29-odd-limit: Difference between revisions

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Proposing separating the lines before the table to be separated in paragraphs, and adding the smallest one that comes closest to consistency
 
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{{odd-limit navigation}}
{{Odd-limit navigation|29}}
{{odd-limit intro|29}}
{{Odd-limit intro|29}}
 
* [[1/1]]
* '''[[30/29]], [[29/15]]'''
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* '''[[32/29]], [[29/16]]'''
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* [[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]]
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* [[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]]


*[[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"
{| class="wikitable center-all right-2 left-5"
!Ratio
! Ratio
!Size ([[cents|¢]])
! Size ([[cents|¢]])
! colspan="2" |[[Color name]]
! colspan="2" |[[Color name]]
!Name
! Name
|-
| [[30/29]]
| 58.692
| 29uy1
| twenuyo unison
| lesser vicesimononal quartertone
|-
|-
|[[30/29]]
| [[29/28]]
|58.692
| 60.751
|29uy1
| 29or1
|twenuyo unison
| twenoru unison
|lesser vicesimononal quartertone
| greater vicesimononal quartertone
|-
|-
|[[29/28]]
| [[29/27]]
|60.751
| 123.712
|29or1
| 29o2
|twenoru unison
| tweno 2nd
|greater vicesimononal quartertone
| vicesimononal minor second
|-
|-
|[[29/27]]
| [[32/29]]
|123.712
| 170.423
|29o2
| 29u2
|tweno 2nd
| twenu 2nd
|vicesimononal minor second
| vicesimononal submajor second
|-
|-
|[[32/29]]
| [[29/26]]
|170.423
| 189.050
|29u2
| 29o3u2
|twenu 2nd
| twenothu 2nd
|vicesimononal submajor second
| vicesimononal major second
|-
|-
|[[29/26]]
| [[29/25]]
|189.050
| 256.950
|29o3u2
| 29ogg3
|twenothu 2nd
| twenogugu 3rd
|vicesimononal major second
| vicesimononal inframinor third
|-
|-
|[[29/25]]
| [[34/29]]
|256.950
| 275.378
|29ogg3
| 29u17o3
|twenogugu 3rd
| twenuso 3rd
|vicesimononal inframinor third
| vicesimononal subminor third
|-
|-
|[[34/29]]
| [[29/24]]
|275.378
| 327.622
|29u17o3
| 29o3
|twenuso 3rd
| tweno 3rd
|vicesimononal subminor third
| vicesimononal minor third
|-
|-
|[[29/24]]
| [[36/29]]
|327.622
| 374.333
|29o3
| 29u3
|tweno 3rd
| twenu 3rd
|vicesimononal minor third
| vicesimononal submajor third
|-
|-
|[[36/29]]
| [[29/23]]
|374.333
| 401.303
|29u3
| 29o23u3
|twenu 3rd
| twenotwethu 3rd
|vicesimononal submajor third
| vicesimononal major third
|-
|-
|[[29/23]]
| [[38/29]]
|401.303
| 467.936
|29o23u3
| 29u19o4
|twenotwethu 3rd
| twenuno 4th
|vicesimononal major third
| vicesimononal subfourth
|-
|-
|[[38/29]]
| [[29/22]]
|467.936
| 478.259
|29u19o4
| 29o1u4
|twenuno 4th
| twenolu 4th
|vicesimononal subfourth
| vicesimononal grave fourth
|-
|-
|[[29/22]]
| [[40/29]]
|478.259
| 556.737
|29o1u4
| 29uy4
|twenolu 4th
| twenuyo 4th
|vicesimononal grave fourth
| lesser vicesimononal superfourth
|-
|-
|[[40/29]]
| [[29/21]]
|556.737
| 558.796
|29uy4
| 29or4
|twenuyo 4th
| twenoru 4th
|lesser vicesimononal superfourth
| greater vicesimononal superfourth
|-
|-
|[[29/21]]
| [[42/29]]
|558.796
| 641.204
|29or4
| 29uz5
|twenoru 4th
| twenuzo 5th
|greater vicesimononal superfourth
