Comma (music)

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Comma (music)

In music theory

Music theory

Music theory is the field of study that deals with how music works. It examines the language and notation of music. It identifies patterns that govern composer techniques....
, a comma is a small or very small interval

Interval (music)

In music theory, the term interval describes the relationship between the pitch of two notes.Intervals may be described as:*vertical if the two notes sound simultaneously...
between two enharmonic

Enharmonic

In modern music and musical notation, an enharmonic equivalent is a note , interval , or key signature which is equivalence to some other note, interval, or key signature, but "spelled", or named, differently....
notes tuned in different ways. For example, an A flat tuned as a major third below C in just intonation

Just intonation

In music, just intonation is any musical tuning in which the frequency of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series ....
, 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

Diesis

A diesis is a Comma type of musical interval, usually meaning the difference between three just intonation major thirds and an octave , equal to 128:125 or about 41.06 Cent s....
, 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

Just intonation

In music, just intonation is any musical tuning in which the frequency of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series ....
.

Tempering of commas
Commas are frequently used in the description of musical temperament

Musical temperament

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In music theory

Music theory

Interval (music)

Enharmonic

Just intonation

Diesis

Just intonation

Comma	Alternative Name	Enharmonic Definition Difference Between		Alternative Definition Difference Between		Cents
Comma	Alternative Name	Note 1	Note 2	Note 1	Note 2	Cents
Pythagorean comma Pythagorean comma The Pythagorean comma , named after the ancient mathematician and philosopher Pythagoras, is the Microtonal music Pythagorean interval defined as the difference between a Pythagorean apotome and a Limma, e.g....	Ditonic comma	Pythagorean major semitone	Pythagorean minor semitone	7 octave Octave In music, an octave The octave is occasionally referred to as a diapason.The octave above an indicated note is sometimes abbreviated 8va, and the octave below 8vb.... s	12 perfect fifth Perfect fifth The perfect fifth is the musical interval between a note and the note seven semitones above it on the musical scale. For example, the note G lies a perfect fifth above C; D is a perfect fifth above G, C is a perfect fifth above F, and so on.... s	23.46
Syntonic comma Syntonic comma In music theory, the syntonic comma , also known as the comma of Didymus the Musician or Ptolemy comma, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 Cent s....	Didymus' comma	Just major tone	Just minor tone	4 perfect fifths	1 major third + 2 octaves	21.51
Schisma Schisma In music, the schisma, also spelled skhisma, is the ratio between a Pythagorean comma and a syntonic comma and equals 32805/32768, which is 1.9537 cent s....		Pythagorean comma	Syntonic comma	8 perfect fifths + 1 major third	5 octaves	1.95
Diaschisma Diaschisma The diaschisma is a small musical interval defined as the difference between four perfect fifths plus two major thirds and three octaves. It can be represented by the ratio 2048:2025 and is about 19.5 cent ....		Syntonic comma	Schisma	4 perfect fifths + 2 major thirds	3 octaves	19.55

Tempering of commas

Commas are frequently used in the description of musical temperament

Musical temperament

In musical tuning, a temperament is a system of tuning which slightly compromises the pure intervals of just intonation in order to meet other requirements of the system....
s , 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

Diesis

A diesis is a Comma type of musical interval, usually meaning the difference between three just intonation major thirds and an octave , equal to 128:125 or about 41.06 Cent s....
, 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
Diesis

A diesis is a Comma type of musical interval, usually meaning the difference between three just intonation major thirds and an octave , equal to 128:125 or about 41.06 Cent s....
, as well as a variety of other commas.
19-TET tempers out the septimal diesis
Septimal diesis

In music, septimal diesis is an Interval with the ratio of 49:48 , which is the difference between the septimal whole tone and the septimal minor third....
and syntonic comma
Syntonic comma

In music theory, the syntonic comma , also known as the comma of Didymus the Musician or Ptolemy comma, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 Cent s....
, but does not temper out the diesis
Diesis

A diesis is a Comma type of musical interval, usually meaning the difference between three just intonation major thirds and an octave , equal to 128:125 or about 41.06 Cent s....
.
22-TET tempers out the septimal comma
Septimal comma

A septimal comma is a small interval in just intonation that contains the number 7 in its prime factorization. There is more than one such interval, so the term septimal comma is ambiguous, but it most commonly refers to the interval 64/63....
of Archytas
Archytas

Archytas was an Ancient Greece philosopher, mathematician, astronomer, statesman, and military strategy. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato....
, but does not temper out the septimal diesis
Septimal diesis

In music, septimal diesis is an Interval with the ratio of 49:48 , which is the difference between the septimal whole tone and the septimal minor third....
or syntonic comma
Syntonic comma

In music theory, the syntonic comma , also known as the comma of Didymus the Musician or Ptolemy comma, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 Cent s....
.
31-TET tempers out the syntonic comma
Syntonic comma

In music theory, the syntonic comma , also known as the comma of Didymus the Musician or Ptolemy comma, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 Cent s....
, 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.

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

Holdrian comma

The Holdrian comma, also called Holder's comma, and sometimes the Arabian comma, is a small musical interval of 22.6415 cent , equal to one step of 53 equal temperament, or ....
and Mercator's comma.

Comma (music)

Tempering of commas

Other intervals called commas

See also