19-limit: Difference between revisions
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The 19-prime-limit can be modeled in a 7-dimensional lattice, with the primes 3, 5, 7, 11, 13, 17, and 19 represented by each dimension. The prime 2 does not appear in the typical 19-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, an eighth dimension is need. | The 19-prime-limit can be modeled in a 7-dimensional lattice, with the primes 3, 5, 7, 11, 13, 17, and 19 represented by each dimension. The prime 2 does not appear in the typical 19-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, an eighth dimension is need. | ||
A list of [[edo]]s with progressively better tunings for 19-limit intervals: {{EDOs| 72, 94, 103h, 111, 121, 130, 140, 152fg, 159, 161, 183, 190g, 193, 212gh, 217, 243e, 270, 311, 400, 422, 460, 525, 581, 742, 935, 954h }} and so on. Another list of edos which provides relatively good tunings for 19-limit intervals ([[TE relative error|relative error]] < 5%): {{EDOs| 72, 111, 217, 243e, 270, 282, 311, 354, 364, 373g, 400, 422, 460, 494(h), 525, 540, 581, 597, 624, 643, 653, 692, 718, 742, 764h, 814, 836f, 882, 908, 925, 935, 954h and }} so on. | == Edo approximations == | ||
A list of [[edo]]s with progressively better tunings for 19-limit intervals: {{EDOs| 72, 94, 103h, 111, 121, 130, 140, 152fg, 159, 161, 183, 190g, 193, 212gh, 217, 243e, 270, 311, 400, 422, 460, 525, 581, 742, 935, 954h }} and so on. | |||
Another list of edos which provides relatively good tunings for 19-limit intervals ([[TE relative error|relative error]] < 5%): {{EDOs| 72, 111, 217, 243e, 270, 282, 311, 354, 364, 373g, 400, 422, 460, 494(h), 525, 540, 581, 597, 624, 643, 653, 692, 718, 742, 764h, 814, 836f, 882, 908, 925, 935, 954h and }} so on. | |||
Note: [[wart notation]] is used to specify the [[val]] chosen for the edo. | |||
== Intervals == | == Intervals == | ||
Revision as of 07:55, 1 August 2023
In 19-limit just intonation, all ratios in the system will contain no primes higher than 19.
The 19-prime-limit can be modeled in a 7-dimensional lattice, with the primes 3, 5, 7, 11, 13, 17, and 19 represented by each dimension. The prime 2 does not appear in the typical 19-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, an eighth dimension is need.
Edo approximations
A list of edos with progressively better tunings for 19-limit intervals: 72, 94, 103h, 111, 121, 130, 140, 152fg, 159, 161, 183, 190g, 193, 212gh, 217, 243e, 270, 311, 400, 422, 460, 525, 581, 742, 935, 954h and so on.
Another list of edos which provides relatively good tunings for 19-limit intervals (relative error < 5%): 72, 111, 217, 243e, 270, 282, 311, 354, 364, 373g, 400, 422, 460, 494(h), 525, 540, 581, 597, 624, 643, 653, 692, 718, 742, 764h, 814, 836f, 882, 908, 925, 935, 954h and so on.
Note: wart notation is used to specify the val chosen for the edo.
Intervals
Here are all the 21-odd-limit intervals of 19-limit:
| Ratio | Cents Value | Color Name | Interval Name | |
|---|---|---|---|---|
| 20/19 | 88.801 | 19uy1 | nuyo 1son | small undevicesimal semitone |
| 19/18 | 93.603 | 19o2 | ino 2nd | large undevicesimal semitone |
| 21/19 | 173.268 | 19uz2 | nuzo 2nd | small undevicesimal whole tone |
| 19/17 | 192.558 | 19o17u2 | nosu 2nd | large undevicesimal whole tone, quasi-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 | small undevicesimal major third |
| 19/15 | 409.244 | 19og4 | nogu 4th | large undevicesimal major third |
| 19/14 | 528.687 | 19or4 | noru 4th | undevicesimal acute fourth |
| 26/19 | 543.015 | 19u3o4 | nutho 4th | undevicesimal super fourth |
| 19/13 | 656.985 | 19o3u5 | nothu 5th | undevicesimal subfifth |
| 28/19 | 671.313 | 19uz5 | nuzo 5th | undevicesimal gravefifth |
| 30/19 | 790.756 | 19uy5 | nuyo 5th | small undevicesimal minor sixth |
| 19/12 | 795.558 | 19o6 | ino 6th | large 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 | small undevicesimal minor seventh |
| 38/21 | 1026.732 | 19or7 | noru 7th | large undevicesimal minor seventh |
| 36/19 | 1106.397 | 19u7 | inu 7th | small undevicesimal major seventh |
| 19/10 | 1111.199 | 19og8 | nogu 8ve | large undevicesimal major seventh |