| lesser vicesimononal subfifth
|-
|-
|[[42/29]]
| [[29/20]]
|641.204
| 643.263
|29uz5
| 29og5
|twenuzo 5th
| twenogu 5th
|lesser vicesimononal subfifth
| greater vicesimononal subfifth
|-
|-
|[[29/20]]
| [[44/29]]
|643.263
| 721.741
|29og5
| 29u1o5
|twenogu 5th
| twenulo 5th
|greater vicesimononal subfifth
| vicesimononal acute fifth
|-
|-
|[[44/29]]
| [[29/19]]
|721.741
| 732.064
|29u1o5
| 29o19u5
|twenulo 5th
| twenonu 5th
|vicesimononal acute fifth
| vicesimononal superfifth
|-
|-
|[[29/19]]
| [[46/29]]
|732.064
| 798.697
|29o19u5
| 29u23o6
|twenonu 5th
| twenutwetho 6th
|vicesimononal superfifth
| vicesimononal minor sixth
|-
|-
|[[46/29]]
| [[29/18]]
|798.697
| 825.667
|29u23o6
| 29o6
|twenutwetho 6th
| tweno 6th
|vicesimononal minor sixth
| vicesimononal supraminor sixth
|-
|-
|[[29/18]]
| [[48/29]]
|825.667
| 872.378
|29o6
| 29u6
|tweno 6th
| twenu 6th
|vicesimononal supraminor sixth
| vicesimononal major sixth
|-
|-
|[[48/29]]
| [[29/17]]
|872.378
| 924.621
|29u6
| 29o17u6
|twenu 6th
| twenosu 6th
|vicesimononal major sixth
| vicesimononal supermajor sixth
|-
|-
|[[29/17]]
| [[50/29]]
|924.621
| 943.050
|29o17u6
| 29uyy6
|twenosu 6th
| twenuyoyo 6th
|vicesimononal supermajor sixth
| vicesimononal ultramajor sixth
|-
|-
|[[50/29]]
| [[52/29]]
|943.050
| 1010.950
|29uyy6
| 29u3o7
|twenuyoyo 6th
| twenutho 7th
|vicesimononal ultramajor sixth
| vicesimononal minor seventh
|-
|-
|[[52/29]]
| [[29/16]]
|1010.950
| 1029.577
|29u3o7
| 29o7
|twenutho 7th
| tweno 7th
|vicesimononal minor seventh
| vicesimononal supraminor seventh
|-
|-
|[[29/16]]
| [[54/29]]
|1029.577
| 1076.288
|29o7
| 29u7
|tweno 7th
| twenu 7th
|vicesimononal supraminor seventh
| vicesimononal major seventh
|-
|-
|[[54/29]]
| [[56/29]]
|1076.288
| 1139.249
|29u7
| 29uz8
|twenu 7th
| twenuzo octave
|vicesimononal major seventh
| lesser vicesimononal infraoctave
|-
|-
|[[56/29]]
| [[29/15]]
|1139.249
| 1141.308
|29uz8
| 29og8
|twenuzo octave
| twenogu octave
|lesser vicesimononal infraoctave
| greater vicesimononal infraoctave
|-
|-
|[[29/15]]
| colspan="5" |Note that 'vicesimononal' is exchangeable with 'undetricesimal', both denoting the presence of factor 29.
|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]] 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 one which is truly consistent is [[282edo]].
 
The one which is distinctly consistent to the same is [[1323edo]].


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

Latest revision as of 14:00, 8 October 2025

← 27-odd-limit  29-odd-limit  31-odd-limit →

The 29-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 29 and k is an integer. To the 27-odd-limit, it adds 14 pairs of octave-reduced intervals involving 29.

Below is a list of all octave-reduced intervals in the 29-odd-limit.

Ratio Size (¢) 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 that comes closest to being consistent in the 29-odd-limit is 217edo (misses 23/14, 23/21, 29/23 and oc.).

The one which is truly consistent is 282edo.

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

Retrieved from "https://en.xen.wiki/index.php?title=29-odd-limit&oldid=212356"