19-odd-limit: Difference between revisions

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This is a list of [[19-odd-limit]] intervals. Also see [[19-limit]].
{{odd-limit navigation}}
{{odd-limit intro|19}}


<ul><li>[[18/17]], [[17/9]]</li><li>[[17/16]], [[32/17]]</li><li>[[16/15]], [[15/8]]</li><li>[[15/14]], [[28/15]]</li><li>[[14/13]], [[13/7]]</li><li>[[13/12]], [[24/13]]</li><li>[[12/11]], [[11/6]]</li><li>[[11/10]], [[20/11]]</li><li>[[10/9]], [[9/5]]</li><li>[[9/8]], [[16/9]]</li><li>[[17/15]], [[30/17]]</li><li>[[8/7]], [[7/4]]</li><li>[[15/13]], [[26/15]]</li><li>[[7/6]], [[12/7]]</li><li>[[20/17]], [[17/10]]</li><li>[[13/11]], [[22/13]]</li><li>[[6/5]], [[5/3]]</li><li>[[17/14]], [[28/17]]</li><li>[[11/9]], [[18/11]]</li><li>[[16/13]], [[13/8]]</li><li>[[5/4]], [[8/5]]</li><li>[[14/11]], [[11/7]]</li><li>[[9/7]], [[14/9]]</li><li>[[22/17]], [[17/11]]</li><li>[[13/10]], [[20/13]]</li><li>[[17/13]], [[26/17]]</li><li>[[4/3]], [[3/2]]</li><li>[[15/11]], [[22/15]]</li><li>[[11/8]], [[16/11]]</li><li>[[18/13]], [[13/9]]</li><li>[[7/5]], [[10/7]]</li><li>[[24/17]], [[17/12]]</li></ul>
*  [[1/1]]
* '''[[20/19]], [[19/10]]'''
* '''[[19/18]], [[36/19]]'''
* [[18/17]], [[17/9]]
* [[17/16]], [[32/17]]
* [[16/15]], [[15/8]]
* [[15/14]], [[28/15]]
* [[14/13]], [[13/7]]
* [[13/12]], [[24/13]]
* [[12/11]], [[11/6]]
* [[11/10]], [[20/11]]
* [[10/9]], [[9/5]]
* '''[[19/17]], [[34/19]]'''
* [[9/8]], [[16/9]]
* [[17/15]], [[30/17]]
* [[8/7]], [[7/4]]
* [[15/13]], [[26/15]]
* '''[[22/19]], [[19/11]]'''
* [[7/6]], [[12/7]]
* [[20/17]], [[17/10]]
* [[13/11]], [[22/13]]
* '''[[19/16]], [[32/19]]'''
* [[6/5]], [[5/3]]
* [[17/14]], [[28/17]]
* [[11/9]], [[18/11]]
* [[16/13]], [[13/8]]
* [[5/4]], [[8/5]]
* '''[[24/19]], [[19/12]]'''
* '''[[19/15]], [[30/19]]'''
* [[14/11]], [[11/7]]
* [[9/7]], [[14/9]]
* [[22/17]], [[17/11]]
* [[13/10]], [[20/13]]
* [[17/13]], [[26/17]]
* [[4/3]], [[3/2]]
* '''[[19/14]], [[28/19]]'''
* [[15/11]], [[22/15]]
* '''[[26/19]], [[19/13]]'''
* [[11/8]], [[16/11]]
* [[18/13]], [[13/9]]
* [[7/5]], [[10/7]]
* [[24/17]], [[17/12]]


<!-- wish {{List}} worked -->
{| class="wikitable center-all right-2 left-5"
! Ratio
! Size ([[cents|¢]])
! colspan="2" | [[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]].


[[Category:Just interval]]
== See also ==
* [[19-limit]] ([[prime limit]])
 
[[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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