Hypophrygian mode

According to Aristoxenus, this octave species was originally described around the year 400 BC by the Harmonicist school of Eratocles in terms of the enharmonic genus of the tetrachord: a series of rising intervals of two quarter tones followed by a ditone, together spanning a perfect fourth.

Ptolemy's system differed from the earlier Aristoxenian model, which had thirteen transpositional levels each a semitone from its neighbours.

The entire double-octave scale system was then transposed onto each of these relative pitch levels, requiring (in modern terms) a different key signature in each case, and therefore a different sequence of whole and half steps in the fixed central octave span.

[3][4] Four centuries later, the term was taken from Ptolemy in exactly the same sense by Boethius, who described these seven names as "toni, tropi, vel modi" (tones, tropes or modes) in the fourth book of his De institutione musica.

In the late 9th century, in the Carolingian treatises Alia musica and in a commentary on it called the Nova expositio, this set of seven terms, supplemented by an eighth name, "Hypermixolydian", was given a new sense, designating a set of diatonic octave species, described as the tonal embodiments of the eight modes of Gregorian chant.