19-odd-limit

Odd limits:

---

• 1-odd-limit
• 3-odd-limit
• 5-odd-limit
• 7-odd-limit
• 9-odd-limit
• 11-odd-limit
• 13-odd-limit
• 15-odd-limit
• 17-odd-limit
• 19-odd-limit
• 21-odd-limit
• 23-odd-limit
• 25-odd-limit
• 27-odd-limit
• 29-odd-limit
• 31-odd-limit

The 19-odd-limit is the set of all rational intervals for which neither the numerator nor the denominator of the frequency ratio exceeds 19, once all powers of 2 are removed. To the 17-odd-limit, it adds 9 interval pairs 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.

See also

• 19-limit (prime limit)