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Comma (music)
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Comma (music)
In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Traditionally, there are two most common commata; the syntonic comma (80:81), "the difference between a just major 3rd and four just perfect 5ths less two octaves", and the Pythagorean comma (524288:531441, approximately 73:74), "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. Pitches separated by either comma are considered the same note because conventional notation does not distinguish Pythagorean intervals from 5-limit intervals. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53 TET, the harmonic seventh 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"[citation needed]. 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. 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.[citation needed] Almost all of the meantone tuning systems produce two different characteristic semitones: A diatonic semitone for short steps in the scale, and chromatic semitone between a natural note, N♮, and its sharp, N♯. Their ratio (or in cents, their difference) is a comma; its size is unique to each meantone tuning. 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 column below labeled "Difference between semitones", min2 is the minor second (diatonic semitone), aug1 is the augmented unison (chromatic semitone), and S1, S2, S3, S4 are semitones as defined here. In the columns labeled "Interval 1" and "Interval 2", all intervals are presumed to be tuned in just intonation. Notice that the Pythagorean comma (κ𝜋) and the syntonic comma (κS) are basic intervals that can be used as yardsticks to define some of the other commas. For instance, the difference between them is a small comma called schisma. A schisma is not audible in many contexts, as its size is narrower than the smallest audible difference between tones (which is around six cents, also known as just-noticeable difference, or JND).
Many other commas have been enumerated and named by microtonalists.
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Comma (music)
In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Traditionally, there are two most common commata; the syntonic comma (80:81), "the difference between a just major 3rd and four just perfect 5ths less two octaves", and the Pythagorean comma (524288:531441, approximately 73:74), "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. Pitches separated by either comma are considered the same note because conventional notation does not distinguish Pythagorean intervals from 5-limit intervals. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53 TET, the harmonic seventh 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"[citation needed]. 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. 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.[citation needed] Almost all of the meantone tuning systems produce two different characteristic semitones: A diatonic semitone for short steps in the scale, and chromatic semitone between a natural note, N♮, and its sharp, N♯. Their ratio (or in cents, their difference) is a comma; its size is unique to each meantone tuning. 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 column below labeled "Difference between semitones", min2 is the minor second (diatonic semitone), aug1 is the augmented unison (chromatic semitone), and S1, S2, S3, S4 are semitones as defined here. In the columns labeled "Interval 1" and "Interval 2", all intervals are presumed to be tuned in just intonation. Notice that the Pythagorean comma (κ𝜋) and the syntonic comma (κS) are basic intervals that can be used as yardsticks to define some of the other commas. For instance, the difference between them is a small comma called schisma. A schisma is not audible in many contexts, as its size is narrower than the smallest audible difference between tones (which is around six cents, also known as just-noticeable difference, or JND).
Many other commas have been enumerated and named by microtonalists.
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