20/19
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Ratio | 20/19 |
Subgroup monzo | 2.5.19 [2 1 -1⟩ |
Size in cents | 88.800698¢ |
Names | small undevicesimal semitone, undevicesimal chroma, Eratosthenes' semitone |
Color name | 19uy1, nuyo unison |
FJS name | [math]\text{A1}^{5}_{19}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 8.56986 |
Weil height (log_{2} max(n, d)) | 8.64386 |
Wilson height (sopfr (nd)) | 28 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.31189 bits |
Comma size | medium |
[sound info] | |
open this interval in xen-calc |
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