35-odd-limit - Revision history

FloraC: + category

2025-09-23T15:33:31Z

+ category

← Older revision		Revision as of 15:33, 23 September 2025
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	\|}		\|}
	The smallest [[equal division of the octave]] which is consistent to the 35-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]] (by virtue of it being consistent in the [[37-odd-limit]]).		The smallest [[equal division of the octave]] which is consistent to the 35-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]] (by virtue of it being consistent in the [[37-odd-limit]]).

			[[Category:35-odd-limit\| ]] <!-- main article -->

FloraC at 15:31, 23 September 2025

2025-09-23T15:31:19Z

← Older revision		Revision as of 15:31, 23 September 2025
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	{{Odd-limit navigation}}~~The 35'''-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'' ≤~~ 35 ~~and ''k'' is an integer. To the [[33-odd-limit]], it adds 12 pairs of [[octave-reduced]] intervals involving 35.~~		{{Odd-limit navigation\|35}}
			{{Odd-limit intro\|35}}
	~~Below is a list of all octave-reduced intervals in the 35-odd-limit.~~

	* [[1/1]]		* [[1/1]]
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	{\| class="wikitable"		{\| class="wikitable"
	~~\|'''~~Ratio~~'''~~		! Ratio
	~~\|'''~~Size (~~'''~~[[~~Cents~~\|¢]]~~'''~~)~~'''~~		! Size ([[cents\|¢]])
	\|Color name		! Color name
	\|Name		! Name
	\|-		\|-
	\|36/35		\| 36/35
	\|48.77		\| 48.77
	\|		\|
	\|		\|
	\|-		\|-
	\|35/34		\| 35/34
	\|50.184		\| 50.184
	\|		\|
	\|		\|
	\|-		\|-
	\|35/33		\| 35/33
	\|101.867		\| 101.867
	\|		\|
	\|		\|
	\|-		\|-
	\|38/35		\| 38/35
	\|142.353		\| 142.353
	\|		\|
	\|		\|
	\|-		\|-
	\|35/32		\| 35/32
	\|155.14		\| 155.14
	\|		\|
	\|		\|
	\|-		\|-
	\|35/31		\| 35/31
	\|210.104		\| 210.104
	\|		\|
	\|		\|
	\|-		\|-
	\|35/29		\| 35/29
	\|325.562		\| 325.562
	\|		\|
	\|		\|
	\|-		\|-
	\|44/35		\| 44/35
	\|396.178		\| 396.178
	\|		\|
	\|		\|
	\|-		\|-
	\|35/27		\| 35/27
	\|449.275		\| 449.275
	\|		\|
	\|		\|
	\|-		\|-
	\|46/35		\| 46/35
	\|473.135		\| 473.135
	\|		\|
	\|		\|
	\|-		\|-
	\|35/26		\| 35/26
	\|514.612		\| 514.612
	\|		\|
	\|		\|
	\|-		\|-
	\|48/35		\| 48/35
	\|546.815		\| 546.815
	\|		\|
	\|		\|
	\|-		\|-
	\|35/24		\| 35/24
	\|653.185		\| 653.185
	\|		\|
	\|		\|
	\|-		\|-
	\|52/35		\| 52/35
	\|685.388		\| 685.388
	\|		\|
	\|		\|
	\|-		\|-
	\|35/23		\| 35/23
	\|726.865		\| 726.865
	\|		\|
	\|		\|
	\|-		\|-
	\|54/35		\| 54/35
	\|750.725		\| 750.725
	\|		\|
	\|		\|
	\|-		\|-
	\|35/22		\| 35/22
	\|803.822		\| 803.822
	\|		\|
	\|		\|
	\|-		\|-
	\|58/35		\| 58/35
	\|874.438		\| 874.438
	\|		\|
	\|		\|
	\|-		\|-
	\|62/35		\| 62/35
	\|989.896		\| 989.896
	\|		\|
	\|		\|
	\|-		\|-
	\|64/35		\| 64/35
	\|1044.86		\| 1044.86
	\|		\|
	\|		\|
	\|-		\|-
	\|35/19		\| 35/19
	\|1057.627		\| 1057.627
	\|		\|
	\|		\|
	\|-		\|-
	\|66/35		\| 66/35
	\|1098.133		\| 1098.133
	\|		\|
	\|		\|
	\|-		\|-
	\|68/35		\| 68/35
	\|1149.816		\| 1149.816
	\|		\|
	\|		\|
	\|-		\|-
	\|35/18		\| 35/18
	\|1151.23		\| 1151.23
	\|		\|
	\|		\|
	\|}		\|}
	The smallest [[equal division of the octave]] which is consistent to the 35-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]] (by virtue of it being consistent in the [[37~~-odd-limit\|35~~-odd-limit]]).		The smallest [[equal division of the octave]] which is consistent to the 35-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]] (by virtue of it being consistent in the [[37-odd-limit]]).

