De institutione musica IV.15: De modorum exordiis, in quo dispositio notarum per singulos modos ac voces.
...each mode and voice.
XV. From the species of the consonance of the octave there arise those which are called modes, which they also name tropes or tones. Tropes are constitutions differing in the whole orders of the voices by depth or height. A constitution is as it were the full body of a melody, consisting of the joining of consonances, such as the octave, or the octave and fourth, or the double octave. The octave constitution is, namely, from proslambanomenos to mese, with the other voices lying between counted in; or again from mese to nete hyperboleon with the voices interposed; or from hypate meson to nete diezeugmenon with those which the extreme voices enclose in the middle. The synemmenon constitution is that which consists from proslambanomenos to nete synemmenon with those which are interposed in the middle. The double octave is considered from proslambanomenos to nete hyperboleon with those which are interposed in the middle. If anyone makes these constitutions wholly higher, or lowers them wholly toward the deeper, according to the aforesaid species of the consonance of the octave, he will make seven modes, whose names are these: Hypodorian, Hypophrygian, Hypolydian, Dorian, Phrygian, Lydian, Mixolydian. Their order proceeds thus. Let the order of voices in the diatonic kind be arranged from proslambanomenos to nete hyperboleon, and let this be the Hypodorian mode.
If anyone, then, raises proslambanomenos by a tone to the high, and thins hypate hypaton by the same tone, and makes all the others higher by a tone, the whole order will come out higher than it was before it received the raising of a tone. The whole constitution, made higher, will then be the Hypophrygian mode. If in the Hypophrygian the voices again receive the raising of a tone, the melody of the Hypolydian will arise. And if anyone raises the Hypolydian by a semitone, he will make the Dorian. And in the others the progress to height and raising is similar; and so that the reasoning may be grasped not by understanding only, but the form also be recognized by the eyes, the description handed down by the ancient musicians must be set below. But since among the ancient musicians each voice was marked by different little signs in each mode, it seems that the description of the little signs should be set first, so that, these being first known by themselves, the survey in the description of the modes may be easier.