What is a Comma?
In terms of music, a Comma is a word used when
referring to the discrepancies of distance between intervals
inside of any given system.
* There is no single unit that represents a comma but there are
2 main numeric values in widespread historical use:
The Pythagorean Comma
(also known as the Ditonic comma)
is the discrepancy between twelve pure 5th's
& seven pure octaves.
It's the comma used in constructing the Equal Temperament system
& is defined by the ratio 531441:524288
and the decimal 1.0136433.
The Syntonic Comma
(also known as the Diatonic comma)
is the discrepancy between four pure 5th's
& two octaves plus a Major 3rd.
It's equivalent to the ratio 81:80
and the decimal 1.0125.
What is a Diesis?
A Diesis is the difference between
a major semitone & a minor semitone.
The distance of a diesis varies depending on
the amount of tempering used in constructing the 5ths.
The greater the tempering of the 5th's, the greater the difference between
major & minor semitones (the diesis).
* Quarter-Comma Meantone tuning has a larger diesis than the 6th-Comma Meantone tuning system.. A quarter (1/4) is larger than a sixth (1/6).