In the whole of this exposition of music I have been trying to bring out clearly that it expresses in a perfectly universal language, in a homogeneous material, mere tones, and with the greatest determinateness and truth, the inner nature, the in-itself of the world, which we think under the concept of will, because will is its most distinct manifestation. Further, according to my view and contention, philosophy is nothing but a complete and accurate repetition or expression of the nature of the world in very general concepts, for only in such is it possible to get a view of that whole nature which will everywhere be adequate and applicable. Thus, whoever has followed me and entered into my mode of thought, will not think it so very paradoxical if I say, that supposing it were possible to give a perfectly accurate, complete explanation of music, extending even to particulars, that is to say, a detailed repetition in concepts of what it expresses, this would also be a sufficient repetition and explanation of the world in concepts, or at least entirely parallel to such an explanation, and thus it would be the true philosophy. Consequently the saying of Leibnitz quoted above, which is quite accurate from a lower standpoint, may be parodied in the following way to suit our higher view of music: Musica est exercitium metaphysices occultum nescientis se philosophari animi; for scire, to know, always means to have fixed in abstract concepts. But further, on account of the truth of the saying of Leibnitz, which is confirmed in various ways, music, regarded apart from its ?sthetic or inner significance, and looked at merely externally and purely empirically, is simply the means of comprehending directly and in the concrete[pg 343] large numbers and complex relations of numbers, which otherwise we could only know indirectly by fixing them in concepts. Therefore by the union of these two very different but correct views of music we may arrive at a conception of the possibility of a philosophy of number, such as that of Pythagoras and of the Chinese in Y-King, and then interpret in this sense the saying of the Pythagoreans which Sextus Empiricus quotes (adv. Math., L. vii.):τ? αριθμ? δε τα παντ? επεοικεν (numero cuncta assimilantur). And if, finally, we apply this view to the interpretation of harmony and melody given above, we shall find that a mere moral philosophy without an explanation of Nature, such as Socrates wanted to introduce, is precisely analogous to a mere melody without harmony, which Rousseau exclusively desired; and, in opposition to this mere physics and metaphysics without ethics, will correspond to mere harmony without melody. Allow me to add to these cursory observations a few more remarks concerning the analogy of music with the phenomenal world. We found in the second book that the highest grade of the objectification of will, man, could not appear alone and isolated, but presupposed the grades below him, as these again presupposed the grades lower still. In the same way music, which directly objectifies the will, just as the world does, is complete only in full harmony. In order to achieve its full effect, the high leading voice of the melody requires the accompaniment of all the other voices, even to the lowest bass, which is to be regarded as the origin of all. The melody itself enters as an integral part into the harmony, as the harmony enters into it, and only thus, in the full harmonious whole, music expresses what it aims at expressing. Thus also the one will outside of time finds its full objectification only in the complete union of all the steps which reveal its nature in the innumerable ascending grades of distinctness. The following analogy is also very remarkable. We have seen in the preceding book that notwithstanding [pg 344] the self-adaptation of all the phenomena of will to each other as regards their species, which constitutes their teleological aspect, there yet remains an unceasing conflict between those phenomena as individuals, which is visible at every grade, and makes the world a constant battle-field of all those manifestations of one and the same will, whose inner contradiction with itself becomes visible through it. In music also there is something corresponding to this. A complete, pure, harmonious system of tones is not only physically but arithmetically impossible. The numbers themselves by which the tones are expressed have inextricable irrationality. There is no scale in which, when it is counted, every fifth will be related to the keynote as 2 to 3, every major third as 4 to 5, every minor third as 5 to 6, and so on. For if they are correctly related to the keynote, they can no longer be so to each other; because, for example, the fifth must be the minor third to the third, &c. For the notes of the scale may be compared to actors who must play now one part, now another. Therefore a perfectly accurate system of music cannot even be thought, far less worked out; and on this account all possible music deviates from perfect purity; it can only conceal the discords essential to it by dividing them among all the notes, i.e., by temperament. On this see Chladni's "Akustik," § 30, and his "Kurze Uebersicht der Schall- und Klanglehre."[63]