Музыкадағы үзіліс интервалы

Very small interval arising from discrepancies in tuning
the interval

In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Strictly speaking, there are only two kinds of comma, the syntonic comma, "the difference between a just major 3rd and four just perfect 5ths less two octaves", and the Pythagorean comma, "the difference between twelve 5ths and seven octaves". The word comma used without qualification refers to the syntonic comma, 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. Intervals separated by the ratio 81:80 are considered the same note because the 12 note Western chromatic scale does not distinguish Pythagorean intervals from 5 limit intervals in its notation. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53TET, B and A are both approximated by the same interval although they are a septimal kleisma apart.

Translated in this context, "comma" means "a hair" as in "off by just a hair". The word "comma" came via Latin from Greek κόμμα, from earlier *κοπ μα: "the result or effect of cutting". A more complete etymology is given in the article κόμμα (Ancient Greek) in the Wiktionary.

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 are not 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. 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.

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. This method was called the extended Helmholtz Ellis JI pitch notation. Sabat and Schweinitz take the "conventional" flats, naturals and sharps as a Pythagorean series of perfect fifths. Thus, a series of perfect fifths beginning with F proceeds and so on. The advantage for musicians is that conventional reading of the basic fourths and fifths remains familiar. 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). 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). For higher primes, additional signs have been designed. To facilitate quick estimation of pitches, cents indications may be added (downward deviations below and upward deviations above the respective accidental). 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. One of the great advantages of any such a notation is that it allows the natural harmonic series to be precisely notated. A complete legend and fonts for the notation (see samples) are open source and available from Plainsound Music Edition. Thus a Pythagorean scale is C D E F G A B C, while a just scale is C D E F G A B C.

Composer Ben Johnston uses a "−" as an accidental to indicate a note is lowered a syntonic comma, or a "+" to indicate a note is raised a syntonic comma; however, Johnston's "basic scale" (the plain nominals A B C D E F G) is tuned to just intonation and thus already includes the syntonic comma. Thus a Pythagorean scale is C D E+ F G A+ B+ C, while a just scale is C D E F G A B.

A comma sequence defines a musical temperament through a unique sequence of commas at increasing prime limits. The first comma of the comma sequence is in the q limit, where q is the n‑th odd prime (prime 2 being ignored because it represents the octave) and n is the number of generators. Subsequent commas are in prime limits, each the next prime in sequence above the last.

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 and Mercator's commas,
and the pitch to pitch step size in .