128/125
| Ratio | 128/125 |
| Factorization | 27 × 5-3 |
| Monzo | [7 0 -3⟩ |
| Size in cents | 41.058858¢ |
| Names | diesis, augmented comma, enharmonic diesis, enharmonic comma |
| Color name | g32, trigu 2nd, Trigu comma |
| FJS name | [math]\text{d2}_{5,5,5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 13.9658 |
| Weil height (log2 max(n, d)) | 14 |
| Wilson height (sopfr (nd)) | 29 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.73912 bits |
| 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 a stack of three 5/4 just major thirds and the octave, or in other words 2/(5/4)3.
Approximations
This interval 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 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.
Temperaments
As a comma
Tempering out this comma leads to augmented temperament. See augmented family for the family where it is tempered out.
As an interval
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 5-limit scales.
Trivia
This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.
See also
- Diesis (disambiguation page)