20/19: Difference between revisions

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 cents.

@@ Line 4: / Line 4: @@
 | Monzo = 2 0 1 0 0 0 0 -1
 | Cents = 88.80070
-| Name = small undevicesimal semitone <br>small undevicesimal limma <br>undevicesimal augmented unison
+| Name = small undevicesimal semitone <br>undevicesimal chroma <br>Eratosthenes' semitone
 | Color name = 19uy1, nuyo unison
+| FJS name = A1<sup>5</sup><sub>19</sub>
 | Sound = Ji-20-19-csound-foscil-220hz.mp3
 }}
-In [[19-limit]] [[just intonation]], '''20/19''' is the '''small undevicesimal semitone''', measuring about 88.8¢ (almost exactly 1/3 of a subminor third of [[7/6]]). Its [[octave complement]] is [[19/10]], the "undevicesimal diminished octave". It is very close to 2 steps out of [[27edo]], or 88.8889 cents.
+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''.
-The small comma (7/6)/(20/19)^3 = 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 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.
-The password comma, (256/243)/(20/19) = (19/18)/(135/128) = 1216/1215 is tempered out in {{EDOs| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692 EDOs}}, leading to a variety of temperaments which identifies 20/19 with [[256/243|Pythagorean limma]] and [[19/18]] with [[135/128|major limma]] respectively.
+It is very close to 2 steps out of [[27edo]], or 88.8889 cents.
 == See also ==
+* [[19/10]] – its [[octave complement]], the undevicesimal diminished octave
+* [[19/18]] – the large undevicesimal semitone
 * [[Gallery of just intervals]]
-* [[19/18]] - greater undevicesimal semitone
+* [[List of superparticular intervals]]
-* [[21/20]]
 * [[88cET]]
@@ Line 25: / Line 26: @@
 [[Category:Interval ratio]]
 [[Category:Semitone]]
-[[Category:Second]]
+[[Category:Chroma]]
-[[Category:Minor second]]
 [[Category:Superparticular]]
+[[Category:Eratosthenes]]
 [[Category:Listen]]

20/19: Difference between revisions

Revision as of 07:02, 6 February 2021

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