Тетрахорд: теория и применение в музыке

Series of four notes separated by three intervals

In music theory, a tetrachord (τετράχορδoν; ) 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 proportion (approx. 498 cents)—but in modern use it means any four note segment of a scale or tone row, not necessarily related to a particular tuning system.

The name comes from tetra (from Greek—"four of something") and chord (from Greek chordon—"string" or "note"). In ancient Greek music theory, tetrachord signified a segment of the greater and lesser perfect systems bounded by immovable notes ; the notes between these were movable It literally means four strings, originally in reference to harp like instruments such as the lyre or the kithara, with the implicit understanding that the four strings produced adjacent (i. e., conjunct) notes. Modern music theory uses the octave as the basic unit for determining tuning, where ancient Greeks used the tetrachord. Ancient Greek theorists recognized that the octave is a fundamental interval but saw it as built from two tetrachords and a whole tone.

Theorists of the later 20th century often use the term "tetrachord" to describe any four note set when analysing music of a variety of styles and historical periods. The expression "chromatic tetrachord" may be used in two different senses: to describe the special case consisting of a four note segment of the chromatic scale, or, in a more historically oriented context, to refer to the six chromatic notes used to fill the interval of a perfect fourth, usually found in descending bass lines. It may also be used to describes sets of fewer than four notes, when used in scale like fashion to span the interval of a perfect fourth.

Allen Forte occasionally uses the term tetrachord to mean what he elsewhere calls a tetrad or simply a "4 element set" – a set of any four pitches or pitch classes. In twelve tone theory, the term may have the special sense of any consecutive four notes of a twelve tone row.

The tetrachord, a fundamentally incomplete fragment, is the basis of two compositional forms constructed upon repetition of that fragment: the complaint and the litany. The descending tetrachord from tonic to dominant, typically in minor (e. g. A–G–F–E in A minor), had been used since the Renaissance to denote a lamentation. Well known cases include the ostinato bass of Dido's aria When I am laid in earth in Henry Purcell's Dido and Aeneas, the Crucifixus in Johann Sebastian Bach's Mass in B minor, BWV 232, or the Qui tollis in Mozart's Mass in C minor, KV 427, etc. This tetrachord, known as lamento ("complaint", "lamentation"), has been used until today. A variant form, the full chromatic descent (e. g. A–G–G–F–F–E in A minor), has been known as Passus duriusculus in the Baroque Figurenlehre. There exists a short, free musical form of the Romantic Era, called complaint or complainte (Fr.) or lament. It is typically a set of harmonic variations in homophonic texture, wherein the bass descends through some tetrachord, possibly that of the previous paragraph, but usually one suggesting a minor mode. This tetrachord, treated as a very short ground bass, is repeated again and again over the length of the composition. Another musical form, of the same time period, is the litany or litanie (Fr. ), or lytanie (OE spur). It is also a set of harmonic variations in homophonic texture, but in contrast to the lament, here the tetrachordal fragment – ascending or descending and possibly reordered – is set in the upper voice in the manner of a chorale prelude. Because of the extreme brevity of the theme and number of repetitions required, and free of the binding of chord progression to tetrachord in the lament, the breadth of the harmonic excursion in litany is usually notable.