§ 24. Relation of the Species to the Keys.
Looking at the octaves which on our key-board, as on the Greek scale, exhibit the several species, we cannot but be struck with the peculiar relation in which they stand to the Keys. In the tables given above the keys stand in the order of their pitch, from the Mixo-lydian down to the Hypo-dorian: the species of the same names follow the reverse order, from b-b upwards to a-a. This, it is obvious, cannot be an accidental coincidence. The two uses of this famous series of names cannot have originated independently. Either the naming of the species was founded on that of the keys, or the converse relation obtained between them. Which of these two uses, then, was the original and which the derived one? Those who hold that the species were the basis of the ancient Modes or harmoniai must regard the keys as derivative. Now Aristoxenus tells us, in one of the passages just quoted, that the seven species had long been recognised by theorists. If the scheme of keys was founded upon the seven species, it would at once have been complete, both in the number of the keys and in the determination of the intervals between them. But Aristoxenus also tells us that down to his time there were only six keys,—one of them not yet generally recognised,—and that their relative pitch was not settled. Evidently then the keys, which were scales in practical use, were still incomplete when the species of the Octave had been worked out in the theory of music.
The view now taken of the seven species is supported by the whole treatment of musical scales (systêmata) as we find it in Aristoxenus. That treatment from first to last is purely abstract and theoretical. The rules which Aristoxenus lays down serve to determine the sequence of intervals, but are not confined to scales of any particular compass. His Systems, accordingly, are not scales in practical use: they are parts taken anywhere on an ideal unlimited scale. And the seven species of the Octave are regarded by Aristoxenus as a scheme of the same abstract order. They represent the earlier teaching on which he had improved. He condemned that teaching for its want of generality, because it was confined to the compass of the Octave and to the Enharmonic genus, and also because it rested on no principles that would necessarily limit the species of the Octave to seven. On the other hand the diagrams of the earlier musicians were unscientific, in the opinion of Aristoxenus, on the ground that they divided the scale into a succession of quarter-tones. Such a division, he urged, is impossible in practice and musically wrong (ekmeles). All this goes to show that the earlier treatment of Systems, including the seven Species, had the same theoretical character as his own exposition. The only System which he recognises for practical purposes is the old standard octave, from Hypatê to Nêtê: and that System, with the enlargements which turned it into the Perfect System, kept its ground with all writers of the Aristoxenean school.
Even in the accounts of the pseudo-Euclid and the later writers, who treat of the Species of the Octave under the names of the Keys, there is much to show that the species existed chiefly or wholly in musical theory. The seven species of the Octave are given along with the three species of the Fourth and the four species of the Fifth, neither of which appear to have had any practical application. Another indication of this may be seen in the seventh or Hypo-dorian species, which was also called Locrian and Common (ps. Eucl. p. 16 Meib.). Why should this species have more than one name? In the Perfect System it is singular in being exemplified by two different octaves, viz. that from Proslambanomenos to Mesê, and that from Mesê to Nêtê Hyperbolaiôn. Now we have seen that the higher the octave which represents a species, the lower the key of the same name. In this case, then, the upper of the two octaves answers to the Hypo-dorian key, and the lower to the Locrian. But if the species has its two names from these two keys, it follows that the names of the species are derived from the keys. The fact that the Hypo-dorian or Locrian species was also called Common is a further argument to the same purpose. It was doubtless 'common' in the sense that it characterised the two octaves which made up the Perfect System. Thus the Perfect System was recognised as the really important scale.
Another consideration, which has been overlooked by Westphal and those who follow him, is the difference between the species of the Octave in the several genera, especially the difference between the Diatonic and the Enharmonic. This is not felt as a difficulty with all the species. Thus the so-called Dorian octave e-e is in the Enharmonic genus e e* f a b b* c e, a scale which may be regarded as the Diatonic with g and d omitted, and the semitones divided. But the Phrygian d-d cannot pass in any such way into the Enharmonic Phrygian c e e* f a b b* c, which answers rather to the Diatonic scale of the species c-c (the Lydian). The scholars who connect the ancient Modes with the species generally confine themselves to octaves of the Diatonic genus. In this they are supported by later Greek writers—notably, as we shall see, by Ptolemy—and by the analogy of the mediaeval Modes or Tones. But on the other side we have the repeated complaints of Aristoxenus that the earlier theorists confined themselves to Enharmonic octave scales. We have also the circumstance that the writer or compiler of the pseudo-Euclidean treatise, who is our earliest authority for the names of the species, gives these names for the Enharmonic genus only. Here, once more, we feel the difference between theory and practice. To a theorist there is no great difficulty in the terms Diatonic Phrygian and Enharmonic Phrygian meaning essentially different things. But the 'Phrygian Mode' in practical music must have been a tolerably definite musical form.