20/19: Difference between revisions

Interval information
Ratio	20/19
Subgroup monzo	2.5.19 [2 1 -1⟩
Size in cents	88.8007¢
Name	small undevicesimal semitone ; undevicesimal chroma ; Eratosthenes' semitone
Color name	19uy1, nuyo unison
FJS name	[math]\displaystyle{ \text{A1}^{5}_{19} }[/math]
Special properties	superparticular,; reduced
Tenney norm (log2 nd)	8.56986
Weil norm (log2 max(n, d))	8.64386
Wilson norm (sopfr(nd))	28
	https://en.xen.wiki/w/File:Ji-20-19-csound-foscil-220hz.mp3; [sound info]
	Open this interval in xen-calc

Revision as of 14:35, 21 March 2022

In 19-limit just intonation, 20/19 is the small undevicesimal semitone or Eratosthenes' semitone, measuring about 88.8 ¢. It is flat of the Pythagorean limma (256/243) by 1216/1215, the password aka Eratosthenes' comma.

It is almost exactly 1/3 of a subminor third of 7/6. The small comma (7/6)/(20/19)³ = 48013/48000 is tempered out in 12, 41, 53, 68, 80, 94, 121, 161, 190, 202, 217, 229, 243, 270, 282, 311, 323, 364, 460, 472, 513, 525, 540, 581, 742, 783, 795, 1012, 1053, 1106, 1308, 1323, 1578, 1848, 1889, and 2320 EDOs, leading to a variety of temperaments in which three semitones make up a subminor third.

It is very close to 2 steps out of 27edo, or 88.8889 ¢.

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 {{Infobox Interval
-| Icon =
 | Ratio = 20/19
 | Monzo = 2 0 1 0 0 0 0 -1
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 }}
-In [[19-limit]] [[just intonation]], '''20/19''' is the '''small undevicesimal semitone''' or '''Eratosthenes' semitone''', measuring about 88.8¢. It is flat of the [[256/243|Pythagorean limma (256/243)]] by [[1216/1215]], the ''password'' aka ''Eratosthenes' comma''.
+In [[19-limit]] [[just intonation]], '''20/19''' is the '''small undevicesimal semitone''' or '''Eratosthenes' semitone''', measuring about 88.8{{cent}}. It is flat of the [[256/243|Pythagorean limma (256/243)]] by [[1216/1215]], the ''password'' aka ''Eratosthenes' comma''.
 It is almost exactly 1/3 of a subminor third of [[7/6]]. The small comma (7/6)/(20/19)<sup>3</sup> = 48013/48000 is tempered out in {{EDOs| 12, 41, 53, 68, 80, 94, 121, 161, 190, 202, 217, 229, 243, 270, 282, 311, 323, 364, 460, 472, 513, 525, 540, 581, 742, 783, 795, 1012, 1053, 1106, 1308, 1323, 1578, 1848, 1889, and 2320 EDOs}}, leading to a variety of temperaments in which three semitones make up a subminor third.
-It is very close to 2 steps out of [[27edo]], or 88.8889 cents.
+It is very close to 2 steps out of [[27edo]], or 88.8889{{cent}}.
 == See also ==
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 [[Category:19-limit]]
-[[Category:Interval ratio]]
 [[Category:Semitone]]
 [[Category:Chroma]]
 [[Category:Superparticular]]
 [[Category:Eratosthenes]]