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All-interval tetrachord

 

 
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All-interval tetrachord
 
 
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An all-interval tetrachord is a tetrachord
Tetrachord

Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row....
 from which any interval class
Interval class

In musical set theory, an interval class is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 = 7 ....
 can be extracted by means of various inversions
Inversion (music)

In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices....
. There are only two possible all-interval tetrachords. In set theory notation, these are [0,1,4,6] and [0,1,3,7]. The interval vector
Interval vector

In musical set theory, an interval vector is an array that expresses the intervallic content of a pitch-class set .In equal temperament it has six digits, with each digit standing for the number of times an interval class appears in the set....
 for both all-interval tetrachords is [1,1,1,1,1,1].

he examples below, the tetrachords [0,1,4,6] and [0,1,3,7] are built on C.


unique qualities of the all-interval tetrachord have made it very popular in 20th-century music.






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An all-interval tetrachord is a tetrachord
Tetrachord

Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row....
 from which any interval class
Interval class

In musical set theory, an interval class is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 = 7 ....
 can be extracted by means of various inversions
Inversion (music)

In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices....
. There are only two possible all-interval tetrachords. In set theory notation, these are [0,1,4,6] and [0,1,3,7]. The interval vector
Interval vector

In musical set theory, an interval vector is an array that expresses the intervallic content of a pitch-class set .In equal temperament it has six digits, with each digit standing for the number of times an interval class appears in the set....
 for both all-interval tetrachords is [1,1,1,1,1,1].

Table of interval classes as relating to all-interval tetrachords

In the examples below, the tetrachords [0,1,4,6] and [0,1,3,7] are built on C.


Use in modern music

The unique qualities of the all-interval tetrachord have made it very popular in 20th-century music. Composers such as Elliott Carter
Elliott Carter

Elliott Cook Carter, Jr. is a two-time Pulitzer Prize for Music-winning American composer born and living in New York City. He studied with Nadia Boulanger in Paris in the 1930s, and then returned to the United States....
 and George Perle
George Perle

George Perle was a composer and music theory. He was born in Bayonne, New Jersey. A student of Ernst Krenek, Perle composed with a technique of his own devising called "twelve-tone tonality," which is different from, but related to, twelve-tone technique ....
 used it extensively, as did Webern and Schoenberg
Schoenberg

Schoenberg is the surname of several persons.* Arnold Schoenberg , Austrian-American composer of 20th Century music* Isaac Jacob Schoenberg , Romanian mathematician...
. (Although the term all-interval tetrachord and indeed set theory itself was not in use during most of their life times.)

See also

  • Monad
    Monad (music)

    In music, a monad is a single note or pitch . The Western chromatic scale, for example, is composed of twelve monads. Monads are contrasted to dyad , groups of two notes, triad , groups of three, and so on....
  • Dyad
    Dyad (music)

    In music, a dyad is a set of two note or pitch . Although most chords have three or more notes, in certain contexts a dyad may be considered to be a chord....
  • Trichord
    Trichord

    Depending on the context, a trichord is either a contiguous segment of a musical scale or of a twelve-tone row, or a musical triad, that is, any three-note pitch collection....
  • Tetrachord
    Tetrachord

    Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row....
  • Hexachord
    Hexachord

    In music, a hexachord is a six-note segment of a scale or tone row. The term was adopted in the Middle Ages and adapted in the twentieth-century in Milton Babbitt serialism....
  • musical set theory
  • Interval class
    Interval class

    In musical set theory, an interval class is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 = 7 ....
  • Serialism
    Serialism

    In music, serialism is a technique for Musical composition#A musical composition that uses Set to describe Aspect of music, and allows the Permutation of those sets....


External links

  • all-interval tetrachord tutorial
  • the use of all-interval tetrachords in Elliott Carter
    Elliott Carter

    Elliott Cook Carter, Jr. is a two-time Pulitzer Prize for Music-winning American composer born and living in New York City. He studied with Nadia Boulanger in Paris in the 1930s, and then returned to the United States....
  • a comprehensive analysis of all-interval tetrachords