19/10

Interval information

Ratio	19/10
Subgroup monzo	2.5.19 [-1 -1 1⟩
Size in cents	1111.199¢
Names	undeviceismal diminished octave, Eratosthenes' major seventh
Color name	19og8, nogu octave
FJS name	[math]\displaystyle{ \text{d8}^{19}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	7.56986
Weil norm (log2 max(n, d))	8.49586
Wilson norm (sopfr(nd))	26
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In 19-limit just intonation, 19/10 is the undevicesimal diminished octave, measuring about 1111.2¢. In the Functional Just System and Helmholtz-Ellis notation, it is a diminished octave, obtained by adding 81/80 and 513/512 to the Pythagorean diminished octave, but it may be called the Eratosthenes' major seventh as it is sharp of the Pythagorean major seventh (243/128) by 1216/1215, the password aka Eratosthenes' comma.

Approximation

Edo approximations for 19/10 (1111.20 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
13	12\13	1107.69	-3.51	-3.80
14	13\14	1114.29	+3.09	+3.60
26	24\26	1107.69	-3.51	-7.60
27	25\27	1111.11	-0.09	-0.20
28	26\28	1114.29	+3.09	+7.20
40	37\40	1110.00	-1.20	-4.00
41	38\41	1112.20	+1.00	+3.40
53	49\53	1109.43	-1.77	-7.80
54	50\54	1111.11	-0.09	-0.40
55	51\55	1112.73	+1.53	+7.00
67	62\67	1110.45	-0.75	-4.20
68	63\68	1111.76	+0.57	+3.20
80	74\80	1110.00	-1.20	-8.00