20/19: Difference between revisions
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| Cents = 88.80070 | | Cents = 88.80070 | ||
| Name = small undevicesimal semitone <br>small undevicesimal limma <br>undevicesimal augmented unison | | Name = small undevicesimal semitone <br>small undevicesimal limma <br>undevicesimal augmented unison | ||
| Sound = | | Sound = Ji-20-19-csound-foscil-220hz.mp3 | ||
| Color name = 19uy1, nuyo unison | | Color name = 19uy1, nuyo unison | ||
}} | }} | ||
In [[19-limit]] [[ | 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". | ||
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. | 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. | ||
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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. | 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. | ||
==See also== | == See also == | ||
* [[Gallery of just intervals]] | |||
* [[19/18]] - greater undevicesimal semitone | * [[19/18]] - greater undevicesimal semitone | ||
* [[21/20]] | |||
* [[88cET]] | * [[88cET]] | ||
[[Category:Interval]] | [[Category:19-limit]] | ||
[[Category:Interval ratio]] | |||
[[Category:Semitone]] | |||
[[Category:Superparticular]] | |||
Revision as of 14:30, 21 June 2020
| Interval information |
small undevicesimal limma
undevicesimal augmented unison
reduced
[sound info]
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".
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.
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 Pythagorean limma and greater undevicesimal semitone with major limma respectively.
See also
- Gallery of just intervals
- 19/18 - greater undevicesimal semitone
- 21/20
- 88cET