Concept
Music and mathematics
Related concepts (16)
Dyad (music)
In music, a dyad (less commonly, diad) is a set of two notes or pitches that, in particular contexts, may imply a chord. Dyads can be classified by the interval between the notes. For example, the interval between C and E is a major third, which can imply a C major chord, made up of the notes C, E and G. When the pitches of a dyad occur in succession, they form a melodic interval. When they occur simultaneously, they form a harmonic interval. The harmonic series is built over a fundamental pitch, and the rest of the partials in the series are called overtones.
Musical temperament
In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure. "Any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals in the circle of fifths so that they accommodate pure octaves and produce certain sizes of major thirds is called a temperament.
Superparticular ratio
In mathematics, a superparticular ratio, also called a superparticular number or epimoric ratio, is the ratio of two consecutive integer numbers. More particularly, the ratio takes the form: where n is a positive integer. Thus: A superparticular number is when a great number contains a lesser number, to which it is compared, and at the same time one part of it. For example, when 3 and 2 are compared, they contain 2, plus the 3 has another 1, which is half of two.
12 equal temperament
12 equal temperament (12-ET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That resulting smallest interval, the width of an octave, is called a semitone or half step. Twelve-tone equal temperament is the most widespread system in music today. It has been the predominant tuning system of Western music, starting with classical music, since the 18th century, and Europe almost exclusively used approximations of it for millennia before that.
Beat (acoustics)
In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies. With tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively.
Musical acoustics
Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology (classification of the instruments), physiology, music theory, ethnomusicology, signal processing and instrument building, among other disciplines. As a branch of acoustics, it is concerned with researching and describing the physics of music – how sounds are employed to make music.
Arabic music
Arabic music (al-mūsīqā al-ʿarabīyyah) is the music of the Arab world with all its diverse music styles and genres. Arabic countries have many rich and varied styles of music and also many linguistic dialects, with each country and region having their own traditional music. Arabic music has a long history of interaction with many other regional musical styles and genres. It represents the music of all the peoples that make up the Arab world today.
Quarter tone
A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (orally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches. Quarter tones have their roots in the music of the Middle East and more specifically in Persian traditional music. However, the first evidenced proposal of the equally-tempered quarter tone scale, or 24 equal temperament, was made by 19th-century music theorists Heinrich Richter in 1823 and Mikhail Mishaqa about 1840.
Pitch (music)
Pitch is a perceptual property of sounds that allows their ordering on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property; it is a subjective psychoacoustical attribute of sound.
Musical tuning
In music, there are two common meanings for tuning: Tuning practice, the act of tuning an instrument or voice. Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases. Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones. Tuning is usually based on a fixed reference, such as A = 440 Hz. The term "out of tune" refers to a pitch/tone that is either too high (sharp) or too low (flat) in relation to a given reference pitch.