19/16

Interval information

Ratio	19/16
Subgroup monzo	2.19 [-4 1⟩
Size in cents	297.513¢
Names	otonal minor third, octave-reduced 19th harmonic
Color name	19o3, ino 3rd
FJS name	[math]\displaystyle{ \text{m3}^{19} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	8.24793
Weil norm (log2 max(n, d))	8.49586
Wilson norm (sopfr(nd))	27
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19/16 is a 19-limit interval, 297.5 cents in size, the otonal minor third or octave-reduced 19th harmonic, which is extremely close to the minor third of 12edo (300 cents). It is an undevicesimal comma aka Boethius' comma (513/512) above the Pythagorean minor third.

Approximation

19/16 is very accurately approximated by 121edo (30\121), although technically there is a slight difference, as that of 121edo is 0.007645 cents sharper.

Edo approximations for 19/16 (297.51 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	1\4	300.00	+2.49	+0.83
8	2\8	300.00	+2.49	+1.66
12	3\12	300.00	+2.49	+2.49
16	4\16	300.00	+2.49	+3.32
20	5\20	300.00	+2.49	+4.14
24	6\24	300.00	+2.49	+4.97
28	7\28	300.00	+2.49	+5.80
32	8\32	300.00	+2.49	+6.63
36	9\36	300.00	+2.49	+7.46
40	10\40	300.00	+2.49	+8.29
44	11\44	300.00	+2.49	+9.12
48	12\48	300.00	+2.49	+9.95
73	18\73	295.89	-1.62	-9.87
77	19\77	296.10	-1.41	-9.04

See also

• 32/19 – its octave complement
• 24/19 – its fifth complement
• Gallery of just intervals