20/19: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = small undevicesimal semitone, undevicesimal chroma, Eratosthenes' semitone | |||
| Comma = yes | |||
| Name = small undevicesimal semitone | |||
| 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''' or '''Eratosthenes' semitone''', measuring about 88. | 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 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 | It is very close to 2 steps out of [[27edo]], or 88.8889{{cent}}. | ||
== See also == | == See also == | ||
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* [[88cET]] | * [[88cET]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Eratosthenes]] | [[Category:Eratosthenes]] | ||
[[Category:Commas named after polymaths]] | |||
[[Category:Commas named after their interval size]] | |||
Latest revision as of 02:01, 4 November 2024
| Interval information |
undevicesimal chroma,
Eratosthenes' semitone
reduced
[sound info]
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
- 19/10 – its octave complement, the undevicesimal diminished octave
- 19/18 – the large undevicesimal semitone
- Gallery of just intervals
- List of superparticular intervals
- 88cET