19-odd-limit: Difference between revisions

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This is a list of 19-[[Odd limit|odd-limit]] intervals. To [[17-odd-limit]], it adds 9 additional interval pairs involving 19. Also see [[19-limit]].
{{odd-limit navigation}}
{{odd-limit intro|19}}


*'''[[20/19]]''', '''[[19/10]]'''
*  [[1/1]]
*'''[[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]]
*[[11/10]], [[20/11]]
* [[12/11]], [[11/6]]
*[[10/9]], [[9/5]]
* [[11/10]], [[20/11]]
*'''[[19/17]]''', '''[[34/19]]'''
* [[10/9]], [[9/5]]
*[[9/8]], [[16/9]]
* '''[[19/17]], [[34/19]]'''
*[[17/15]], [[30/17]]
* [[9/8]], [[16/9]]
*[[8/7]], [[7/4]]
* [[17/15]], [[30/17]]
*[[15/13]], [[26/15]]
* [[8/7]], [[7/4]]
*'''[[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]]'''
*[[17/14]], [[28/17]]
* [[6/5]], [[5/3]]
*[[11/9]], [[18/11]]
* [[17/14]], [[28/17]]
*[[16/13]], [[13/8]]
* [[11/9]], [[18/11]]
*[[5/4]], [[8/5]]
* [[16/13]], [[13/8]]
*'''[[24/19]]''', '''[[19/12]]'''
* [[5/4]], [[8/5]]
*'''[[19/15]]''', '''[[30/19]]'''
* '''[[24/19]], [[19/12]]'''
*[[14/11]], [[11/7]]
* '''[[19/15]], [[30/19]]'''
*[[9/7]], [[14/9]]
* [[14/11]], [[11/7]]
*[[22/17]], [[17/11]]
* [[9/7]], [[14/9]]
*[[13/10]], [[20/13]]
* [[22/17]], [[17/11]]
*[[17/13]], [[26/17]]
* [[13/10]], [[20/13]]
*[[4/3]], [[3/2]]
* [[17/13]], [[26/17]]
*'''[[19/14]]''', '''[[28/19]]'''
* [[4/3]], [[3/2]]
*[[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]]
*[[7/5]], [[10/7]]
* [[18/13]], [[13/9]]
*[[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(s)
|-
|-
! | Ratio
| [[20/19]]
! | Cents Value
| 88.801
! colspan="2" |[[Kite's color notation|Color name]]
| 19uy1
! | Name
| nuyo unison
| lesser undevicesimal semitone
|-
|-
| | [[20/19]]
| [[19/18]]
| | 88.801
| 93.603
| | 19uy1
| 19o2
| | nuyo unison
| ino 2nd
| | lesser undevicesimal semitone
| greater undevicesimal semitone
|-
|-
| | [[19/18]]
| [[19/17]]
| | 93.603
| 192.558
| | 19o2
| 19o17u2
| | ino 2nd
| nosu 2nd
| | greater undevicesimal semitone
| undevicesimal whole tone / "meantone"
|-
|-
| | [[19/17]]
| [[22/19]]
| | 192.558
| 253.805
| | 19o17u2
| 19u1o2
| | nosu 2nd
| nulo 2nd
| | undevicesimal whole tone ("meantone")
| undevicesimal second–third
|-
|-
| | [[22/19]]
| [[19/16]]
| | 253.805
| 297.513
| | 19u1o2
| 19o3
| | nulo 2nd
| ino 3rd
| | undevicesimal second–third
| undevicesimal minor third
|-
|-
| | [[19/16]]
| [[24/19]]
| | 297.513
| 404.442
| | 19o3
| 19u3
| | ino 3rd
| inu 3rd
| | undevicesimal minor third
| lesser undevicesimal major third
|-
|-
| | [[24/19]]
| [[19/15]]
| | 404.442
| 409.244
| | 19u3
| 19og4
| | inu 3rd
| nogu 4th
| | lesser undevicesimal major third
| greater undevicesimal major third
|-
|-
| | [[19/15]]
| [[19/14]]
| | 409.244
| 528.687
| | 19og4
| 19or4
| | nogu 4th
| noru 4th
| | greater undevicesimal major third
| undevicesimal acute fourth
|-
|-
| | [[19/14]]
| [[26/19]]
| | 528.687
| 543.015
| | 19or4
| 19u3o4
| | noru 4th
| nutho 4th
| | undevicesimal acute fourth
| undevicesimal superfourth
|-
|-
| | [[26/19]]
| [[19/13]]
| | 543.015
| 656.985
| | 19u3o4
| 19o3u5
| | nutho 4th
| nothu 5th
| | undevicesimal superfourth
| undevicesimal subfifth
|-
|-
| | [[19/13]]
| [[28/19]]
| | 656.985
| 671.313
| | 19o3u5
| 19uz5
| | nothu 5th
| nuzo 5th
| | undevicesimal subfifth
| undevicesimal grave fifth
|-
|-
| | [[28/19]]
| [[30/19]]
| | 671.313
| 790.756
| | 19uz5
| 19uy5
| | nuzo 5th
| nuyo 5th
| | undevicesimal grave fifth
| lesser undevicesimal minor sixth
|-
|-
| | [[30/19]]
| [[19/12]]
| | 790.756
| 795.558
| | 19uy5
| 19o6
| | nuyo 5th
| ino 6th
| | lesser undevicesimal minor sixth
| lesser undevicesimal minor sixth
|-
|-
| | [[19/12]]
| [[32/19]]
| | 795.558
| 902.487
| | 19o6
| 19u6
| | ino 6th
| inu 6th
| | lesser undevicesimal minor sixth
| undevicesimal major sixth
|-
|-
| | [[32/19]]
| [[19/11]]
| | 902.487
| 946.195
| | 19u6
| 19o1u7
| | inu 6th
| nolu 7th
| | undevicesimal major sixth
| undevicesimal sixth–seventh
|-
|-
| | [[19/11]]
| [[34/19]]
| | 946.195
| 1007.442
| | 19o1u7
| 19u17o7
| | nolu 7th
| nuso 7th
| | undevicesimal sixth–seventh
| undevicesimal minor seventh
|-
|-
| | [[34/19]]
| [[36/19]]
| | 1007.442
| 1106.397
| | 19u17o7
| 19u7
| | nuso 7th
| inu 7th
| | undevicesimal minor seventh
| lesser undevicesimal major seventh
|-
|-
| | [[36/19]]
| [[19/10]]
| | 1106.397
| 1111.199
| | 19u7
| 19og8
| | inu 7th
| nogu octave
| | lesser undevicesimal major seventh
| greater undevicesimal major seventh
|-
| | [[19/10]]
| | 1111.199
| | 19og8
| | nogu octave
| | greater undevicesimal major seventh
|}
|}
The smallest [[equal division of the octave]] which is consistent in the 19-odd-limit is [[80edo]]; that which is distinctly consistent in the same is [[217edo]].
== See also ==
* [[19-limit]] ([[prime limit]])


