31-odd-limit - Revision history

Eufalesio: Proposing separating the lines before the table to be separated in paragraphs

2025-10-08T14:14:11Z

Proposing separating the lines before the table to be separated in paragraphs

← Older revision		Revision as of 14:14, 8 October 2025
Line 296:		Line 296:
	\| greater tricesimoprimal infraoctave		\| greater tricesimoprimal infraoctave
	\|}		\|}
	The smallest [[equal division of the octave]] that comes closest to being consistent in the 31-odd-limit is [[217edo]] (misses 23/14, 23/21, 29/23, and ~~their octave complements~~)~~, the~~ one which is truly consistent is [[311edo]] (by virtue of it being consistent through the 41-odd-limit)~~; that~~ which is distinctly consistent to the same is [[1600edo]] (by virtue of it being distinctly consistent through the 37-odd-limit).		The smallest [[equal division of the octave]] that comes closest to being consistent in the 31-odd-limit is [[217edo]] (misses 23/14, 23/21, 29/23, and [[Octave complement\|oc.]]).

			The one which is truly consistent is [[311edo]] (by virtue of it being consistent through the 41-odd-limit).

			The one which is distinctly consistent to the same is [[1600edo]] (by virtue of it being distinctly consistent through the 37-odd-limit).

	[[Category:31-odd-limit\| ]] <!-- main article -->		[[Category:31-odd-limit\| ]] <!-- main article -->

FloraC at 15:26, 23 September 2025

2025-09-23T15:26:29Z

Show changes

Eufalesio: Proposed adding the smallest edo that comes closest to consistency

2025-09-17T10:02:43Z

Proposed adding the smallest edo that comes closest to consistency

← Older revision		Revision as of 10:02, 17 September 2025
Line 294:		Line 294:
	\|greater tricesimoprimal infraoctave		\|greater tricesimoprimal infraoctave
	\|}		\|}
	The smallest [[equal division of the octave]] ~~which is~~ consistent to the 31-odd-limit is [[311edo]] (by virtue of it being consistent through the 41-odd-limit); that which is distinctly consistent to the same is [[1600edo]] (by virtue of it being distinctly consistent through the 37-odd-limit).		The smallest [[equal division of the octave]] that comes closest to being consistent in the 31-odd-limit is [[217edo]] (misses 23/14, 23/21, 29/23, and their octave complements), the one which is truly consistent is [[311edo]] (by virtue of it being consistent through the 41-odd-limit); that which is distinctly consistent to the same is [[1600edo]] (by virtue of it being distinctly consistent through the 37-odd-limit).

	[[Category:31-odd-limit\| ]] <!-- main article -->		[[Category:31-odd-limit\| ]] <!-- main article -->

Xenllium at 12:35, 27 April 2025

2025-04-27T12:35:42Z

← Older revision		Revision as of 12:35, 27 April 2025
Line 178:		Line 178:
	\|31uy4		\|31uy4
	\|thiwuyo 4th		\|thiwuyo 4th
	\|tricesimoprimal ~~subminor~~ fourth		\|tricesimoprimal semidiminished fourth
	\|-		\|-
	\|[[31/24]]		\|[[31/24]]
Line 232:		Line 232:
	\|31og5		\|31og5
	\|thiwogu 5th		\|thiwogu 5th
	\|tricesimoprimal ~~supramajor~~ fifth		\|tricesimoprimal semiaugmented fifth
	\|-		\|-
	\|[[50/31]]		\|[[50/31]]

Xenllium: Fixed typo

2025-04-27T11:54:00Z

Fixed typo

← Older revision		Revision as of 11:54, 27 April 2025
Line 63:		Line 63:
	*[[28/23]], [[23/14]]		*[[28/23]], [[23/14]]
	*[[11/9]], [[18/11]]		*[[11/9]], [[18/11]]
	*'''[[38/31]], [[31/17]]'''		*'''[[38/31]], [[31/19]]'''
	*[[27/22]], [[44/27]]		*[[27/22]], [[44/27]]
	*[[16/13]], [[13/8]]		*[[16/13]], [[13/8]]

FloraC: +category

2023-11-19T08:48:23Z

+category

← Older revision		Revision as of 08:48, 19 November 2023
Line 295:		Line 295:
	\|}		\|}
	The smallest [[equal division of the octave]] which is consistent to the 31-odd-limit is [[311edo]] (by virtue of it being consistent through the 41-odd-limit); that which is distinctly consistent to the same is [[1600edo]] (by virtue of it being distinctly consistent through the 37-odd-limit).		The smallest [[equal division of the octave]] which is consistent to the 31-odd-limit is [[311edo]] (by virtue of it being consistent through the 41-odd-limit); that which is distinctly consistent to the same is [[1600edo]] (by virtue of it being distinctly consistent through the 37-odd-limit).

