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Syntonic comma on C Pythagorean comma on C . In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. [1] Traditionally, there are two most common 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 ...
The comma that musical temperaments often "temper" is the Pythagorean comma. [ 3 ] The Pythagorean comma can be also defined as the difference between a Pythagorean apotome and a Pythagorean limma [ 4 ] (i.e., between a chromatic and a diatonic semitone , as determined in Pythagorean tuning); the difference between 12 just perfect fifths and ...
Study of the comma pump dates back at least to the sixteenth century when the Italian scientist Giovanni Battista Benedetti composed a piece of music to illustrate syntonic comma drift. [5] Note that a descending perfect fourth (3/4) is the same as a descending octave (1/2) followed by an ascending perfect fifth (3/2). Namely, (3/4) = (1/2) × ...
The Pythagorean comma does not coincide with the diminished second, as its size (524288:531441) is the reciprocal of the Pythagorean diminished second (531441:524288). Also ditone and semiditone are specific for Pythagorean tuning, while tone and tritone are used generically for all tuning systems.
The Pythagorean A ♭ (at the left) is at 792 cents, G ♯ (at the right) at 816 cents; the difference is the Pythagorean comma. Equal temperament by definition is such that A ♭ and G ♯ are at the same level. 1 ⁄ 4-comma meantone produces the "just" major third (5:4, 386 cents, a syntonic comma lower than the Pythagorean one of 408 cents).
Musical symbols are marks and symbols in musical notation that indicate various aspects of how a piece of music is to be performed. There are symbols to communicate information about many musical elements, including pitch, duration, dynamics, or articulation of musical notes; tempo, metre, form (e.g., whether sections are repeated), and details about specific playing techniques (e.g., which ...
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Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory.