81/20
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Ratio
81/20
Factorization
2-2 × 34 × 5-1
Monzo
[-2 4 -1⟩
Size in cents
2421.506¢
Name
syntonic double octave
Color name
g15, gu double octave
FJS name
[math]\text{P15}_{5}[/math]
Tenney height (log2 nd)
10.6618
Weil height (log2 max(n, d))
12.6797
Wilson height (sopfr(nd))
21
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.20215 bits
open this interval in xen-calc
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
The ratio of 81/20 is the distance between the 81st and 20th harmonic, which can be seen as a double octave that is augmented by a syntonic comma (81/80). This interval spans the size of about 2421.5 cents. It is also the result of stacking 4 6/5's and 3 5/4's. This suggests that an octave stretch of half a syntonic comma is a good way to optimise a diatonic scale for pure thirds, resulting in whole tones of approximately 193 cents and semitones of 122.