81/20
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| Ratio | 81/20 |
| Factorization | 2-2 × 34 × 5-1 |
| Monzo | [-2 4 -1⟩ |
| Size in cents | 2421.5063¢ |
| 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 | |
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.