Comma (music)

The word "comma" came via Latin from Greek κόμμα, from earlier *κοπ-μα: "the result or effect of cutting".

Within the same tuning system, two enharmonically equivalent notes (such as G♯ and A♭) may have a slightly different frequency, and the interval between them is a comma.

[citation needed] Each meantone temperament tuning system produces a 12-tone scale characterized by two different kinds of semitones (diatonic and chromatic), and hence by a comma of unique size.

For instance, a commonly used version of five-limit tuning produces a 12-tone scale with four kinds of semitones and four commas.

The size of commas is commonly expressed and compared in terms of cents – 1⁄1200 fractions of an octave on a logarithmic scale.

Musicians in late Middle Ages recognized that by slightly tempering the pitch of some notes, the Pythagorean thirds could be made consonant.

For instance, if you decrease the frequency of E by a syntonic comma (81:80), C–E (a major third) and E–G (a minor third) become just: C–E is flattened to a just ratio of and at the same time E–G is sharpened to the just ratio of This led to the creation of a new tuning system, known as quarter-comma meantone, which permitted the full development of music with complex texture, such as polyphonic music, or melodies with instrumental accompaniment.

In the years 2000–2004, Marc Sabat and Wolfgang von Schweinitz worked together in Berlin to develop a method to exactly indicate pitches in staff notation.

Such an approach has also been advocated by Daniel James Wolf and by Joe Monzo, who refers to it by the acronym HEWM (Helmholtz-Ellis-Wolf-Monzo).

[9] In the Sabat-Schweinitz design, syntonic commas are marked by arrows attached to the flat, natural or sharp sign, septimal commas using Giuseppe Tartini's symbol, and undecimal quartertones using the common practice quartertone signs (a single cross and backwards flat).

The convention used is that the cents written refer to the tempered pitch implied by the flat, natural, or sharp sign and the note name.

A complete legend and fonts for the notation (see samples) are open source and available from Plainsound Music Edition.

The widely used 12 tone equal temperament tempers out the diesis, and thus does not distinguish between the two different types of semitones.