Medieval Mixolydian and Hypomixolydian
Originally used to designate one of the traditional harmoniai of Greek theory, the name was appropriated (along with six others) by the 2nd-century theorist Ptolemy to designate his seven tonoi, or transposition keys. Four centuries later, Boethius interpreted Ptolemy in Latin, still with the meaning of transposition keys, not scales. When chant theory was first being formulated in the 9th century, these seven names plus an eighth, Hypermixolydian (later changed to Hypomixolydian), were again re-appropriated in the anonymous treatise Alia Musica. A commentary on that treatise, called the Nova expositio, first gave it a new sense as one of a set of eight diatonic species of the octave, or scales. The name Mixolydian came to be applied to one of the eight modes of medieval church music: the seventh mode. This mode does not run from B to B on white notes, as the Greek mode, but was defined in two ways: as the diatonic octave species from G up one octave to the G above, or as a mode whose final was G and whose ambitus runs from the F below the final to the G above, with possible extensions "by licence" up to A above and even down to E below, and in which the note D (the tenor of the corresponding seventh psalm tone) had an important melodic function. This medieval theoretical construction led to the modern use of the term for the natural scale from G to G.
The seventh mode of western church music is an authentic mode based on and encompassing the natural scale from G to G, with the perfect fifth (the D in a G to G scale) as the dominant, reciting note or tenor.
The plagal eighth mode was termed Hypomixolydian (or "lower Mixolydian") and, like the Mixolydian, was defined in two ways: as the diatonic octave species from D to the D an octave higher, divided at the mode final, G (thus D–E–F–G + G–A–B–C–D); or as a mode with a final of G and an ambitus from C below the final to E above it, in which the note C (the tenor of the corresponding eighth psalm tone) had an important melodic function.
Read more about this topic: Mixolydian Mode
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