Comma (music) - Commas in Different Contexts - Alternative Definitions

Alternative Definitions

In quarter-comma meantone, and any kind of meantone temperament tuning system which tempers the fifth to a size smaller than 700 cents, the comma is a diminished second, which can be equivalently defined as the difference between:

• minor second and augmented unison (also known as diatonic and chromatic semitones), or
• major second and diminished third, or
• minor third and augmented second, or
• major third and diminished fourth, or
• perfect fourth and augmented third, or
• augmented fourth and diminished fifth, or
• perfect fifth and diminished sixth, or
• minor sixth and augmented fifth, or
• major sixth and diminished seventh, or
• minor seventh and augmented sixth, or
• major seventh and diminished octave.

In Pythagorean tuning, and any kind of meantone temperament tuning system which tempers the fifth to a size larger than 700 cents (such as 1/12-comma meantone), the comma is the opposite of a diminshed second, and therefore the opposite of the above mentioned differences. For instance, the Pythagorean comma can be computed as the difference between a chromatic and a diatonic semitone, which is the opposite of a Pythagorean diminished second.

In each of the above mentioned tuning systems, these differences have all the same size. For instance, in Pythagorean tuning they are all equal to the opposite of a Pythagorean comma, and in quarter-comma meantone they are all equal to a diesis.