20/19: Difference between revisions

Line 4:

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

| Cents = 88.80070

| Name = small undevicesimal semitone ~~small~~ undevicesimal ~~limma~~ ~~undevicesimal augmented unison~~

| Name = small undevicesimal semitone undevicesimal chroma Eratosthenes' semitone

| Color name = 19uy1, nuyo unison

| FJS name = A1519

| 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)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.

~~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]]

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[[Category:Interval ratio]]

[[Category:Semitone]]

[[Category:~~Second]]~~

[[Category:Chroma]]

~~[[Category:Minor second~~]]

[[Category:Superparticular]]

[[Category:Eratosthenes]]

[[Category:Listen]]

@@ 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]]