Eufalesio: Birth (Intervals TBA)

2025-09-18T21:26:14Z

Birth (Intervals TBA)

New page

{{Odd-limit navigation}}The 35'''-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'' ≤ 35 and ''k'' is an integer. To the [[33-odd-limit]], it adds 12 pairs of [[octave-reduced]] intervals involving 35.

Below is a list of all octave-reduced intervals in the 35-odd-limit.

* [[1/1]]
* '''[[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]]
* [[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]]
* [[13/12]], [[24/13]]
* '''[[38/35]], [[35/19]]'''
* [[25/23]], [[46/25]]
* [[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]]
* [[9/8]], [[16/9]]
* '''[[35/31]], [[62/35]]'''
* [[26/23]], [[23/13]]
* [[17/15]], [[30/17]]
* [[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]]
* [[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]]
* [[25/21]], [[42/25]]
* [[31/26]], [[52/31]]
* [[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]]
* [[21/17]], [[34/21]]
* [[26/21]], [[21/13]]
* [[31/25]], [[50/31]]
* [[36/29]], [[29/18]]
* [[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]]
* [[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]]'''
* [[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]]
* [[4/3]], [[3/2]]
* '''[[35/26]], [[52/35]]'''
* [[31/23]], [[46/31]]
* [[27/20]], [[40/27]]
* [[23/17]], [[34/23]]
* [[42/31]], [[31/21]]
* [[19/14]], [[28/19]]
* [[34/25]], [[25/17]]
* [[15/11]], [[22/15]]
* [[26/19]], [[19/13]]
* '''[[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]]
* [[38/27]], [[27/19]]
* [[31/22]], [[44/31]]
* [[24/17]], [[17/12]]

{| class="wikitable"
|'''Ratio'''
|'''Size ('''[[Cents|¢]]''')'''
|Color name
|Name
|-
|36/35
|48.77
|
|
|-
|35/34
|50.184
|
|
|-
|35/33
|101.867
|
|
|-
|38/35
|142.353
|
|
|-
|35/32
|155.14
|
|
|-
|35/31
|210.104
|
|
|-
|35/29
|325.562
|
|
|-
|44/35
|396.178
|
|
|-
|35/27
|449.275
|
|
|-
|46/35
|473.135
|
|
|-
|35/26
|514.612
|
|
|-
|48/35
|546.815
|
|
|-
|35/24
|653.185
|
|
|-
|52/35
|685.388
|
|
|-
|35/23
|726.865
|
|
|-
|54/35
|750.725
|
|
|-
|35/22
|803.822
|
|
|-
|58/35
|874.438
|
|
|-
|62/35
|989.896
|
|
|-
|64/35
|1044.86
|
|
|-
|35/19
|1057.627
|
|
|-
|66/35
|1098.133
|
|
|-
|68/35
|1149.816
|
|
|-
|35/18
|1151.23
|
|
|}
The smallest [[equal division of the octave]] which is consistent to the 35-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]] (by virtue of it being consistent in the [[37-odd-limit|35-odd-limit]]).