A scale-series of four notes. The word in its modern sense signifies a half of the octave scale. [Stainer, John; Barrett, W.A.; A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]
Tetrachord System: The early form of the system now known as Tonic Sol-fa. [Stainer, John; Barrett, W.A.; A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]
Interesting comments about the terms 'diatonic' 'chromatic' and 'enharmonic:
First of all, the basis for Greek scale construction was the tetrachord (= '4 strings'). Their theory (at least Aristoxenus and after) was based on the lyre (a sort of small harp), and not on any wind instruments.
So the tetrachord designates 4 notes, of which two are fixed and two are moveable. [see 4-note chord]
The fixed notes are those bounding the tetrachord, which are always assumed to be the interval of the Pythagorean 'perfect 4th', with the ratio 3:4. It's the position of the two moveable notes that was argued about so much, and which makes this stuff so interesting to tuning theorists.
(BTW, John Chalmers's book Divisions of the Tetrachord is entirely about specifically this.)
Those various divisions are what determine the different genera (plural of genus - the actual Greek word is genos, but commentators writing in English generally use the Latin form). There were 3 basic genera: Diatonic (= 'thru tones'), Chromatic (= 'colored' or 'thru the shades'), and Enharmonic (= 'properly attuned').
Apparently the Enharmonic derived from the ancient scales which were called harmonia, thus its name. That was the one with 'quarter-tones'. The chromatic had a pattern that more-or-less involved a succession of 2 semitones, and the Diatonic is the one we're most familiar with, using mainly 'whole tones' with a few semitones. from http://www.ixpres.com/interval/monzo/aristoxenus/tutorial.htm
The Greeks most probably constructed their musical tetrachords in a symmetrical order in analogy with their sculpture, and showed the ear identical with the eye in its love of symmetry. With them, therefore, the Dorian mode would have a certain pre-eminence. Beginning this mode on D, without knowing the musical mystery that resides in D, they had two tetrachords with the semitones symmetrically in the middle in one mode; it was next possible for them to arrange in pairs, symmetrically, the other tetrachords.
among the Greeks on account of having symmetry in itself. The primitive scale was doubtless that which is the model of all major music; and our minor model is its dual, as Ramsay has shown, which in its genesis indicates the duality of all the rest of the notes, although it is not probable that the Greeks saw the musical elements in this light. It is remarkable and significant that in their modes the Greeks did not lift up the scale of Nature into different pitches, preserving its model form as we do in our twelve major scales, but keeping the model form at one pitch they built up their symmetrical tetrachords, allowing the larger and lesser tones of the primitive scale to arrange themselves in every variety of place, as we have shown in the table of tetrachord modes above. Without seeing the genetic origin of music's duality they were led to arrange the modes by symmetry, which is one of the phases of duality. Symmetry is duality in practice. It may not always be apparent how symmetry originates in Nature; but in music, the art of the ear, duality emerges in the genesis of the minor scale; in the true mathematical build of the major on the root of the major subdominant F, and the true relation of the minor to it in the inverse genesis descending from the top of the minor dominant B. [Scientific Basis and Build of Music, page 46]