19-odd-limit: Difference between revisions
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{{odd-limit navigation}} | {{odd-limit navigation}} | ||
{{odd-limit intro|19}} | |||
* [[1/1]] | * [[1/1]] | ||
*'''[[20/19]], [[19/10]]''' | * '''[[20/19]], [[19/10]]''' | ||
*'''[[19/18]], [[36/19]]''' | * '''[[19/18]], [[36/19]]''' | ||
*[[18/17]], [[17/9]] | * [[18/17]], [[17/9]] | ||
*[[17/16]], [[32/17]] | * [[17/16]], [[32/17]] | ||
*[[16/15]], [[15/8]] | * [[16/15]], [[15/8]] | ||
*[[15/14]], [[28/15]] | * [[15/14]], [[28/15]] | ||
*[[14/13]], [[13/7]] | * [[14/13]], [[13/7]] | ||
*[[13/12]], [[24/13]] | * [[13/12]], [[24/13]] | ||
*[[12/11]], [[11/6]] | * [[12/11]], [[11/6]] | ||
*[[11/10]], [[20/11]] | * [[11/10]], [[20/11]] | ||
*[[10/9]], [[9/5]] | * [[10/9]], [[9/5]] | ||
*'''[[19/17]], [[34/19]]''' | * '''[[19/17]], [[34/19]]''' | ||
*[[9/8]], [[16/9]] | * [[9/8]], [[16/9]] | ||
*[[17/15]], [[30/17]] | * [[17/15]], [[30/17]] | ||
*[[8/7]], [[7/4]] | * [[8/7]], [[7/4]] | ||
*[[15/13]], [[26/15]] | * [[15/13]], [[26/15]] | ||
*'''[[22/19]], [[19/11]]''' | * '''[[22/19]], [[19/11]]''' | ||
*[[7/6]], [[12/7]] | * [[7/6]], [[12/7]] | ||
*[[20/17]], [[17/10]] | * [[20/17]], [[17/10]] | ||
*[[13/11]], [[22/13]] | * [[13/11]], [[22/13]] | ||
*'''[[19/16]], [[32/19]]''' | * '''[[19/16]], [[32/19]]''' | ||
*[[6/5]], [[5/3]] | * [[6/5]], [[5/3]] | ||
*[[17/14]], [[28/17]] | * [[17/14]], [[28/17]] | ||
*[[11/9]], [[18/11]] | * [[11/9]], [[18/11]] | ||
*[[16/13]], [[13/8]] | * [[16/13]], [[13/8]] | ||
*[[5/4]], [[8/5]] | * [[5/4]], [[8/5]] | ||
*'''[[24/19]], [[19/12]]''' | * '''[[24/19]], [[19/12]]''' | ||
*'''[[19/15]], [[30/19]]''' | * '''[[19/15]], [[30/19]]''' | ||
*[[14/11]], [[11/7]] | * [[14/11]], [[11/7]] | ||
*[[9/7]], [[14/9]] | * [[9/7]], [[14/9]] | ||
*[[22/17]], [[17/11]] | * [[22/17]], [[17/11]] | ||
*[[13/10]], [[20/13]] | * [[13/10]], [[20/13]] | ||
*[[17/13]], [[26/17]] | * [[17/13]], [[26/17]] | ||
*[[4/3]], [[3/2]] | * [[4/3]], [[3/2]] | ||
*'''[[19/14]], [[28/19]]''' | * '''[[19/14]], [[28/19]]''' | ||
*[[15/11]], [[22/15]] | * [[15/11]], [[22/15]] | ||
*'''[[26/19]], [[19/13]]''' | * '''[[26/19]], [[19/13]]''' | ||
*[[11/8]], [[16/11]] | * [[11/8]], [[16/11]] | ||
*[[18/13]], [[13/9]] | * [[18/13]], [[13/9]] | ||
*[[7/5]], [[10/7]] | * [[7/5]], [[10/7]] | ||
*[[24/17]], [[17/12]] | * [[24/17]], [[17/12]] | ||
{| class="wikitable center-all right-2 left-5" | {| class="wikitable center-all right-2 left-5" | ||
| Line 159: | Line 159: | ||
| greater undevicesimal major seventh | | 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 == | ||
[[Category: | * [[19-limit]] ([[prime limit]]) | ||
[[Category:19-odd-limit| ]] <!-- main article --> | |||
Latest revision as of 14:15, 17 November 2023
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.
- 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
| 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.