23-odd-limit: Difference between revisions

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This is a list of 23-[[Odd_limit|odd-limit]] intervals. To [[21-odd-limit]], it adds 11 additional interval pairs involving 23. It contains all the wonders of [[94edo]].
{{odd-limit navigation}}
{{odd-limit intro|23}} It contains all the wonders of [[94edo]].


*'''[[24/23]]''', '''23/12'''
* [[1/1]]
*'''[[23/22]]''', '''44/23'''
* '''[[24/23]], [[23/12]]'''
*[[22/21]], [[21/11]]
* '''[[23/22]], [[44/23]]'''
*[[21/20]], [[40/21]]
* [[22/21]], [[21/11]]
*[[20/19]], [[19/10]]
* [[21/20]], [[40/21]]
*[[19/18]], [[36/19]]
* [[20/19]], [[19/10]]
*[[18/17]], [[17/9]]
* [[19/18]], [[36/19]]
*[[17/16]], [[32/17]]
* [[18/17]], [[17/9]]
*[[16/15]], [[15/8]]
* [[17/16]], [[32/17]]
*[[15/14]], [[28/15]]
* [[16/15]], [[15/8]]
*[[14/13]], [[13/7]]
* [[15/14]], [[28/15]]
*[[13/12]], [[24/13]]
* [[14/13]], [[13/7]]
*[[12/11]], [[11/6]]
* [[13/12]], [[24/13]]
*'''23/21''', '''42/23'''
* [[12/11]], [[11/6]]
*[[11/10]], [[20/11]]
* '''[[23/21]], [[42/23]]'''
*[[21/19]], [[38/21]]
* [[11/10]], [[20/11]]
*[[10/9]], [[9/5]]
* [[21/19]], [[38/21]]
*[[19/17]], [[34/19]]
* [[10/9]], [[9/5]]
*[[9/8]], [[16/9]]
* [[19/17]], [[34/19]]
*'''26/23''', '''23/13'''
* [[9/8]], [[16/9]]
*[[17/15]], [[30/17]]
* '''[[26/23]], [[23/13]]'''
*[[8/7]], [[7/4]]
* [[17/15]], [[30/17]]
*'''23/20''', '''40/23'''
* [[8/7]], [[7/4]]
*[[15/13]], [[26/15]]
* '''[[23/20]], [[40/23]]'''
*[[22/19]], [[19/11]]
* [[15/13]], [[26/15]]
*[[7/6]], [[12/7]]
* [[22/19]], [[19/11]]
*[[20/17]], [[17/10]]
* [[7/6]], [[12/7]]
*[[13/11]], [[22/13]]
* [[20/17]], [[17/10]]
*[[19/16]], [[32/19]]
* [[13/11]], [[22/13]]
*[[6/5]], [[5/3]]
* [[19/16]], [[32/19]]
*'''23/19''', '''38/23'''
* [[6/5]], [[5/3]]
*[[17/14]], [[28/17]]
* '''[[23/19]], [[38/23]]'''
*'''28/23''', '''23/14'''
* [[17/14]], [[28/17]]
*[[11/9]], [[18/11]]
* '''[[28/23]], [[23/14]]'''
*[[16/13]], [[13/8]]
* [[11/9]], [[18/11]]
*[[21/17]], [[34/21]]
* [[16/13]], [[13/8]]
*[[26/21]], [[21/13]]
* [[21/17]], [[34/21]]
*[[5/4]], [[8/5]]
* [[26/21]], [[21/13]]
*[[24/19]], [[19/12]]
* [[5/4]], [[8/5]]
*[[19/15]], [[30/19]]
* [[24/19]], [[19/12]]
*[[14/11]], [[11/7]]
* [[19/15]], [[30/19]]
*'''23/18''', '''36/23'''
* [[14/11]], [[11/7]]
*[[9/7]], [[14/9]]
* '''[[23/18]], [[36/23]]'''
*[[22/17]], [[17/11]]
* [[9/7]], [[14/9]]
*[[13/10]], [[20/13]]
* [[22/17]], [[17/11]]
*'''30/23''', '''23/15'''
* [[13/10]], [[20/13]]
*[[17/13]], [[26/17]]
* '''[[30/23]], [[23/15]]'''
*[[21/16]], [[32/21]]
* [[17/13]], [[26/17]]
*[[4/3]], [[3/2]]
* [[21/16]], [[32/21]]
*'''23/17''', '''34/23'''
* [[4/3]], [[3/2]]
*[[19/14]], [[28/19]]
* '''[[23/17]], [[34/23]]'''
*[[15/11]], [[22/15]]
* [[19/14]], [[28/19]]
*[[26/19]], [[19/13]]
* [[15/11]], [[22/15]]
*[[11/8]], [[16/11]]
* [[26/19]], [[19/13]]
*[[18/13]], [[13/9]]
* [[11/8]], [[16/11]]
*'''[[32/23]]''', '''[[23/16]]'''
* [[18/13]], [[13/9]]
*[[7/5]], [[10/7]]
* '''[[32/23]], [[23/16]]'''
*[[24/17]], [[17/12]]
* [[7/5]], [[10/7]]
* [[24/17]], [[17/12]]


