19-limit

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:

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	nolu 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	19u3o5	nutho 5th	undevicesimal super fourth
19/13	656.985	19o3u4	nothu 4th	undevicesimal sub fifth
28/19	671.313	19uz5	nuzo 5th	undevicesimal grave fifth
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

See Also

• Harmonic Limit
• 19-odd-limit