19/18

In 19-limit just intonation, 19/18 is the large undevicesimal semitone or Boethius' semitone, measuring about 93.6¢. It is sharp of the Pythagorean limma (256/243) by 513/512, the undevicesimal comma aka Boethius' comma.

Interval information

Ratio	19/18
Subgroup monzo	2.3.19 [-1 -2 1⟩
Size in cents	93.60301¢
Names	large undevicesimal semitone, undevicesimal limma, Boethius' semitone
Color name	19o2, ino 2nd
FJS name	[math]\displaystyle{ \text{m2}^{19} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	8.41785
Weil norm (log2 max(n, d))	8.49586
Wilson norm (sopfr(nd))	27
Comma size	medium
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The small comma (39/35)/(19/18)² = 12636/12635 is tempered out in 53, 130, 140, 243, 270, 422, 513, 665, 742, 795, 935, 1065, 1178, 1205, 1308, 1395, 1448, 1578, 2000, 2190, 2243, 2460, 3125, 3178, 3395, and 4703 EDOs.

Approximation

Edo approximations for 19/18 (93.60 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
12	1\12	100.00	+6.40	+6.40
13	1\13	92.31	-1.30	-1.40
14	1\14	85.71	-7.89	-9.20
25	2\25	96.00	+2.40	+4.99
26	2\26	92.31	-1.30	-2.81
38	3\38	94.74	+1.13	+3.59
39	3\39	92.31	-1.30	-4.21
50	4\50	96.00	+2.40	+9.99
51	4\51	94.12	+0.51	+2.19
52	4\52	92.31	-1.30	-5.61
63	5\63	95.24	+1.64	+8.58
64	5\64	93.75	+0.15	+0.78
65	5\65	92.31	-1.30	-7.02
76	6\76	94.74	+1.13	+7.18
77	6\77	93.51	-0.10	-0.62
78	6\78	92.31	-1.30	-8.42

See also

• 36/19 – its octave complement, the undevicesimal major seventh
• 20/19 – the small undevicesimal semitone
• Gallery of just intervals
• List of superparticular intervals