{| class="wikitable"
{| class="wikitable center-all right-2 left-5"
! Ratio
! Size ([[cents|¢]])
! colspan="2" | [[Color name]]
! Name
|-
|-
! | Ratio
| [[24/23]]
! | Cents Value
| 73.681
! colspan="2" |[[Kite's color notation|Color name]]
| 23u1
! | Name
| twethu unison
| lesser vicesimotertial semitone
|-
|-
| | [[24/23]]
| [[23/22]]
| | 73.681
| 76.956
| | 23u1
| 23o1u2
| | twenty-thu unison
| twetholu 2nd
| | lesser vicesimotertial semitone
| greater vicesimotertial semitone
|-
|-
| | [[23/22]]
| [[23/21]]
| | 76.956
| 157.493
| | 23o1u2
| 23or2
| | twenty-tholu 2nd
| twethoru 2nd
| | greater vicesimotertial semitone
| vicesimotertial neutral second
|-
|-
| | 23/21
| [[26/23]]
| | 157.493
| 212.253
| | 23or2
| 23u3o2
| | twenty-thoru 2nd
| twethutho 2nd
| | vicesimotertial neutral second
| vicesimotertial whole tone
|-
|-
| | 26/23
| [[23/20]]
| | 212.253
| 241.961
| | 23u3o2
| 23og3
| | twenty-thutho 2nd
| twethogu 3rd
| | vicesimotertial whole tone
| vicesimotertial inframinor third
|-
|-
| | 23/20
| [[23/19]]
| | 241.961
| 330.761
| | 23og3
| 23o19u3
| | twenty-thogu 3rd
| twethonu 3rd
| | vicesimotertial subminor third
| vicesimotertial supraminor third
|-
|-
| | 23/19
| [[28/23]]
| | 330.761
| 340.552
| | 23o19u3
| 23uz3
| | twenty-thonu 3rd
| twethuzo 3rd
| | vicesimotertial supraminor third
| vicesimotertial neutral third
|-
|-
| | 28/23
| [[23/18]]
| | 340.552
| 424.364
| | 23uz3
| 23o4
| | twenty-thuzo 3rd
| twetho 4th
| | vicesimotertial neutral third
| vicesimotertial diminished fourth
|-
|-
| | 23/18
| [[30/23]]
| | 424.364
| 459.994
| | 23o4
| 23uy3
| | twenty-tho 4th
| twethuyo 3rd
| | vicesimotertial diminished fourth
| vicesimotertial ultramajor third
|-
|-
| | 30/23
| [[23/17]]
| | 459.994
| 523.319
| | 23uy3
| 23o17u4
| | twenty-thuyo 3rd
| twethosu 4th
| | vicesimotertial ultramajor third
| vicesimotertial acute fourth
|-
|-
| | 23/17
| [[32/23]]
| | 523.319
| 571.726
| | 23o17u4
| 23u4
| | twenty-thosu 4th
| twethu 4th
| | vicesimotertial fourth
| vicesimotertial narrow tritone
|-
|-
| | [[32/23]]
| [[23/16]]
| | 571.726
| 628.274
| | 23u4
| 23o5
| | twenty-thu 4th
| twetho 5th
| | vicesimotertial narrow tritone
| vicesimotertial high tritone
|-
|-
| | [[23/16]]
| [[34/23]]
| | 628.274
| 676.681
| | 23o5
| 23u17o5
| | twenty-tho 5th
| twethuso 5th
| | vicesimotertial high tritone
| vicesimotertial grave fifth
|-
| [[23/15]]
| 740.006
| 23og6
| twethogu 6th
| vicesimotertial ultraminor sixth
|-
| [[36/23]]
| 775.636
| 23u5
| twethu 5th
| vicesimotertial augmented fifth
|-
| [[23/14]]
| 859.448
| 23or6
| twethoru 6th
| vicesimotertial neutral sixth
|-
| [[38/23]]
| 869.239
| 23u19o6
| twethuno 6th
| vicesimotertial submajor sixth
|-
| [[40/23]]
| 958.039
| 23uy6
| twethuyo 6th
| vicesimotertial ultramajor sixth
|-
| [[23/13]]
| 987.747
| 23o3u7
| twethothu 7th
| vicesimotertial minor seventh
|-
| [[42/23]]
| 1042.507
| 23uz7
| twethuzo 7th
| vicesimotertial neutral seventh
|-
| [[44/23]]
| 1123.044
| 23u1o7
| twethulo 7th
| vicesimotertial major seventh
|-
| [[23/12]]
| 1126.319
| 23o8
| twetho octave
| vicesimotertial diminished octave
|}
|}
[[94edo]] is the smallest [[equal division of the octave]] to be consistent in the 23-odd limit; the smallest to be distinctly consistent in the same is [[282edo]].
== See also ==
* [[23-limit]] ([[prime limit]])


