significance of music with this its physical and arithmetical basis depends upon the fact that what resists our _apprehension_, the irrational relation, or the dissonance, becomes the natural type of what resists our _will_; and, conversely, the consonance, or the rational relation, which easily adapts itself to our apprehension, becomes the type of the satisfaction of the will. And further, since that rational and irrational element in the numerical relations of the vibrations admits of innumerable degrees, shades of difference, sequences, and variations, by means of it music becomes the material in which all the movements of the human heart, _i.e._, of the will, movements whose essential nature is always satisfaction and dissatisfaction, although in innumerable degrees, can be faithfully portrayed and rendered in all their finest shades and modifications, which takes place by means of the invention of the melody. Thus we see here the movements of the will transferred to the province of the mere idea, which is the exclusive scene of the achievements of the fine arts, for they absolutely demand that the _will itself_ shall not interfere, and that we shall conduct ourselves as pure _knowing_ subjects. Therefore the affections of the will itself, thus actual pain and actual pleasure, must not be excited, but only their substitutes, that which is agreeable to _the intellect_, as a _picture_ of the satisfaction of the will, and that which is more or less repugnant to it, as a _picture_ of greater or less pain. Only thus does music never cause us actual sorrow, but even in its most melancholy strains is still pleasing, and we gladly hear in its language the secret history of our will, and all its emotions and strivings, with their manifold protractions, hindrances, and griefs, even in the saddest melodies. When, on the other hand, in reality and its terrors, it is our _will itself_ that is roused and tormented, we have not then to do with tones and their numerical relations, but are rather now ourselves the trembling string that is stretched and twanged.