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::Comma (music)

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Comma::tuning    Align::center    Between::music    Commas::meantone    Syntonic::major    Diesis::right

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Syntonic comma on C About this sound Play 
Pythagorean comma on C About this sound Play 

In music theory, a comma is a minute interval, the difference resulting from tuning one note two different ways.<ref>Waldo Selden Pratt (1922). Grove's Dictionary of Music and Musicians, Volume 1, p.568. John Alexander Fuller-Maitland, Sir George Grove, eds. Macmillan.</ref> The word comma used without qualification refers to the syntonic comma,<ref>Benson, Dave (2006). Music: A Mathematical Offering, p. 171. ISBN 0-521-85387-7.</ref> which can be defined, for instance, as the difference between an F tuned using the D-based Pythagorean tuning system, and another F tuned using the D-based quarter-comma meantone tuning system.

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. For example, in extended scales produced with five-limit tuning an A tuned as a major third below C5 and a G tuned as two major thirds above C4 will not be exactly the same note, as they would be in equal temperament. The interval between those notes, the diesis, is an easily audible comma (its size is more than 40% of a semitone).

Commas are often defined as the difference in size between two semitones. 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. The same is true for Pythagorean tuning.

Lesser diesis defined in quarter-comma meantone as difference between semitones (m2 − A1), or interval between enharmonically equivalent notes (from C to D). The interval from C to D is narrower than in Pythagorean tuning (see below). About this sound Play 
Pythagorean comma (PC) defined in Pythagorean tuning as difference between semitones (A1 − m2), or interval between enharmonically equivalent notes (from D to C). The interval from C to D is wider than in quarter-comma meantone (see above).

In just intonation, more than two kinds of semitones may be produced. Thus, a single tuning system may be characterized by several different commas. 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.


Comma (music) sections
Intro   Commas in different contexts    Notation   Tempering of commas  Other intervals called commas  See also  References  

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