The considerations set forth in the last chapter seem to show that if difference of mode or species cannot be entirely denied of the classical period of Greek music, it occupied a subordinate and almost unrecognised place.

The main elements of the art were, (1) difference of genus,—the sub-divisions of the tetrachord which Aristoxenus and Ptolemy alike recognise, though with important discrepancies in detail; (2) difference of pitch or key; and (3) rhythm. Passing over the last, as not belonging to the subject of Harmonics, we may now say that genus and key are the only grounds of distinction which are evidently of practical importance. No others were associated with the early history of the art, with particular composers or periods, with particular instruments, or with the ethos of music. This, however, is only true in the fullest sense of Greek music before the time of Ptolemy. The main object of Ptolemy's reform of the keys was to provide a new set of scales, each characterised by a particular succession of intervals, while the pitch was left to take care of itself. And it is clear, especially from the specimens which Ptolemy gives of the scales in use in his time, that he was only endeavouring to systematise what already existed, and bring theory into harmony with the developments of practice. We must suppose, therefore, that the musical feeling which sought variety in differences of key came to have less influence on the practical art, and that musicians began to discover, or to appreciate more than they had done, the use of different 'modes' or forms of the octave scale. Along with this change we have to note the comparative disuse of the Enharmonic and Chromatic divisions of the tetrachord. The Enharmonic, according to Ptolemy, had ceased to be employed. Of the three varieties of Chromatic given by Aristoxenus only one remains on Ptolemy's list, and that the one which in the scheme of Aristoxenus involved no interval less than a semitone. And although Ptolemy distinguished at least three varieties of Diatonic, it is worth notice that only one of these was admitted in the tuning of the lyre,—the others being confined to the more elaborate cithara. In Ptolemy's time, therefore, music was rapidly approaching the stage in which all its forms are based upon a single scale—the natural diatonic scale of modern Europe.

In the light of these facts it must occur to us that Westphal's theory of seven modes or species of the Octave is really open to an a priori objection as decisive in its nature as any of the testimony which has been brought against it. Is it possible, we may ask, that a system of modes analogous to the ecclesiastical Tones can have subsisted along with a system of scales such as the genera and 'colours' of early Greek music? The reply may be that Ptolemy himself combines the two systems. He supposes five divisions of the tetrachord, and seven modes based upon so many species of the Octave—in all thirty-five different scales (or seventy, if we bring in the distinction of octaves apo nÊtÊs and apo mesÊs). But when we come to the scales actually used on the chief Greek instrument, the cithara, the number falls at once to six. Evidently the others, or most of them, only existed on paper, as the mathematical results of certain assumptions which Ptolemy had made. And if this can be said of Ptolemy's theory, what would be the value of a similar scheme combining the modes with the Enharmonic and the different varieties of the Chromatic genus? The truth is, surely, that such a scheme tries to unite elements which belong to different times, which in fact are the fundamental ideas of different stages of art.

The most striking characteristic of Greek music, especially in its earlier periods, is the multiplicity and delicacy of the intervals into which the scale was divided. A sort of frame-work was formed by the division of the octave into tetrachords, completed by the so-called disjunctive tone; and so far all Greek music was alike. But within the tetrachord the reign of diversity was unchecked. Not only were there recognised divisions containing intervals of a fourth, a third, and even three-eighths of a tone, but we gather from several things said by Aristoxenus that the number of possible divisions was regarded as theoretically unlimited. Thus he tells us that there was a constant tendency to flatten the 'moveable' notes of the Chromatic genus, and thus diminish the small intervals, for the sake of 'sweetness' or in order to obtain a plaintive tone [48];— that the Lichanos of a tetrachord may in theory be any note between the Enharmonic Lichanos (f in the scale e-e*-f-a) and the Diatonic (g in the scale e-f-g-a) [49];— and that the magnitude of the smaller intervals and division of the tetrachord generally belongs to the indefinite or indeterminate element in music [50]. Moreover, in spite of the disuse of several of the older scales, much of this holds good for the time of Ptolemy. The modern diatonic scale is fully recognised by him, but only as one of several different divisions. And the division which he treats as the ordinary or standard form of the octave is not the modern diatonic scale, but one of the so-called 'soft' or flattened varieties. It is clear that in the best periods of Greek music these refinements of melody, which modern musicians find scarcely conceivable, were far from being accidental or subordinate features. Rather, they were as much bound up with the fundamental nature of that music as complex harmony is with the music of modern Europe.

The mediaeval modes or Tones, on the other hand, are essentially based on the diatonic scale,—the scale that knows only of tones and semitones. To suppose that they held in the earliest Greek music the prominent place which we find assigned to the ancient Modes or harmoniai is to suppose that the art of music was developed in Greece in two different directions, under the influence of different and almost opposite ideas. Yet nothing is more remarkable in all departments of Greek art than the strictness with which it confines itself within the limits given once for all in the leading types, and the consequent harmony and consistency of all the forms which it takes in the course of its growth.

The dependence of artistic forms in their manifold developments upon a central governing idea or principle has never been more luminously stated than by the illustrious physicist Helmholtz, in the thirteenth chapter of his Tonempfindungen. I venture to think that in applying that truth to the facts of Greek music he was materially hindered by the accepted theory of the Greek modes. The scales which he analyses under that name were certainly the basis of all music in the Middle Ages, and are much more intelligible as such than in relation to the primitive Greek forms of the art [51].