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29-odd-limit: Difference between revisions

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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|29}}
{{Odd-limit intro|29}}
 
* [[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]]


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"
{| 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 -->
Retrieved from "https://en.xen.wiki/w/29-odd-limit"