81/20

Interval information

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]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~4.20215 bits
Open this interval in xen-calc

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 four 6/5's and three 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.