20/19

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Interval information
Ratio 20/19
Monzo |2 0 1 0 0 0 0 -1>
Size in cents 88.80070
Name(s) small undevicesimal semitone
small undevicesimal limma
undevicesimal augmented unison
Color name 19uy1, nuyo unison
270px
[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