The most direct testimony in support of the view that the ancient Modes were differentiated by the succession of their intervals has still to be considered. It is the account given by Aristides Quintilianus (p. 21 Meib.) of the six Modes (harmoniai) of Plato's Republic. After describing the genera and their varieties the 'colours,' he goes on to say that there were other divisions of the tetrachord (tetrachordikai diaireseis) which the most ancient musicians used for the harmoniai, and that these were sometimes greater in compass than the octave, sometimes less. He then gives the intervals of the scale for each of the six Modes mentioned by Plato, and adds the scales in the ancient notation. They are of the Enharmonic genus, and may be represented by modern notes as follows:—

Comparing these scales with the Species of the Octave, we find a certain amount of correspondence. As has been already noticed (p. 22), the names Syntono-lydian and Lydian answer to the ordinary Lydian and Hypo-lydian respectively. Accordingly the Lydian of Aristides agrees with the Hypo-lydian species as given in the pseudo-Euclidean Introductio. The Dorian of Aristides is the Dorian species of the Introductio, but with an additional note, a tone below the HypatÊ.

The Phrygian of Aristides is not the Enharmonic Phrygian species; but it is derived from the diatonic Phrygian octave d-e-f-g-a-b-c-d by inserting the enharmonic notes e* and b*, and omitting the diatonic g. By a similar process the Mixo-lydian of Aristides may be derived from the diatonic octave b-b, except that a as well as g is omitted, and on the other hand d is retained. If the scale of the Syntono-lydian is completed by the lower c (as analogy would require), it will answer similarly to the Lydian species (c-c).