20/19: Difference between revisions

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{{Infobox Interval
{{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
| Cents = 88.80070
| Name = small undevicesimal semitone <br>small undevicesimal limma <br>undevicesimal augmented unison
| Color name = 19uy1, nuyo unison
| Color name = 19uy1, nuyo unison
| Sound = Ji-20-19-csound-foscil-220hz.mp3
| 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{{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 {{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{{cent}}.


== See also ==
== See also ==
 
* [[19/10]] – its [[octave complement]], the undevicesimal diminished octave
* [[19/18]] – the large undevicesimal semitone
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[19/18]] - greater undevicesimal semitone
* [[List of superparticular intervals]]
* [[21/20]]
* [[88cET]]
* [[88cET]]


[[Category:19-limit]]
[[Category:Interval ratio]]
[[Category:Semitone]]
[[Category:Semitone]]
[[Category:Second]]
[[Category:Chroma]]
[[Category:Minor second]]
[[Category:Eratosthenes]]
[[Category:Superparticular]]
[[Category:Commas named after polymaths]]
[[Category:Listen]]
[[Category:Commas named after their interval size]]

Latest revision as of 02:01, 4 November 2024

Interval information
Ratio 20/19
Subgroup monzo 2.5.19 [2 1 -1⟩
Size in cents 88.8007¢
Names 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 height (log2 nd) 8.56986
Weil height (log2 max(n, d)) 8.64386
Wilson height (sopfr(nd)) 28
Comma size medium

[sound info]
Open this interval in xen-calc

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 ¢.

See also

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