19/10: Difference between revisions

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
	https://en.xen.wiki/w/File:Jid_19_10_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

Latest revision as of 13:04, 3 November 2025

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.

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

@@ Line 1: / Line 1: @@
-'''19/10'''
+{{Infobox Interval
-|-1 0 -1 0 0 0 0 1&gt;
+| Name = undeviceismal diminished octave, Eratosthenes' major seventh
+| Color name = 19og8, nogu octave
+| Sound = jid_19_10_pluck_adu_dr220.mp3
+}}
-.1993 cents
+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 [[4096/2187|Pythagorean diminished octave]], but it may be called the '''Eratosthenes' major seventh''' as it is sharp of the [[243/128|Pythagorean major seventh (243/128)]] by [[1216/1215]], the ''password'' aka ''Eratosthenes' comma''.
+== Approximation ==
+{{Interval edo approximation|19/10}}
-[[File:jid_19_10_pluck_adu_dr220.mp3]] [[:File:jid_19_10_pluck_adu_dr220.mp3|sound sample]]
+[[Category:Octave]]
+[[Category:Diminished octave]]
-[[category:interval]]
+[[Category:Seventh]]
-[[category:19-limit]]
+[[Category:Major seventh]]
-[[Category:todo:expand]]
+[[Category:Eratosthenes]]