19-limit: Difference between revisions
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== Intervals == | == Intervals == | ||
Here are all the [[21-odd-limit]] intervals of 19: | Here are all the [[21-odd-limit]] intervals of 19-limit: | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 15: | Line 15: | ||
! Interval Name | ! Interval Name | ||
|- | |- | ||
| 20/19 | | [[20/19]] | ||
| 88.801 | | 88.801 | ||
| 19uy1 | | 19uy1 | ||
| Line 21: | Line 21: | ||
| small undevicesimal semitone | | small undevicesimal semitone | ||
|- | |- | ||
| 19/18 | | [[19/18]] | ||
| 93.603 | | 93.603 | ||
| 19o2 | | 19o2 | ||
| Line 27: | Line 27: | ||
| large undevicesimal semitone | | large undevicesimal semitone | ||
|- | |- | ||
| 21/19 | | [[21/19]] | ||
| 173.268 | | 173.268 | ||
| 19uz2 | | 19uz2 | ||
| Line 33: | Line 33: | ||
| small undevicesimal whole tone | | small undevicesimal whole tone | ||
|- | |- | ||
| 19/17 | | [[19/17]] | ||
| 192.558 | | 192.558 | ||
| 19o17u2 | | 19o17u2 | ||
| Line 39: | Line 39: | ||
| large undevicesimal whole tone, quasi-meantone | | large undevicesimal whole tone, quasi-meantone | ||
|- | |- | ||
| 22/19 | | [[22/19]] | ||
| 253.805 | | 253.805 | ||
| 19u1o2 | | 19u1o2 | ||
| Line 45: | Line 45: | ||
| undevicesimal second-third | | undevicesimal second-third | ||
|- | |- | ||
| 19/16 | | [[19/16]] | ||
| 297.513 | | 297.513 | ||
| 19o3 | | 19o3 | ||
| Line 51: | Line 51: | ||
| undevicesimal minor third | | undevicesimal minor third | ||
|- | |- | ||
| 24/19 | | [[24/19]] | ||
| 404.442 | | 404.442 | ||
| 19u3 | | 19u3 | ||
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| small undevicesimal major third | | small undevicesimal major third | ||
|- | |- | ||
| 19/15 | | [[19/15]] | ||
| 409.244 | | 409.244 | ||
| 19og4 | | 19og4 | ||
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| large undevicesimal major third | | large undevicesimal major third | ||
|- | |- | ||
| 19/14 | | [[19/14]] | ||
| 528.687 | | 528.687 | ||
| 19or4 | | 19or4 | ||
| Line 69: | Line 69: | ||
| undevicesimal acute fourth | | undevicesimal acute fourth | ||
|- | |- | ||
| 26/19 | | [[26/19]] | ||
| 543.015 | | 543.015 | ||
| 19u3o4 | | 19u3o4 | ||
| Line 75: | Line 75: | ||
| undevicesimal super fourth | | undevicesimal super fourth | ||
|- | |- | ||
| 19/13 | | [[19/13]] | ||
| 656.985 | | 656.985 | ||
| 19o3u5 | | 19o3u5 | ||
| nothu 5th | | nothu 5th | ||
| undevicesimal | | undevicesimal subfifth | ||
|- | |- | ||
| 28/19 | | [[28/19]] | ||
| 671.313 | | 671.313 | ||
| 19uz5 | | 19uz5 | ||
| nuzo 5th | | nuzo 5th | ||
| undevicesimal | | undevicesimal gravefifth | ||
|- | |- | ||
| 30/19 | | [[30/19]] | ||
| 790.756 | | 790.756 | ||
| 19uy5 | | 19uy5 | ||
| Line 93: | Line 93: | ||
| small undevicesimal minor sixth | | small undevicesimal minor sixth | ||
|- | |- | ||
| 19/12 | | [[19/12]] | ||
| 795.558 | | 795.558 | ||
| 19o6 | | 19o6 | ||
| Line 99: | Line 99: | ||
| large undevicesimal minor sixth | | large undevicesimal minor sixth | ||
|- | |- | ||
| 32/19 | | [[32/19]] | ||
| 902.487 | | 902.487 | ||
| 19u6 | | 19u6 | ||
| Line 105: | Line 105: | ||
| undevicesimal major sixth | | undevicesimal major sixth | ||
|- | |- | ||
| 19/11 | | [[19/11]] | ||
| 946.195 | | 946.195 | ||
| 19o1u7 | | 19o1u7 | ||
| Line 111: | Line 111: | ||
| undevicesimal sixth-seventh | | undevicesimal sixth-seventh | ||
|- | |- | ||
| 34/19 | | [[34/19]] | ||
| 1007.442 | | 1007.442 | ||
| 19u17o7 | | 19u17o7 | ||
| Line 117: | Line 117: | ||
| small undevicesimal minor seventh | | small undevicesimal minor seventh | ||
|- | |- | ||
| 38/21 | | [[38/21]] | ||
| 1026.732 | | 1026.732 | ||
| 19or7 | | 19or7 | ||
| Line 123: | Line 123: | ||
| large undevicesimal minor seventh | | large undevicesimal minor seventh | ||
|- | |- | ||
| 36/19 | | [[36/19]] | ||
| 1106.397 | | 1106.397 | ||
| 19u7 | | 19u7 | ||
| Line 129: | Line 129: | ||
| small undevicesimal major seventh | | small undevicesimal major seventh | ||
|- | |- | ||
| 19/10 | | [[19/10]] | ||
| 1111.199 | | 1111.199 | ||
| 19og8 | | 19og8 | ||
| Line 136: | Line 136: | ||
|} | |} | ||
== See | == See also == | ||
* [[Harmonic limit]] | * [[Harmonic limit]] | ||
Revision as of 19:58, 17 December 2021
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.
EDOs which provides an excellent tuning for 19-limit intervals are: 80, 94, 111, 121, 217, 270, 282, 311, 320, 364, 388, 400, 422, 436, 460, 525, 581, 597, 624, 643, 653, 692, 718, 742, 771, 860, 867, 882, 908, 925, 935, 954, and 997 among others.
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 |