20/19: Difference between revisions

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{{Infobox Interval

| ~~Icon~~ =

| Name = small undevicesimal semitone, undevicesimal chroma, Eratosthenes' semitone

| ~~Ratio~~ = ~~20/19~~

| Comma = yes

| ~~Monzo~~ = ~~2 0 1 0 0 0 0 -1~~

| Color name = 19uy1, nuyo unison

~~| Cents = 88.80070~~

~~| Name = small undevicesimal semitone <br>small undevicesimal limma <br>undevicesimal augmented~~ unison

| Sound = Ji-20-19-csound-foscil-220hz.mp3

~~| Color name = 19uy1, nuyo unison~~

}}

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{{cent}}. 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 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 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 small undevicesimal semitone with~~ [[~~256/243|Pythagorean limma~~]] ~~and greater undevicesimal semitone with [[135/128|major limma]] respectively~~.

It is very close to 2 steps out of [[27edo]], or 88.8889{{cent}}.

== 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]]

~~[[Category:19-limit]]~~

~~[[Category:Interval ratio]]~~

[[Category:Semitone]]

[[Category:~~Superparticular~~]]

[[Category:Chroma]]

[[Category:Eratosthenes]]

[[Category:Commas named after polymaths]]

[[Category:Commas named after their interval size]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = small undevicesimal semitone, undevicesimal chroma, Eratosthenes' semitone
-| Ratio = 20/19
+| Comma = yes
-| Monzo = 2 0 1 0 0 0 0 -1
+| Color name = 19uy1, nuyo unison
-| Cents = 88.80070
-| Name = small undevicesimal semitone <br>small undevicesimal limma <br>undevicesimal augmented unison
 | Sound = Ji-20-19-csound-foscil-220hz.mp3
-| Color name = 19uy1, nuyo unison
 }}
-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{{cent}}. 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 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 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 small undevicesimal semitone with [[256/243|Pythagorean limma]] and greater undevicesimal semitone with [[135/128|major limma]] respectively.
+It is very close to 2 steps out of [[27edo]], or 88.8889{{cent}}.
 == 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]]
-[[Category:19-limit]]
-[[Category:Interval ratio]]
 [[Category:Semitone]]
-[[Category:Superparticular]]
+[[Category:Chroma]]
+[[Category:Eratosthenes]]
+[[Category:Commas named after polymaths]]
+[[Category:Commas named after their interval size]]