III
We have seen that the Greeks recognized the consonance of the octave. Similarly they recognized at an early period the close relationship of the interval of the perfect fifth, and its inversion, the perfect fourth. The latter became the basis of the Greek system of scales. They divided the interval into unequal smaller intervals according to three methods, or genera, in each case placing the larger steps at the top and the smaller at the bottom. (An equal division of the interval has, as far as we know, never been attempted and is entirely foreign to natural impulses.) The results obtained were as follows:
The Three Genera.
![[PNG]](#7492430724626623457_pag99_score1.png.id-5858102293735349509.wrap-0.html.html){kind=link}
Of these three tetrachords (from [Greek: tetra] = four and [Greek: chordon] = string) only the first was generally accepted, the chromatic was rarely used and the enharmonic probably only by virtuosi, for we have the testimony of Aristoxenus that the ear accustomed itself only with difficulty to the distinction of quarter tones.
By joining two diatonic tetrachords together we obtain a series of notes corresponding to the Dorian scale or mode ([Greek: harmonia])—more properly ‘octave species’—which was accounted the oldest of all the modes:
Dorian.
![[PNG]](#7492430724626623457_pag99_score2.png.id-5627543359112453233.wrap-0.html.html){kind=link}
Associated with this we soon find the Phrygian mode, supposed to be of Asiatic origin and introduced into Greece by Terpander of Lesbos, one of the earliest known composers of antiquity:
Phrygian.
![[PNG]](#7492430724626623457_pag100_score1.png.id-7532642429410811574.wrap-0.html.html){kind=link}
and also the Lydian, the name of which indicates its origin:
Lydian.
![[PNG]](#7492430724626623457_pag100_score2.png.id-5607503797945376808.wrap-0.html.html){kind=link}
Around these three may be grouped all the modes in use in classic times. These scales or octave species may be compared rather to our present major and minor modes than to our modern transposition scales, in that their identity is determined not by their absolute pitch, but by the intrinsic character of each mode, based upon the distribution of the large and small steps or intervals within the octave. But here the analogy ends, for the Greek modes cannot really be thought of in the same way as either modern scales or modes, which by long association with our harmonic system have become inseparably identified with it, so that every step of the scale has a harmonic significance as well as a melodic. Hence, there is associated with our scales the idea of tonality, which in its modern sense is entirely foreign to Greek music. Nevertheless a distinct character or ethos was ascribed to their scales by the Greeks (just as our major and minor have their individual character). The Lydian, for instance, was thought of as plaintive and adaptable to songs of sorrow; the Dorian as manly and strong, hence to be employed in warlike strains; and so on.[36]
It will be seen that the above three scales correspond to the three series of notes comprised within the octaves from e to e´, d to d´, and c to c´, produced by the white keys of the piano. (While this does not indicate their absolute pitch, it represents the relative pitch at which they appear as part of the entire system, or ‘foundation scale,’ of the Greeks, illustrated on page 103.) By a transposition of the tetrachord divisions of each of these scales, the Greeks obtained two additional scales out of each of the above three. These derived scales were denoted by the prefixes hypo and hyper (low and high), respectively:
(It is evident from this table that the Hypodorian corresponds to the Hyperphrygian, and the Hypophrygian to the Hyperlydian; hence there are only seven different modes.)
A common relationship was thus clearly recognized between the three scales of each group, which may be thought of as having one common tonic. It may be noted, however, that the Hypodorian probably had an independent existence before being associated with the Dorian, as is indicated by its own ethnological name of ‘Æolian,’ and as such was supposed to be of great antiquity. The Hyperdorian enjoyed an independent existence as ‘Mixolydian.’ Its invention has been variously ascribed to Sappho, Damon and Pythocleides.
We have seen how, by joining two tetrachords, the Greeks constructed their Dorian scale (octachord). By joining additional tetrachords to this scale at either end they obtained their double octave scale or ‘Perfect Immutable System’:
![[PNG]](#7492430724626623457_pag102_score.png.id-4609346945931030775.wrap-0.html.html){kind=link}
It should be noted, however, that the new tetrachords are added conjunctively, i. e., so that one of their notes (e) coincides with the terminal notes of the original octave, while the two tetrachords making up that octave were placed in juxtaposition with a whole tone step between them. This was called the tone of disjunction (diezeuxis). For purposes of modulation (metabole) they now laid across the middle of this system an additional diatonic tetrachord (from d to a) in such a way that one of its tones (b♭) came half way between the two notes of the diezeuxis.[37] The low A was added to round out the octave. (It is a curious fact that what we call low the Greeks called high and vice versa.) The two tetrachords Meson and Hypaton, together with the conjunctive (Synemmenon), were also considered as an independent system called the Lesser Perfect System. The relation of these systems as well as the names of the individual notes are set forth on the accompanying table.
Double Octave Scale, or Perfect Immutable System
By carving out of the Greater Perfect System (which we may call simply the Complete System) overlapping octave sections, each beginning on a different note, the Greek theorists found these to correspond in their intervals to each of the seven different modes, as follows: Thus all scales came to be thought of theoretically as transpositions of the corresponding octave sections in the Complete System (Foundation Scale). Indeed, the entire system was considered as transposed and the individual tones retained their names regardless of pitch, i. e., in the Dorian mode the mese would always be the fourth note from the bottom, in the Phrygian the fifth, etc.
![[PNG]](#7492430724626623457_pag104_score.png.id-8959813043464157267.wrap-0.html.html){kind=link}
As an example, let us transpose the Foundation Scale one tone above its natural pitch:
The middle octave will now be seen to be Phrygian (corresponding to No. 3 above) instead of Dorian as before. Now in their system of transposition scales (in reality transposed Complete Systems) the Greeks gave to every scale the name corresponding to the mode of its middle octave. Before the time of Aristoxenus only seven of these transposition scales, or keys ([Greek: tonoi]) were in use. That theoretician eventually rounded out the scheme to eighteen (of which six appear in modern notation as duplicates or octave transpositions). He did this systematically by taking the interval of the perfect fifth as a basis and building on each semi-tone degree a group of three scales (natural, hypo, and hyper). As there were not enough of the original modes to supply names for all of the new scales, it was, of course, necessary to invent arbitrary names for the superfluous ones. By this achievement it was possible to transpose a melody into any one of the eighteen (or really twelve) keys without changing its modal character. We may therefore assume with some justification that Aristoxenus’ system in a way did for the Greeks what our own equal temperament has done for modern music.
We end our brief sketch of Greek theory at this point, which may be assumed as the highest development of the system. Later systems were either based on Aristoxenus or were of reactionary nature. We must, however, for a moment retrace our steps to explain briefly the achievements of an earlier theoretician, the great philosopher Pythagoras, in the field of musical acoustics.