344 THE WORLD AS IDEA. bk. iii.
withstanding 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."[1]
I might still have something to say about the way in which music is perceived, namely, in and through time alone, with absolute exclusion of space, and also apart from the influence of the knowledge of causality, thus without understanding; for the tones make the aesthetic impression as effect, and without obliging us to go back to their causes, as in the case of perception. I do not wish, however, to lengthen this discussion, as I have perhaps already gone too much into detail with regard to
- ↑ Cf. Ch. xxxix. of Supplement.
