It appears, then, that the Mesê of the Greek standard System had the functions of a key-note in that System. In other words, the music was in the mode (using that term in the modern sense) represented by the octave a-a of the natural key—the Hypo-dorian or Common Species. We do not indeed know how the predominant character of the Mesê was shown—whether, for example, the melody ended on the Mesê. The supposed evidence for an ending on the Hypatê has been shown to be insufficient. But we may at least hold that as far as the Mesê was a key-note, so far the Greek scale was that of the modern Minor mode (descending). The only way of escape from this conclusion is to deny that the Mesê of Probl. xix. 20 was the note which we have understood by the term—the Mesê of the standard System. This, as we shall presently see, is the plea to which Westphal has recourse.
§ 21. The Species of a Scale.
The object of the preceding discussion has been to make it clear that the theory of a system of modes—in the modern sense of the word—finds no support from the earlier authorities on Greek music. There is, however, evidence to show that Aristoxenus, and perhaps other writers of the time, gave much thought to the varieties to be obtained by taking the intervals of a scale in different order. These varieties they spoke of as the forms or species (schêmata, eidê) of the interval which measured the compass of the scale in question. Thus, the interval of the Octave (dia pasôn) is divided into seven intervals, and these are, in the Diatonic genus, five tones and two semitones, in the Enharmonic two ditones, four quarter-tones, and a tone. As we shall presently see in detail, there are seven species of the Octave in each genus. That is to say, there are seven admissible octachord scales (systêmata emmelê), differing only in the succession of the intervals which compose them.
Further, there is evidence which goes to connect the seven species of the Octave with the Modes or harmoniai. In some writers these species are described under names which are familiar to us in their application to the modes. A certain succession of intervals is called the Dorian species of the Octave, another succession is called the Phrygian species, and so on for the Lydian, Mixo-lydian, Hypo-dorian, Hypo-phrygian, and Hypo-lydian. It seems natural to conclude that the species or successions of intervals so named were characteristic in some way of the modes which bore the same names, consequently that the modes were not keys, but modes in the modern sense of the term.
In order to estimate the value of this argument, it is necessary to ask, (1) how far back we can date the use of these names for the species of the Octave, and (2) in what degree the species of the Octave can be shown to have entered into the practice of music at any period. The answer to these questions must be gathered from a careful examination of all that Aristoxenus and other early writers say of the different musical scales in reference to the order of their intervals.
§ 22. The Scales as treated by Aristoxenus.
The subject of the musical scales (systêmata) is treated by Aristoxenus as a general problem, without reference to the scales in actual use. He complains that his predecessors dealt only with the octave scale, and only with the Enharmonic genus, and did not address themselves to the real question of the melodious sequence of intervals. Accordingly, instead of beginning with a particular scale, such as the octave, he supposes a scale of indefinite compass,—just as a mathematician postulates lines and surfaces of unlimited magnitude. His problem virtually is, given any interval known to the particular genus supposed, to determine what intervals can follow it on a musical scale, either ascending or descending. In the Diatonic genus, for example, a semitone must be followed by two tones, so as to make up the interval of a Fourth. In the Enharmonic genus the dieses or quarter-tones can only occur two together, and every such pair of dieses (pyknon) must be followed in the ascending order by a ditone, in the descending order by a ditone or a tone. By these and similar rules, which he deduces mathematically from one or two general principles of melody, Aristoxenus in effect determines all the possible scales of each genus, without restriction of compass or pitch [20]. But whenever he refers for the purpose of illustration to a scale in actual use, it is always the standard octave already described (from Hypatê to Nêtê), or a part of it. Thus nothing can be clearer than the distinction which he makes between the theoretically infinite scale, subject only to certain principles or laws determining the succession of intervals, and the eight notes, of fixed relative pitch, which constituted the gamut of practical music.
The passages in which Aristoxenus dwells upon the advance which he has made upon the methods of his predecessors are of considerable importance for the whole question of the species of the Octave. There are three or four places which it will be worth while to quote.