Hexachord
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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: οικόσαχορδος, compounded from ὀικός (ōkos, six) and χορδή (χορδή, 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).
Hexachord ostinato, in cello, which opens Die Jakobsleiter by Arnold Schoenberg, notable for its compositional use of hexachords Play:ⓘ*
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: οικόσαχορδος, compounded from ὀικός (ōkos, six) and χορδή (χορδή, 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).
Middle Ages
The hexachord as a mnemonic device was first described by Guido of Arezzo, in his Epistola de ignoto cantu. In each hexachord, all adjacent pitches are a whole tone apart, except for the middle two, which are separated by a semitone. These six pitches are named ut, re, mi, fa, sol, and la, with the semitone between mi and fa. These six names are derived from the first syllable of each half-verse of the first stanza of the 8th-century Vesper hymn [Ut queant laxis re sonare fibris / Mi ra gestorum fa muli tuorum], Melodies with a range wider than a major sixth required the device of mutation to a new hexachord. For example, the hexachord beginning on C and rising to A, named hexachordum naturale, has its only semitone between the notes E and F, and stops short of the note B or B♭. A melody moving a semitone higher than la (namely, from A to the B♭ above) required changing the la to mi so that the required B♭ becomes fa. Because B♭ was named by the "soft" or rounded letter B, the hexachord with this note in it was called the hexachordum molle (soft hexachord). Similarly, the hexachord with mi and fa expressed by notes B♮ and C was called the hexachordum durum (hard hexachord), because the B♮ was represented by a squared-off or "hard" B. Starting in the 14th century, these three hexachords were extended in order to accommodate the increasing use of signed accidentals on other notes.
The introduction of these new notes was principally a product of polyphony, which required placing a perfect fifth not only above the old note B♮ but also below its newly created variant. This entailed introducing still newer variants such as F♯ and E♭ with corresponding consequences for these last notes C♯ and A♭. The new notes were introduced into music due to their inability to be written down formally since they did not exist within existing gamuts.
20th Century
Allen Forte in The Structure of Atonal Music redefines 'six-note series' to mean what other theorists like Howard Hanson defined as 'six-note pitch collections'. David Lewin used this definition interchangeably with 'six-note intervals', while Carlton Gamer does so less frequently.