Comma (music) - Tempering of Commas

Tempering of Commas

Commas are frequently used in the description of musical temperaments, where they describe distinctions between musical intervals that are eliminated by that tuning system. A comma can be viewed as the distance between two musical intervals. When a given comma is tempered out in a tuning system, the ability to distinguish between those two intervals in that tuning is eliminated. For example, the difference between the diatonic semitone and chromatic semitone is called the diesis. The widely used 12-tone equal temperament tempers out the diesis, and thus does not distinguish between the two different types of semitones. On the other hand, 19-tone equal temperament does not temper out this comma, and thus it distinguishes between the two semitones.

Examples:

• 12-TET tempers out the diesis, as well as a variety of other commas.
• 19-TET tempers out the septimal diesis and syntonic comma, but does not temper out the diesis.
• 22-TET tempers out the septimal comma of Archytas, but does not temper out the septimal diesis or syntonic comma.
• 31-TET tempers out the syntonic comma, as well as the comma defined by the ratio (99:98), but does not temper out the diesis, septimal diesis, or septimal comma of Archytas.