128/125

Interval information

Ratio	128/125
Factorization	27 × 5-3
Monzo	[7 0 -3⟩
Size in cents	41.05886¢
Names	diesis, augmented comma
Color name	g32, trigu 2nd, Trigu 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
Comma size	medium
S-expression	S4 / S5
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 34edo, and by two steps of 53-, 59- or 65edo. In any tuning with pure octaves and just major thirds, such as quarter-comma meantone, it will be exact. Furthermore, in quarter-comma meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called enharmonic diesis or 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.

If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce 7-limit and 11-limit harmony into the 5-limit.

See also

• Diesis (disambiguation page)