20/19: Difference between revisions
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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". | 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 41, 68, 80, 94, 121, 161, 190, 217, 243, 270, 282, 311, 364, 460, 525, 581, 742, 1012, 1308, 1323, 1578, 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. | ||
The password comma (256/243)/(20/19) = (19/18)/(135/128) = 1216/1215 is tempered out in 29, 41, 53, 77, 87, 94, 99, 111, 118, 130, 140, 152, 159, 183, 193, 217, 270, 282, 311, 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== | ||
Revision as of 06:21, 2 February 2019
| 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.