In music, a hexachord (also hexachordon) is a six-note series, as exhibited in a scale (hexatonic or hexad) or tone row. The term was adopted in this sense during the Middle Ages and adapted in the 20th century in Milton Babbitt's serial theory. The word is taken from the Greek: ἑξάχορδος, compounded from ἕξ (hex, six) and χορδή (chordē, string [of the lyre], whence "note"), and was also the term used in music theory up to the 18th century for the interval of a sixth ("hexachord major" being the major sixth and "hexachord minor" the minor sixth).
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👉 Hexachord in the context of Gregorian chant
Gregorian chant is the central tradition of Western plainchant, a form of monophonic, unaccompanied sacred song in Latin (and occasionally Greek) of the Roman Catholic Church. Gregorian chant developed mainly in western and central Europe during the 9th and 10th centuries, with later additions and redactions. Although popular legend credits Pope Gregory I with inventing Gregorian chant, scholars believe that he only ordered a compilation of melodies throughout the whole Christian world, after having instructed his emissaries in the Schola Cantorum, where the neumatical notation was perfected, with the result of most of those melodies being a later Carolingian synthesis of the Old Roman chant and Gallican chant.
Gregorian chants were organized initially into four, then eight, and finally 12 modes. Typical melodic features include a characteristic ambitus, and also characteristic intervallic patterns relative to a referential mode final, incipits and cadences, the use of reciting tones at a particular distance from the final, around which the other notes of the melody revolve, and a vocabulary of musical motifs woven together through a process called centonization to create families of related chants. The scale patterns are organized against a background pattern formed of conjunct and disjunct tetrachords, producing a larger pitch system called the gamut. The chants can be sung by using six-note patterns called hexachords. Gregorian melodies are traditionally written using neumes, an early form of musical notation from which the modern four-line and five-line staff developed. Multi-voice elaborations of Gregorian chant, known as organum, were an early stage in the development of Western polyphony.
In this Dossier
Hexachord in the context of Unified field
In music, unified field is the 'unity of musical space' created by the free use of melodic material as harmonic material and vice versa.
The technique is most associated with the twelve-tone technique, created by its 'total thematicism' where a tone-row (melody) generates all (harmonic) material. It was also used by Alexander Scriabin, though from a diametrically opposed direction, created by his use of extremely slow harmonic rhythm which eventually led to his use of unordered pitch-class sets, usually hexachords (of six pitches) as harmony from which melody may also be created.
Hexachord in the context of Die Jakobsleiter
Die Jakobsleiter (Jacob's Ladder) is an oratorio by Arnold Schoenberg that marks his transition from a contextual or free atonality to the twelve-tone technique anticipated in the oratorio's use of hexachords. Though unfinished by Schoenberg, the piece was ultimately completed and prepared for performance by Schoenberg student Winfried Zillig at the request of Gertrude Schoenberg.
Schoenberg began the libretto in 1914-15, which he published as a stand-alone text in 1917. He began the music in 1915, finishing most of his work on it in 1926, and finished a small amount of orchestration in 1944, leaving 700 measures at his death.
Hexachord in the context of Combinatoriality
In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates (all twelve tones). Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively."
Combinatoriality is a side effect of derived rows, where the initial segment or set may be combined with its transformations (T,R,I,RI) to create an entire row. "Derivation refers to a process whereby, for instance, the initial trichord of a row can be used to arrive at a new, 'derived' row by employing the standard twelve-tone operations of transposition, inversion, retrograde, and retrograde-inversion."