128/125
| Interval information |
augmented comma,
enharmonic diesis,
enharmonic comma,
cyberisma
Trigu comma
reduced subharmonic
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.
Approximation
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.
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 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
Tempering out this comma leads to augmented temperament. See augmented family for the family where it is tempered out.
Walker temperament
Walker temperament flattens the octave in order to temper out the difference between 2^10 and 10^3, which is an occurrence of the diesis. 40ed10 is an example of Walker temperament. It was created by Vector Graphics (Jay Walker) before he even knew what temperament was, as an attempt to align powers of 2 and powers of 10. In the context of Walker temperament, the augmented comma can be called the cyberisma, after its appearance in computing.
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)
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