128/125

Interval information

Ratio	128/125
Factorization	27 × 5-3
Monzo	[7 0 -3⟩
Size in cents	41.05886¢
Names	diesis, augmented comma
FJS name	[math]\displaystyle{ \text{d2}_{5,5,5} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	13.9658
Weil height (log2 max(n, d))	14
Wilson height (sopfr(nd))	29
Open this interval in xen-calc

The 41.059 cent interval of 128/125 is called the diesis or augmented comma; it represents the gap between three 5/4 just major thirds and the octave, or in other words 2/(5/4)^3. It is fairly accurately represented by a single step in 28, 31 or 34 EDO, and by two steps of 53, 59 or 65 EDO. In any tuning with just major thirds, such as quarter-comma meantone, it will be exact. Furthermore, in quarter-comma meantone it appears as difference between sharps and flats, e.g. between D# and Eb. It is also called enharmonic comma for this reason. Tempering it out leads to augmented temperament.

This interval can also be called a kilobyte comma, since it represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.