[[Category:Just interval]]
[[Category:23-odd-limit| ]] <!-- main article -->

Latest revision as of 13:44, 4 June 2025

Odd limits:

The 23-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 23 and k is an integer. To the 21-odd-limit, it adds 11 pairs of octave-reduced intervals involving 23.

Below is a list of all octave-reduced intervals in the 23-odd-limit. It contains all the wonders of 94edo.

Ratio Size (¢) Color name Name
24/23 73.681 23u1 twethu unison lesser vicesimotertial semitone
23/22 76.956 23o1u2 twetholu 2nd greater vicesimotertial semitone
23/21 157.493 23or2 twethoru 2nd vicesimotertial neutral second
26/23 212.253 23u3o2 twethutho 2nd vicesimotertial whole tone
23/20 241.961 23og3 twethogu 3rd vicesimotertial inframinor third
23/19 330.761 23o19u3 twethonu 3rd vicesimotertial supraminor third
28/23 340.552 23uz3 twethuzo 3rd vicesimotertial neutral third
23/18 424.364 23o4 twetho 4th vicesimotertial diminished fourth
30/23 459.994 23uy3 twethuyo 3rd vicesimotertial ultramajor third
23/17 523.319 23o17u4 twethosu 4th vicesimotertial acute fourth
32/23 571.726 23u4 twethu 4th vicesimotertial narrow tritone
23/16 628.274 23o5 twetho 5th vicesimotertial high tritone
34/23 676.681 23u17o5 twethuso 5th vicesimotertial grave fifth
23/15 740.006 23og6 twethogu 6th vicesimotertial ultraminor sixth
36/23 775.636 23u5 twethu 5th vicesimotertial augmented fifth
23/14 859.448 23or6 twethoru 6th vicesimotertial neutral sixth
38/23 869.239 23u19o6 twethuno 6th vicesimotertial submajor sixth
40/23 958.039 23uy6 twethuyo 6th vicesimotertial ultramajor sixth
23/13 987.747 23o3u7 twethothu 7th vicesimotertial minor seventh
42/23 1042.507 23uz7 twethuzo 7th vicesimotertial neutral seventh
44/23 1123.044 23u1o7 twethulo 7th vicesimotertial major seventh
23/12 1126.319 23o8 twetho octave vicesimotertial diminished octave

94edo is the smallest equal division of the octave to be consistent in the 23-odd limit; the smallest to be distinctly consistent in the same is 282edo.

See also

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