[[Category:Just interval]]
[[Category:19-odd-limit| ]] <!-- main article -->

Latest revision as of 14:15, 17 November 2023

Odd limits:

The 19-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 19 and k is an integer. To the 17-odd-limit, it adds 9 pairs of octave-reduced intervals involving 19.

Below is a list of all octave-reduced intervals in the 19-odd-limit.

Ratio Size (¢) Color name Name(s)
20/19 88.801 19uy1 nuyo unison lesser undevicesimal semitone
19/18 93.603 19o2 ino 2nd greater undevicesimal semitone
19/17 192.558 19o17u2 nosu 2nd undevicesimal whole tone / "meantone"
22/19 253.805 19u1o2 nulo 2nd undevicesimal second–third
19/16 297.513 19o3 ino 3rd undevicesimal minor third
24/19 404.442 19u3 inu 3rd lesser undevicesimal major third
19/15 409.244 19og4 nogu 4th greater undevicesimal major third
19/14 528.687 19or4 noru 4th undevicesimal acute fourth
26/19 543.015 19u3o4 nutho 4th undevicesimal superfourth
19/13 656.985 19o3u5 nothu 5th undevicesimal subfifth
28/19 671.313 19uz5 nuzo 5th undevicesimal grave fifth
30/19 790.756 19uy5 nuyo 5th lesser undevicesimal minor sixth
19/12 795.558 19o6 ino 6th lesser undevicesimal minor sixth
32/19 902.487 19u6 inu 6th undevicesimal major sixth
19/11 946.195 19o1u7 nolu 7th undevicesimal sixth–seventh
34/19 1007.442 19u17o7 nuso 7th undevicesimal minor seventh
36/19 1106.397 19u7 inu 7th lesser undevicesimal major seventh
19/10 1111.199 19og8 nogu octave greater undevicesimal major seventh

The smallest equal division of the octave which is consistent in the 19-odd-limit is 80edo; that which is distinctly consistent in the same is 217edo.

See also

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