Tetrachord

(from Gk. tetra: ‘four’; chordē: ‘lyre string’).

(1) In ancient Greek theory (see Greece, §I), a system of four notes, contained within the limits of a perfect 4th. It serves as a basis for melodic construction in much the same way as the Hexachord functions in medieval polyphony and the major and minor scales in tonal music. Essentially tetrachords fall into three types, or genera, according to the size of the intervals between their notes: diatonic, chromatic and enharmonic. Reckoned upwards, the diatonic genus comprises the intervals semitone–tone–tone; the chromatic genus is based on the succession semitone–semitone–minor 3rd; the enharmonic genus is built on the intervals quarter-tone–quarter-tone–major 3rd. In medieval theory (for example in Musica enchiriadis) the form tone–semitone–tone was common.

The tetrachord was also used to define a particular register within the general notational systems as set forth by Aristoxenus; the Greater and Lesser Perfect Systems. The lowest of these tetrachords, the hypaton, consisted of the interval from B to e; the meson extended from e to a. The diezeugmenon was an octave higher than the hypaton (b to e'); the highest tetrachord, called the hyperbolaion, was an octave higher than the meson (e' to a').

(2) In 20th-century theory, a Set of four pitch classes. In The Structure of Atonal Music (New Haven, CT, 1973), Allen Forte identified 29 possible tetrachords (plus inversional equivalents) available from the 12 notes of the tempered scale. In this definition the name ‘Bach’ (see B–a–c–h) can be derived from a chromatic tetrachord A–B–B–C (in Forte’s system, set 4–1), but in the order B–A–C–B. Webern in his string quartet op.28 employed a 12-note row consisting of this tetrachord and two transpositions (D–E–C–D and G–F–A–G), the first of them inverted.