20/19

Interval information

Ratio	20/19
Subgroup monzo	2.5.19 [2 1 -1⟩
Size in cents	88.8007¢
Names	small undevicesimal semitone, undevicesimal chroma, Eratosthenes' semitone
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
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.31189 bits
Comma size	medium
[sound info]
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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