Alypius has left us the notation of fifteen Greek scales; afterwards reduced by Claudius Ptolemaios, in the interest of simplicity, to seven. But were these fifteen all the scales ever noted? Clearly there were others, which must have possessed notations. Thus:—

1. Mixo-Lydian. This scale is mentioned by many writers. Plato (Rep. III, 398) describes it as ‘wailful.’ Bacchius (Eisagoge Harmonikon, § 46) mentions and places it.

2. Chalaro-Lydian. This scale is referred to by Plato (Rep. III, 399a).

3. Syntono-Lydiak. Plato (Rep. III, 398) describes this scale also as wailful. Athenaios (Deipnosophistae, XIV, 624 f.) quoting the poet Pratinas, mentions and by inference places it.

4. Hyper-Mixo-Lydian. Cleonidas (Harmonicum Introductorum, XII, 5) mentions this scale and defines its place.

5. Hypo-Mixo-Lydian. This scale, though not mentioned by Greek writers, has its name preserved in the Roman Gregorian ‘Modes,’ where it appears as the Eighth Tone. It is curious, though of no importance as evidence, to observe that the ‘Final’ of the Roman Tone is G; the note we shall claim to have been the highest of the vocal octave of the scale.