If we now cast a glance at purely instrumental music, a symphony of Beethoven presents to us the greatest confusion, which yet has the most perfect order at its foundation, the most vehement conflict, which is transformed the next moment into the most beautiful concord. It is _rerum concordia discors_, a true and perfect picture of the nature of the world which rolls on in the boundless maze of innumerable forms, and through constant destruction supports itself. But in this symphony all human passions and emotions also find utterance; joy, sorrow, love, hatred, terror, hope, &c., in innumerable degrees, yet all, as it were, only _in abstracto_, and without any particularisation; it is their mere form without the substance, like a spirit world without matter. Certainly we have a tendency to realise them while we listen, to clothe them in imagination with flesh and bones, and to see in them scenes of life and nature on every hand. Yet, taken generally, this is not required for their comprehension or enjoyment, but rather imparts to them a foreign and arbitrary addition: therefore it is better to apprehend them in their immediacy and purity. Since now, in the foregoing remarks, and also in the text, I have considered music only from the metaphysical side, that is, with reference to the inner significance of its performances, it is right that I should now also subject to a general consideration the means by which, acting upon our mind, it brings these about; therefore that I should show the connection of that metaphysical side of music, and the physical side, which has been fully investigated, and is well known, I start from the theory which is generally known, and has by no means been shaken by recent objections, that all harmony of the notes depends upon the coincidence of their vibrations, which when two notes sound together occurs perhaps at every second, or at every third, or at every fourth vibration, according to which, then, they are the octave, the fifth, or the fourth of each other, and so on. So long as the vibrations of two notes have a rational relation to each other, which can be expressed in small numbers, they can be connected together in our apprehension through their constantly recurring coincidence: the notes become blended, and are thereby in consonance. If, on the other hand, that relation is an irrational one, or one which can only be expressed in larger numbers, then no coincidence of the vibrations which can be apprehended occurs, but _obstrepunt sibi perpetuo_, whereby they resist being joined together in our apprehension, and accordingly are called a dissonance. Now, according to this theory, music is a means of making rational and irrational relations of numbers comprehensible, not like arithmetic by the help of the concept, but by bringing them to a knowledge which is perfectly directly and simultaneously sensible. Now the connection of the metaphysical