			[[Category:31-odd-limit\| ]] <!-- main article -->

Iwuqety: Creation

2023-11-18T11:48:29Z

Creation

New page

{{Odd-limit navigation}}
{{odd-limit intro|31}}
*[[1/1]]
*'''[[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]]
*[[17/16]], [[32/17]]
*[[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]]
*[[25/23]], [[46/25]]
*[[12/11]], [[11/6]]
*[[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]]
*[[26/23]], [[23/13]]
*[[17/15]], [[30/17]]
*[[25/22]], [[44/25]]
*[[8/7]], [[7/4]]
*'''[[31/27]], [[54/31]]'''
*[[23/20]], [[40/23]]
*[[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]]
*[[13/11]], [[22/13]]
*[[32/27]], [[27/16]]
*[[19/16]], [[32/19]]
*[[25/21]], [[42/25]]
*'''[[31/26]], [[52/31]]'''
*[[6/5]], [[5/3]]
*[[29/24]], [[48/29]]
*[[23/19]], [[38/23]]
*[[17/14]], [[28/17]]
*[[28/23]], [[23/14]]
*[[11/9]], [[18/11]]
*'''[[38/31]], [[31/17]]'''
*[[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]]
*[[34/27]], [[27/17]]
*[[29/23]], [[46/29]]
*[[24/19]], [[19/12]]
*[[19/15]], [[30/19]]
*[[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]]
*[[13/10]], [[20/13]]
*[[30/23]], [[23/15]]
*[[17/13]], [[26/17]]
*[[38/29]], [[29/19]]
*[[21/16]], [[32/21]]
*[[25/19]], [[38/25]]
*[[29/22]], [[44/29]]
*[[4/3]], [[3/2]]
*'''[[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]]
*[[11/8]], [[16/11]]
*[[40/29]], [[29/20]]
*[[29/21]], [[42/29]]
*[[18/13]], [[13/9]]
*[[25/18]], [[36/25]]
*[[32/23]], [[23/16]]
*[[7/5]], [[10/7]]
*[[38/27]], [[27/19]]
*'''[[31/22]], [[44/31]]'''
*[[24/17]], [[17/12]]
{| class="wikitable center-all right-2 left-5"
!Ratio
!Size ([[cents|¢]])
! colspan="2" |[[Color name]]
!Name
|-
|[[32/31]]
|54.964
|31u2
|thiwu 2nd
|lesser tricesimoprimal quartertone
|-
|[[31/30]]
|56.767
|31og1
|thiwogu unison
|greater tricesimoprimal quartertone
|-
|[[31/29]]
|115.458
|31o29u1
|thiwotwenu unison
|tricesimoprimal augmented unison
|-
|[[34/31]]
|159.920
|31u17o3
|thiwuso 3rd
|tricesimoprimal diminished third
|-
|[[31/28]]
|176.210
|31or1
|thiworu unison
|tricesimoprimal superaugmented unison
|-
|[[31/27]]
|239.171
|31o2
|thiwo 2nd
|tricesimoprimal supermajor second
|-
|[[36/31]]
|258.874
|31u3
|thiwu 3rd
|tricesimoprimal inframinor third
|-
|[[31/26]]
|304.508
|31o3u2
|thiwothu 2nd
|tricesimoprimal augmented second
|-
|[[38/31]]
|352.477
|31u19o4
|thiwuno 4th
|tricesimoprimal diminished fourth
|-
|[[31/25]]
|372.408
|31ogg3
|thiwogugu 3rd
|tricesimoprimal submajor third
|-
|[[40/31]]
|441.278
|31uy4
|thiwuyo 4th
|tricesimoprimal subminor fourth
|-
|[[31/24]]
|443.081
|31o3
|thiwo 3rd
|tricesimoprimal supermajor third
|-
|[[31/23]]
|516.761
|31o23u3
|thiwotwethu 3rd
|tricesimoprimal augmented third
|-
|[[42/31]]
|525.745
|31uz5
|thiwuzo 5th
|tricesimoprimal diminished fifth
|-
|[[31/22]]
|593.718
|31o1u4
|thiwolu 4th
|lesser tricesimoprimal tritone
|-
|[[44/31]]
|606.282
|31u1o5
|thiwulo 5th
|greater tricesimoprimal tritone
|-
|[[31/21]]
|674.255
|31or4
|thiworu 4th
|tricesimoprimal augmented fourth
|-
|[[46/31]]
|683.239
|31u23o6
|thiwotwetho 6th
|tricesimoprimal subminor sixth
|-
|[[48/31]]
|756.919
|31u6
|thiwu 6th
|tricesimoprimal supermajor sixth
|-
|[[31/20]]
|758.722
|31og5
|thiwogu 5th
|tricesimoprimal supramajor fifth
|-
|[[50/31]]
|827.592
|31uyy6
|thiwuyoyo 6th
|tricesimoprimal supraminor sixth
|-
|[[31/19]]
|847.523
|31o19u5
|thiwonu 5th
|tricesimoprimal augmented fifth
|-
|[[52/31]]
|895.492
|31u3o7
|thiwutho 7th
|tricesimoprimal diminished seventh
|-
|[[31/18]]
|941.126
|31o6
|thiwo 6th
|tricesimoprimal ultramajor sixth
|-
|[[54/31]]
|960.829
|31u7
|thiwu 7th
|tricesimoprimal subminor seventh
|-
|[[56/31]]
|1023.790
|31uz8
|thiwuzo octave
|tricesimoprimal supradiminished octave
|-
|[[31/17]]
|1040.080
|31o17u6
|thiwosu 6th
|tricesimoprimal augmented sixth
|-
|[[58/31]]
|1084.542
|31u29o8
|thiwutweno octave
|tricesimoprimal diminished octave
|-
|[[60/31]]
|1143.233
|31uy8
|thiwuyo octave
|lesser tricesimoprimal infraoctave
|-
|[[31/16]]
|1145.036
|31o7
|thiwo 7th
|greater tricesimoprimal infraoctave
|}
The smallest [[equal division of the octave]] which is consistent to the 31-odd-limit is [[311edo]] (by virtue of it being consistent through the 41-odd-limit); that which is distinctly consistent to the same is [[1600edo]] (by virtue of it being distinctly consistent through the 37-odd-limit).