648/625
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Ratio | 648/625 |
Factorization | 2^{3} × 3^{4} × 5^{-4} |
Monzo | [3 4 -4⟩ |
Size in cents | 62.565148¢ |
Names | diminished comma, major diesis |
Color name | g^{4}2, quadgu 2nd, Quadgu comma |
FJS name | [math]\text{d2}_{5,5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 18.6276 |
Weil height (log_{2} max(n, d)) | 18.6797 |
Wilson height (sopfr (nd)) | 38 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.76624 bits |
Comma size | medium |
[sound info] | |
open this interval in xen-calc |
The interval 648/625 is known as the diminished comma or major diesis. It is the amount by which four 6/5 minor thirds exceed an octave, in other words (6/5)^{4} / 2.
Approximations
This interval is approximately one step of 19edo, which is the amount by which four 19edo minor thirds exceed an octave.
Temperaments
Tempering out this comma leads to the 5-limit diminished temperament.