29-odd-limit - Revision history

Eufalesio: Proposing separating the lines before the table to be separated in paragraphs, and adding the smallest one that comes closest to consistency

2025-10-08T14:00:07Z

Proposing separating the lines before the table to be separated in paragraphs, and adding the smallest one that comes closest to consistency

← Older revision		Revision as of 14:00, 8 October 2025
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	\| twenogu octave		\| twenogu octave
	\| greater vicesimononal infraoctave		\| greater vicesimononal infraoctave
			\|-
			\| colspan="5" \|Note that 'vicesimononal' is exchangeable with 'undetricesimal', both denoting the presence of factor 29.
	\|}		\|}
	~~Note~~ that ~~'vicesimononal'~~ is ~~exchangeable with 'undetricesimal'~~, ~~both denoting the presence of factor~~ 29.		The smallest [[equal division of the octave]] that comes closest to being [[consistent]] in the 29-odd-limit is [[217edo]] (misses [[23/14]], [[23/21]], [[29/23]] and [[Octave complement\|oc]].).

	The ~~smallest [[equal division of the octave]]~~ which is [[consistent~~]] to the 29-odd-limit~~ is [[282edo]]~~; that~~ which is distinctly consistent to the same is [[1323edo]].		The one which is truly consistent is [[282edo]].

			The one which is distinctly consistent to the same is [[1323edo]].

	[[Category:29-odd-limit\| ]] <!-- main article -->		[[Category:29-odd-limit\| ]] <!-- main article -->

FloraC at 15:25, 23 September 2025

2025-09-23T15:25:09Z

Show changes

FloraC: +category

2023-11-18T08:33:36Z

+category

← Older revision		Revision as of 08:33, 18 November 2023
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	The smallest [[equal division of the octave]] which is [[consistent]] to the 29-odd-limit is [[282edo]]; that which is distinctly consistent to the same is [[1323edo]].		The smallest [[equal division of the octave]] which is [[consistent]] to the 29-odd-limit is [[282edo]]; that which is distinctly consistent to the same is [[1323edo]].

			[[Category:29-odd-limit\| ]] <!-- main article -->

Iwuqety at 15:53, 17 November 2023

2023-11-17T15:53:08Z

← Older revision		Revision as of 15:53, 17 November 2023
Line 270:		Line 270:
	Note that 'vicesimononal' is exchangeable with 'undetricesimal', both denoting the presence of factor 29.		Note that 'vicesimononal' is exchangeable with 'undetricesimal', both denoting the presence of factor 29.

	The smallest [[equal division of the octave]] which is [[consistent]] ~~through~~ to the 29-odd-limit is [[282edo]]; that which is distinctly consistent ~~through~~ to the same is [[1323edo]].		The smallest [[equal division of the octave]] which is [[consistent]] to the 29-odd-limit is [[282edo]]; that which is distinctly consistent to the same is [[1323edo]].

Iwuqety at 13:45, 17 November 2023

2023-11-17T13:45:54Z

← Older revision		Revision as of 13:45, 17 November 2023
Line 270:		Line 270:
	Note that 'vicesimononal' is exchangeable with 'undetricesimal', both denoting the presence of factor 29.		Note that 'vicesimononal' is exchangeable with 'undetricesimal', both denoting the presence of factor 29.

	The smallest [[equal division of the octave]] which is [[consistent]] in the 29-odd-limit is [[282edo]]; that which is distinctly consistent in the same is [[1323edo]].		The smallest [[equal division of the octave]] which is [[consistent]] through to the 29-odd-limit is [[282edo]]; that which is distinctly consistent through to the same is [[1323edo]].

Iwuqety: Replaced introduction with templates used in previous odd limit articles

2023-11-17T13:37:37Z

Replaced introduction with templates used in previous odd limit articles

← Older revision		Revision as of 13:37, 17 November 2023
Line 1:		Line 1:
	~~The 29-~~odd-limit ~~is the set of all [[Rational interval\|rational intervals]] for which neither the numerator nor the denominator of the [[frequency ratio]] exceeds 29, once all powers of 2 are removed. To the [[27-~~odd-limit~~]], it adds 14 interval pairs involving~~ 29.		{{odd-limit navigation}}
			{{odd-limit intro\|29}}

	~~Below is a list of all [[octave-reduced]] intervals in the 29-odd-limit.~~
	*[[1/1]]		*[[1/1]]
	*'''[[30/29]], [[29/15]]'''		*'''[[30/29]], [[29/15]]'''

Iwuqety: First draft

2023-11-17T13:35:41Z

First draft

New page

The 29-odd-limit is the set of all [[Rational interval|rational intervals]] for which neither the numerator nor the denominator of the [[frequency ratio]] exceeds 29, once all powers of 2 are removed. To the [[27-odd-limit]], it adds 14 interval pairs involving 29.

