just intonation

In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For a sine wave, it is an integer multiple of the frequency of the wave. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc. In musical terms, harmonics are component pitches of a harmonic tone which sound at whole number multiples above, or "within", the named note being played on a musical instrument. Non-integer mu ...

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Xenharmonic music includes all tuning systems and music using those systems not using the common European twelve-tone equal temperament. The term was coined by Ivor Darreg from the Greek for strange or foreign, xenos, though it often includes all microtonal music. Xenharmonic tunings include nineteen or other tone equal temperament, some tunings based on the 'music of the spheres', or less systematic tunings such as Annie Gosfield's purposefully "out of tune" sampler based music. Other composers of xenharmonic music inc ...

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An overtone is a sinusoidal component of a waveform, of greater frequency than its fundamental frequency. Usually the first overtone is the second harmonic, the second overtone is the third harmonic, etc. Use of the term overtone is generally confined to acoustic waves, especially in applications related to music. Despite confused usage, an overtone is either a harmonic or a partial. A harmonic is an integer multiple of the fundamental frequency. A partial or inharmonic overtone is a non-integer multiple of a fundamental freq ...

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Barbershop harmony is a style of unaccompanied vocal music characterized by consonant four-part chords for every melody note in a predominantly homophonic texture. Each of the four parts has its own role: the lead sings the melody, with the tenor harmonizing above the melody, the bass singing the lowest harmonizing notes, and the baritone completing the chord. The melody is not sung by the tenor or bass, except for an infrequent note or two to avoid awkward voice leading, in tags or codas, or when some appropriate embellishing effect can be created. Occasional bri ...

Including:

• Barbershop music - Historical origins
• Barbershop music - Female Barbershop music and Beautyshop quartets
• Barbershop music - Organizations
• Barbershop music - Notable artists
• Barbershop music - Quartets
• Barbershop music - Choruses
• Barbershop music - Typical Barbershop Songs

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The Bohlen-Pierce scale (BP scale) is a musical scale that offers an alternative to the 12-tone equal temperament typical in Western music. It was independently discovered by Heinz Bohlen, Kees van Prooijen, and also John R. Pierce. Pierce, who, with Max V. Mathews and others, published his discovery in 1984, renamed the scale the Bohlen-Pierce scale after learning of Bohlen's earlier publication. While most scales have octave-equivalence, the BP scale instead has tritave equivalence. This means that its pitch classes ar ...

Including:

• Bohlen-Pierce scale - Bohlen-Pierce temperament
• Bohlen-Pierce scale - External link

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A major second is one of three commonly occurring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. The major second is abbreviated as M2 and its inversion is the minor seventh. It occurs naturally and most memorably between the 1st and 2nd degrees of a major scale, as the tonic rising melodically to the supe ...

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Wendy Carlos (born Walter Carlos—see Personal life section below—November 14, 1939 in Pawtucket, Rhode Island) is an American composer and electronic musician. Carlos was one of the first famous performers of electronic music using synthesizers. Wendy Carlos - Work. Switched-On Bach was perhaps the first album to attempt the use of synthesizers as an alternative to an orchestra. Having assisted Robert Moog in the development of his first commercially available synthesizers, Carlos h ...

Including:

• Wendy Carlos - Work
• Wendy Carlos - Personal life
• Wendy Carlos - Discography

Read more here: » Wendy Carlos: Encyclopedia - Wendy Carlos

Arnold Dreyblatt (b. New York City, 1953) is an American composer and visual artist. He studied with Pauline Oliveros, La Monte Young, and Alvin Lucier and has been based in Berlin, Germany since 1984. His compositions are based on harmonics, and thus just intonation, played either through a bowing technique he developed for his modified bass, a children's piano he specially tuned, or conventional instruments. He originally used only a steady pulse provided by the bowing motion on his bass (placing his music in the minimal category), but he eventually ...

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The cent is a logarithmic unit of measure used for musical intervals. Typically cents are used to measure extremely small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive notes. 1200 cents are equal to one octave — a frequency ratio of 2:1 — and an equally tempered semitone (two adjacent piano keys) is equal to 100 cents. This means that a cent is precisely equal to 21/1200, the 120 ...

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The word dominant has several possible meanings: In music theory, the dominant or dominant note (second most important) of a key is that which is a perfect fifth above the tonic; in just intonation the note whose pitch is 1.5 times the frequency of the tonic note's pitch and in twelve tone equal temperament is 7 semitones or 700 cents above the tonic. The dominant of a church mode was the tenor or reciting tone of psalm tones. The dominant is also the diatonic function of the dominant note and chord. In bi

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While his early endeavors were influenced by Stockhausen, Riley changed direction after first encountering La Monte Young, whose Theater of Eternal Music he performed in 1955 and 1956. Riley has referred to him as "the freakiest guy I have ever met in my life," stating that it was Young's ideas that were at the heart of minimalism, though more composers would come to name Riley as an influence. The 1960 String Quartet would be his first work in this new style, followed shortly thereafter by a string trio in which he first latched on to the repe ...

See also:

Terry Riley, Terry Riley - Life, Terry Riley - Musical style and techniques, Terry Riley - Notable works

Read more here: » Terry Riley: Encyclopedia II - Terry Riley - Musical style and techniques

Pythagorean tuning is based on a stack of perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1, which is the ratio of an octave. The two notes A and D, for example, are tuned so that their frequencies are in the ratio 3:2 — if D is tuned to 200 Hz, then the A is tuned to 300 Hz. The E a fifth above that A is also tuned in the ratio 3:2 — with the A at 300 Hz, this puts the E at 450 Hz, 9:4 above the original D. When describing tunings, it is usual to speak of all notes as being within an octave of each other, an ...

