Hexachord

In music, a hexachord (also hexachordon) is a six-note series, as exhibited in a scale 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).

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 resonare fibris / Mira gestorum famuli tuorum, etc. 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 the 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.