Comma (music)
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In music theory, a comma is a small or very small interval between two enharmonic notes tuned in different ways. For example, an A flat tuned as a major third below C in just intonation, and a G sharp tuned as a major third above E, will not be exactly the same note. The difference between those notes, the diesis, is almost a quarter of a semitone, and is easily audible.
All of the intervals mentioned in the table below are presumed to be tuned in just intonation. The sizes of the different commas are measured and may be compared in terms of cents, 1/1200 fractions of an octave on a logarithmic scale; typical commas are between three and four times the smallest noticeable difference between tones of around six cents.
| Comma | Alternative Name | Enharmonic Definition Difference Between |
Alternative Definition Difference Between |
Cents | ||
|---|---|---|---|---|---|---|
| Note 1 | Note 2 | Note 1 | Note 2 | |||
| Pythagorean comma | Ditonic comma | Pythagorean major semitone | Pythagorean minor semitone | 7 octaves | 12 perfect fifths | 23.46 |
| Syntonic comma | Didymus' comma | Just major tone | Just minor tone | 4 perfect fifths | 1 major third + 2 octaves | 21.51 |
| Schisma | Pythagorean comma | Syntonic comma | 8 perfect fifths + 1 major third | 5 octaves | 1.95 | |
| Diaschisma | Syntonic comma | Schisma | 4 perfect fifths + 2 major thirds | 3 octaves | 19.55 | |
[edit] Tempering of commas
Commas are frequently used[citation needed]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 twelve-tone equal temperament tempers out the diesis, and thus does not distinguish between the two different types of semitones. On the other hand, nineteen-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.
[edit] Other intervals called commas
There are also several intervals called commas, which are not technically commas because they are not rational fractions like those above, but are irrational approximations of them. These include the Holdrian comma and Mercator's comma.
