 September 2025
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	\|}		\|}
	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 -->

FloraC at 15:35, 23 September 2025

2025-09-23T15:35:00Z

← Older revision		Revision as of 15:35, 23 September 2025
Line 1:		Line 1:
	{{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 [[35-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]]
Line 152:		Line 151:

	{\| 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]].

Eufalesio at 21:27, 18 September 2025

2025-09-18T21:27:56Z

← Older revision		Revision as of 21:27, 18 September 2025
Line 1:		Line 1:
	{{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}}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 [[35-odd-limit]], it adds 18 pairs of [[octave-reduced]] intervals involving 37.

	Below is a list of all octave-reduced intervals in the 37-odd-limit.		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]]
Line 24:		Line 24:
	* [[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]]
Line 35:		Line 35:
	* [[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]]
Line 52:		Line 52:
	* [[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]]
Line 65:		Line 65:
	* [[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]]
Line 77:		Line 77:
	* [[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]]
Line 92:		Line 92:
	* [[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]]
Line 106:		Line 106:
	* [[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]]
Line 114:		Line 114:
	* [[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]]
Line 124:		Line 124:
	* [[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]]
Line 136:		Line 136:
	* [[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]]
Line 146:		Line 146:
	* [[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]]

Eufalesio: Birth (Intervals TBA)

2025-09-18T21:19:27Z

Birth (Intervals TBA)

New page

{{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.

Below is a list of all octave-reduced intervals in the 37-odd-limit.

* [[1/1]]
* [[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]]
* [[20/19]], [[19/10]]
* [[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]]
* [[29/27]], [[54/29]]
* [[14/13]], [[13/7]]
* [[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]]
* [[10/9]], [[9/5]]
* [[29/26]], [[52/29]]
* [[19/17]], [[34/19]]
* [[28/25]], [[25/14]]
* [[37/33]], [[66/37]]
* [[9/8]], [[16/9]]
* [[35/31]], [[62/35]]
* [[26/23]], [[23/13]]
* [[17/15]], [[30/17]]
* [[42/37]], [[37/21]]
* [[25/22]], [[44/25]]
* [[33/29]], [[58/33]]
* [[8/7]], [[7/4]]
* [[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]]
* [[34/29]], [[29/17]]
* [[27/23]], [[46/27]]
* [[20/17]], [[17/10]]
* [[33/28]], [[56/33]]
* [[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]]
* [[35/29]], [[58/35]]
* [[29/24]], [[48/29]]
* [[23/19]], [[38/23]]
* [[40/33]], [[33/20]]
* [[17/14]], [[28/17]]
* [[28/23]], [[23/14]]
* [[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]]
* [[46/37]], [[37/23]]
* [[5/4]], [[8/5]]
* [[44/35]], [[35/22]]
* [[34/27]], [[27/17]]
* [[29/23]], [[46/29]]
* [[24/19]], [[19/12]]
* [[19/15]], [[30/19]]
* [[33/26]], [[52/33]]
* [[14/11]], [[11/7]]
* [[37/29]], [[58/37]]
* [[23/18]], [[36/23]]
* [[32/25]], [[25/16]]
* [[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]]
* [[29/22]], [[44/29]]
* [[33/25]], [[50/33]]
* [[37/28]], [[56/37]]
* [[4/3]], [[3/2]]
* [[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]]
* [[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]]
* [[46/33]], [[33/23]]
* [[7/5]], [[10/7]]
* [[52/37]], [[37/26]]
* [[38/27]], [[27/19]]
* [[31/22]], [[44/31]]
* [[24/17]], [[17/12]]

{| class="wikitable"
|'''Ratio'''
|'''Size ('''[[Cents|¢]]''')'''
|Color name
|Name
|-
|38/37
|46.169
|
|
|-
|37/36
|47.434
|
|
|-
|37/35
|96.204
|
|
|-
|40/37
|134.97
|
|
|-
|37/34
|146.389
|
|
|-
|37/33
|198.071
|
|
|-
|42/37
|219.437
|
|
|-
|37/32
|251.344
|
|
|-
|44/37
|299.974
|
|
|-
|37/31
|306.308
|
|
|-
|37/30
|363.075
|
|
|-
|46/37
|376.93
|
|
|-
|37/29
|421.767
|
|
|-
|48/37
|450.611
|
|
|-
|37/28
|482.518
|
|
|-
|50/37
|521.283
|
|
|-
|37/27
|545.479
|
|
|-
|52/37
|589.184
|
|
|-
|37/26
|610.816
|
|
|-
|54/37
|654.521
|
|
|-
|37/25
|678.717
|
|
|-
|56/37
|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]].