See also:

Pythagorean tuning, Pythagorean tuning - Method, Pythagorean tuning - Discography, Pythagorean tuning - Source

Read more here: » Pythagorean tuning: Encyclopedia II - Pythagorean tuning - Method

The 53-et tuning equates to the unison, or tempers out, the intervals 32805/32768, known as the schisma, and 15625/15552, known as the kleisma. These are both 5-limit intervals, involving only the primes 2, 3 and 5 in their factorization, and the fact that 53-et tempers out both characterizes it completely as a 5-limit temperament: it is the only regular temperament tempering out both of these intervals, or commas, a fact which seems to have first been recognized by Japanese music theorist Shohé Tanaka. Because it tempers these out, ...

See also:

53 equal temperament, 53 equal temperament - Theoretical properties, 53 equal temperament - Chords of 53 equal temperament, 53 equal temperament - Music in 53 equal temperament, 53 equal temperament - Musical examples

Read more here: » 53 equal temperament: Encyclopedia II - 53 equal temperament - Theoretical properties

Switched-On Bach was perhaps the first album to attempt the use of synthesizers as an alternative to an orchestra. Having assisted Robert Moog in the development of his first commercially available synthesizers, Carlos helped pioneer the technology, which was significantly more difficult to use than it is today. Multitrack recording techniques played a critical role in the time-consuming process of creating this album. On its release, Switched-On Bach became the best-selling classical album of all time, and the first to go plat ...

See also:

Wendy Carlos, Wendy Carlos - Work, Wendy Carlos - Personal life, Wendy Carlos - Discography

Read more here: » Wendy Carlos: Encyclopedia II - Wendy Carlos - Work

Human beings distinguish sounds on the basis of their frequency. Actually what really matters is the ratio between their frequencies. The natural scale is attributed to the Grecian philosopher Aristoxenus Tarentinus and consists in a succession of notes with increasing frequencies. After fixing the frequency of the first note - the C of the scale - the frequencies of the other notes are determined from the ratios indicated in the following table. On the last C the fol ...

See also:

Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament

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In the case of just intonation, we may express pitches in terms of positive rational numbers p/q, expressed by reference to a 1 (often written "1/1") which represents the unison pitch. If a and b are two positive rational numbers, they belong to the same pitch class if and only if a / b = 2n for some integer n. Other systems of tuning also make use of the concept of pitch class. For example, in the case of a meantone tuning in which the chain of fi ...

See also:

Pitch class, Pitch class - Pitch classes in other systems of tuning

Read more here: » Pitch class: Encyclopedia II - Pitch class - Pitch classes in other systems of tuning

As a result of scholarship by Lynn Abbott and Dr. Jim Henry it is now generally accepted that barbershop singing originated in African-American communities in the U.S. around the turn of the century, where barbershops were, and remain today, social gathering places. The four-part harmony of the form has its roots in the black church, where close harmony has a long tradition. The first uses of the term were associated with African-Americans. Henry notes that "The Mills Brothers learned to harmonize in their father's barber shop in Piqu ...

See also:

Barbershop music, Barbershop music - Historical origins, Barbershop music - Female Barbershop music and Beautyshop quartets, Barbershop music - Organizations, Barbershop music - Notable artists, Barbershop music - Quartets, Barbershop music - Choruses, Barbershop music - Typical Barbershop Songs

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In most cases, a sharp raises the pitch of a note one semitone while a flat lowers it a semitone. A natural is used to cancel the effect of a flat or sharp. Since about 1700, accidentals have been understood to continue for the remainder of the measure in which they occur, so that a subsequent note on the same staff position is still affected by that accidental, unless replaced by an accidental of its own. Notes on other staff positions, including those an octave away, are unaffected. Once a barline is passed, the effect of the accide ...

See also:

Accidental music, Accidental music - Standard use of accidentals, Accidental music - Courtesy accidentals, Accidental music - Microtonal notation, Accidental music - History of accidental notation

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The defining characteristic of the barbershop style is the ringing chord. This is a name for one specific and well-defined acoustical effect, also referred to as expanded sound, the angel's voice, the fifth voice, or the overtone. (The barbershopper's "overtone" is not the same as the acoustic physicist's overtone). The physics and psychophysics of the effect are fairly well understood; it occurs when the upper harmonics in the individual voice notes, and the sum and difference frequencies resulting ...

See also:

Barbershop music, Barbershop music - Ringing chords, Barbershop music - Historical origins, Barbershop music - Female Barbershop music and Beautyshop quartets, Barbershop music - Organization, Barbershop music - Notable artists, Barbershop music - Quartets, Barbershop music - Choruses, Barbershop music - Typical Barbershop Songs

Read more here: » Barbershop music: Encyclopedia II - Barbershop music - Ringing chords

The idea of pitch space goes back at least as far as the ancient Greek music theorists known as the Harmonists. To quote one of their number, Bacchius, "And what is a diagram? A representation of a musical system. And we use a diagram so that, for students of the subject, matters which are hard to grasp with the hearing may appear before their eyes." (Bacchius, in Franklin, Diatonic Music in Ancient Greece.) The Harmonists drew geometrical pictures so that the intervals of various scales could be compared visually ...

See also:

Pitch space, Pitch space - History of pitch space, Pitch space - Fibered pitch space, Pitch space - External link

Read more here: » Pitch space: Encyclopedia II - Pitch space - History of pitch space