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An all-interval tetrachord is a
In the examples below, the tetrachords ,1,4,6and ,1,3,7are built on E.
An all-interval tetrachord is a tetrachord
In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency pr ...
, a collection of four 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; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave positio ...
es, containing all six 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 ...
es. There are only two possible all-interval tetrachords (to within inversion), when expressed in prime form. In set theory notation, these are ,1,4,6(4-Z15) and ,1,3,7(4-Z29). Their inversions are ,2,5,6(4-Z15b) and ,4,6,7(4-Z29b). The 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. (That is, a set of pitches where octaves are disregarded.) Other names include: ic vector (or inter ...
for all all-interval tetrachords is ,1,1,1,1,1
Table of interval classes as relating to all-interval tetrachords
In the examples below, the tetrachords ,1,4,6and ,1,3,7are built on E.
Use in modern music
The unique qualities of the all-interval tetrachord have made it very popular in 20th-century music. Composers includingElliott Carter
Elliott Cook Carter Jr. (December 11, 1908 – November 5, 2012) was an American modernist composer. One of the most respected composers of the second half of the 20th century, he combined elements of European modernism and American "ultra- ...
( First String Quartet) and George Perle
George Perle (6 May 1915 – 23 January 2009) was an American composer and music theorist. As a composer, his music was largely atonal, using methods similar to the twelve-tone technique of the Second Viennese School. This serialist style, and ...
used it extensively.
See also
* All-interval twelve-tone row * All-trichord hexachord *Perfect ruler A perfect ruler of length \ell is a ruler with integer markings a_1=0 < a_2 < \dots < a_n=\ell, for which there exists an integer such that any Serialism
*
The All-Interval Tetrachord, A Musical Application of Almost Difference Sets
all-interval tetrachord tutorial
the use of all-interval tetrachords in
Interval String Table
a comprehensive analysis of all-interval tetrachords Chords Post-tonal music theory Hemitonic scales Musical set theory {{music-theory-stub
Trichord
In music theory, a trichord () is a group of three different pitch classes found within a larger group. A trichord is a contiguous three-note set from a musical scale or a twelve-tone row.
In musical set theory there are twelve trichords give ...
References
External links
The All-Interval Tetrachord, A Musical Application of Almost Difference Sets
all-interval tetrachord tutorial
the use of all-interval tetrachords in
Elliott Carter
Elliott Cook Carter Jr. (December 11, 1908 – November 5, 2012) was an American modernist composer. One of the most respected composers of the second half of the 20th century, he combined elements of European modernism and American "ultra- ...
Interval String Table
a comprehensive analysis of all-interval tetrachords Chords Post-tonal music theory Hemitonic scales Musical set theory {{music-theory-stub