Below is a list of all [[octave-reduced]] intervals in the 29-odd-limit.
*[[1/1]]
*'''[[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]]
*[[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]]
*[[11/10]], [[20/11]]
*'''[[32/29]], [[29/16]]'''
*[[21/19]], [[38/21]]
*[[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]]
*[[23/20]], [[40/23]]
*[[15/13]], [[26/15]]
*[[22/19]], [[19/11]]
*'''[[29/25]], [[50/29]]'''
*[[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]]
*[[6/5]], [[5/3]]
*'''[[29/24]], [[48/29]]'''
*[[23/19]], [[38/23]]
*[[17/14]], [[28/17]]
*[[28/23]], [[23/14]]
*[[11/9]], [[18/11]]
*[[27/22]], [[44/27]]
*[[16/13]], [[13/8]]
*[[21/17]], [[34/21]]
*[[26/21]], [[21/13]]
*'''[[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]]
*[[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]]
*[[27/20]], [[40/27]]
*[[23/17]], [[34/23]]
*[[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]]
*[[24/17]], [[17/12]]
{| class="wikitable center-all right-2 left-5"
!Ratio
!Size ([[cents|¢]])
! colspan="2" |[[Color name]]
!Name
|-
|[[30/29]]
|58.692
|29uy1
|twenuyo unison
|lesser vicesimononal quartertone
|-
|[[29/28]]
|60.751
|29or1
|twenoru unison
|greater vicesimononal quartertone
|-
|[[29/27]]
|123.712
|29o2
|tweno 2nd
|vicesimononal minor second
|-
|[[32/29]]
|170.423
|29u2
|twenu 2nd
|vicesimononal submajor second
|-
|[[29/26]]
|189.050
|29o3u2
|twenothu 2nd
|vicesimononal major second
|-
|[[29/25]]
|256.950
|29ogg3
|twenogugu 3rd
|vicesimononal inframinor third
|-
|[[34/29]]
|275.378
|29u17o3
|twenuso 3rd
|vicesimononal subminor third
|-
|[[29/24]]
|327.622
|29o3
|tweno 3rd
|vicesimononal minor third
|-
|[[36/29]]
|374.333
|29u3
|twenu 3rd
|vicesimononal submajor third
|-
|[[29/23]]
|401.303
|29o23u3
|twenotwethu 3rd
|vicesimononal major third
|-
|[[38/29]]
|467.936
|29u19o4
|twenuno 4th
|vicesimononal subfourth
|-
|[[29/22]]
|478.259
|29o1u4
|twenolu 4th
|vicesimononal grave fourth
|-
|[[40/29]]
|556.737
|29uy4
|twenuyo 4th
|lesser vicesimononal superfourth
|-
|[[29/21]]
|558.796
|29or4
|twenoru 4th
|greater vicesimononal superfourth
|-
|[[42/29]]
|641.204
|29uz5
|twenuzo 5th
|lesser vicesimononal subfifth
|-
|[[29/20]]
|643.263
|29og5
|twenogu 5th
|greater vicesimononal subfifth
|-
|[[44/29]]
|721.741
|29u1o5
|twenulo 5th
|vicesimononal acute fifth
|-
|[[29/19]]
|732.064
|29o19u5
|twenonu 5th
|vicesimononal superfifth
|-
|[[46/29]]
|798.697
|29u23o6
|twenutwetho 6th
|vicesimononal minor sixth
|-
|[[29/18]]
|825.667
|29o6
|tweno 6th
|vicesimononal supraminor sixth
|-
|[[48/29]]
|872.378
|29u6
|twenu 6th
|vicesimononal major sixth
|-
|[[29/17]]
|924.621
|29o17u6
|twenosu 6th
|vicesimononal supermajor sixth
|-
|[[50/29]]
|943.050
|29uyy6
|twenuyoyo 6th
|vicesimononal ultramajor sixth
|-
|[[52/29]]
|1010.950
|29u3o7
|twenutho 7th
|vicesimononal minor seventh
|-
|[[29/16]]
|1029.577
|29o7
|tweno 7th
|vicesimononal supraminor seventh
|-
|[[54/29]]
|1076.288
|29u7
|twenu 7th
|vicesimononal major seventh
|-
|[[56/29]]
|1139.249
|29uz8
|twenuzo octave
|lesser vicesimononal infraoctave
|-
|[[29/15]]
|1141.308
|29og8
|twenogu octave
|greater vicesimononal infraoctave
|}
Note that 'vicesimononal' is exchangeable with 'undetricesimal', both denoting the presence of factor 29.

The smallest [[equal division of the octave]] which is [[consistent]] in the 29-odd-limit is [[282edo]]; that which is distinctly consistent in the same is [[1323edo]].