20/19

Interval information

Ratio	20/19
Subgroup monzo	2.5.19 [2 1 -1⟩
Size in cents	88.8007¢
Name	small undevicesimal semitone small undevicesimal limma undevicesimal augmented unison
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
[sound info]
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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". It is very close to 2 steps out of 27edo, or 88.8889 cents.

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 20/19 with Pythagorean limma and 19/18 with major limma respectively.

See also

• Gallery of just intervals
• 19/18 - greater undevicesimal semitone
• 21/20
• 88cET