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39 relations: All-trichord hexachord, Allen Forte, Common tone (scale), Complement (music), Consonance and dissonance, David Lewin, Elliott Carter, Equal temperament, Forte number, Hexachord, Howard Hanson, Interval (music), Interval class, Interval cycle, Interval vector, Inversion (music), Isomer, List of pitch-class sets, Major chord, Milton Babbitt, Monomial, Multiplication (music), Natural number, Octave, Permutation (music), Pitch (music), Pitch class, Pitch interval, Register (music), Sacher hexachord, Schoenberg hexachord, Set (music), Set theory (music), String Quartet No. 2 (Carter), Transformational theory, Transposition (music), Triangular number, Yoke, Zygote.
All-trichord hexachord
In music, the all-trichord hexachord is a unique hexachord that contains all twelve trichords, or from which all twelve possible trichords may be derived.
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Allen Forte
Allen Forte (December 23, 1926 – October 16, 2014) was an American music theorist and musicologist.
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Common tone (scale)
In music, a common tone is a pitch class that is a member of, or common to (shared by) two or more scales or sets.
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Complement (music)
In music theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism.
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Consonance and dissonance
In music, consonance and dissonance are categorizations of simultaneous or successive sounds.
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David Lewin
David Benjamin Lewin (July 2, 1933 – May 5, 2003) was an American music theorist, music critic and composer.
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Elliott Carter
Elliott Cook Carter Jr. (December 11, 1908 – November 5, 2012) was an American composer who was twice awarded the Pulitzer Prize.
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Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio.
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Forte number
In musical set theory, a Forte number is the pair of numbers Allen Forte assigned to the prime form of each pitch class set of three or more members in The Structure of Atonal Music (1973). The first number indicates the number of pitch classes in the pitch class set and the second number indicates the set's sequence in Forte's ordering of all pitch class sets containing that number of pitches.
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Hexachord
In music, a hexachord (also hexachordon) is a six-note series, as exhibited in a scale or tone row.
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Howard Hanson
Howard Harold Hanson (October 28, 1896 – February 26, 1981) was an American composer, conductor, educator, music theorist, and champion of American classical music.
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Interval (music)
In music theory, an interval is the difference between two pitches.
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Interval class
In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'", is the shortest distance in pitch class space between two unordered pitch classes.
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Interval cycle
In music, an interval cycle is a collection of pitch classes created from a sequence of the same interval class.
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Interval vector
In musical set theory, an interval vector is an array of natural numbers which summarize the intervals present in a set of pitch classes.
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Inversion (music)
There are inverted chords, inverted melodies, inverted intervals, and (in counterpoint) inverted voices.
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Isomer
An isomer (from Greek ἰσομερής, isomerès; isos.
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List of pitch-class sets
This is a list of pitch-class sets by Forte number.
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Major chord
In music theory, a major chord is a chord that has a root note, a major third above this root, and a perfect fifth above this root note.
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Milton Babbitt
Milton Byron Babbitt (May 10, 1916 – January 29, 2011) was an American composer, music theorist, and teacher.
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Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.
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Multiplication (music)
The mathematical operations of multiplication have several applications to music.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Octave
In music, an octave (octavus: eighth) or perfect octave is the interval between one musical pitch and another with half or double its frequency.
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Permutation (music)
In music, a permutation (order) of a set is any ordering of the elements of that set.
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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.
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Pitch class
In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves.
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Pitch interval
In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward.
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Register (music)
In music, a register is the relative "height" or range of a note, set of pitches or pitch classes, melody, part, instrument, or group of instruments.
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Sacher hexachord
The Sacher hexachord (6-Z11, musical cryptogram on the name of Swiss conductor Paul Sacher) is a hexachord notable for its use in a set of twelve compositions (12 Hommages à Paul Sacher) created at the invitation of Mstislav Rostropovich for Sacher's seventieth birthday in 1976.
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Schoenberg hexachord
6-Z44 (012569), known as the Schoenberg hexachord, is Arnold Schoenberg's signature hexachord, as one transposition contains the pitches, Es, C, H, B, E, G (A. Schoenberg), E, B, and B being Es, H, and B in German.
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Set (music)
A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects.
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Set theory (music)
Musical set theory provides concepts for categorizing musical objects and describing their relationships.
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String Quartet No. 2 (Carter)
The Second String Quartet by American composer Elliott Carter was completed in 1959.
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Transformational theory
Transformational theory is a branch of music theory David Lewin developed in the 1980s, and formally introduced in his 1987 work, Generalized Musical Intervals and Transformations.
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Transposition (music)
In music transposition refers to the process, or operation, of moving a collection of notes (pitches or pitch classes) up or down in pitch by a constant interval.
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Triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right.
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Yoke
A yoke is a wooden beam normally used between a pair of oxen or other animals to enable them to pull together on a load when working in pairs, as oxen usually do; some yokes are fitted to individual animals.
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Zygote
A zygote (from Greek ζυγωτός zygōtos "joined" or "yoked", from ζυγοῦν zygoun "to join" or "to yoke") is a eukaryotic cell formed by a fertilization event between two gametes.
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APIC vector, Absolute PIC vector, Complement theorem, Hexachord theorem, Interval class vector, Isomeric relation, Isomeric relationship, PIC vector, Z relation, Z-hexachord, Z-relation, Z-relationship.
References
[1] https://en.wikipedia.org/wiki/Interval_vector
