Whatever is fitted in any sort to excite the ideas of pain and danger, that is to say, whatever is in any sort terrible, or is conversant about terrible objects, or operates in a manner analogous to terror, is a source of the sublime; that is, it is productive of the strongest emotion which the mind is capable of feeling. I say the strongest emotion, because I am satisfied the ideas of pain are much more powerful than those which enter on the part of pleasure.This is an extremely important concept in aesthetics. I don't think we could really talk about how a lot of music affects the listener without this concept. Burke goes on as follows:
The passion caused by the great and sublime in nature, when those causes operate most powerfully, is astonishment: and astonishment is that state of the soul in which all its motions are suspended, with some degree of horror.He talks about beauty in this way:
I call beauty a social quality; for where women and men, and not only they, but when other animals give us a sense of joy and pleasure in beholding them (and there are many that do so), they inspire us with sentiments of tenderness and affection towards their persons; we like to have them near us, and we enter willingly into a kind of relation with them, unless we should have strong reasons to the contrary.And about the relation between beauty and the sublime:
It is my design to consider beauty as distinguished from the sublime... By beauty, I mean that quality, or those qualities in bodies, by which they cause love, or some passion similar to it... attending to their quantity, beautiful objects are comparatively small... the beautiful in music will not hear that loudness and strength of sounds, which may be used to raise other passions; nor notes which are shrill, or harsh, or deep; it agrees best with such as are clear, even, smooth, and weak. The second is; that great variety, and quick transitions from one measure or tone to another, are contrary to the genius of the beautiful in music. Such transitions often excite mirth, or other sudden or tumultuous passions; but not that sinking, that melting, that languor, which is the characteristical effect of the beautiful as it regards every sense.He contrasts them as follows:
On closing this general view of beauty, it naturally occurs that we should compare it with the sublime; and in this comparison there appears a remarkable contrast. For sublime objects are vast in their dimensions, beautiful ones comparatively small; beauty should be smooth and polished; the great, rugged and negligent: beauty should shun the right line, yet deviate from it insensibly; the great in many cases loves the right line; and when it deviates, it often makes a strong deviation: beauty should not be obscure; the great ought to be dark and gloomy: beauty should be light and delicate; the great ought to be solid, and even massive. They are indeed ideas of a very different nature, one being founded on pain, the other on pleasure; and, however they may vary afterwards from the direct nature of their causes, yet these causes keep up an eternal distinction between them, a distinction never to be forgotten by any whose business it is to affect the passions.We notice when listening to music that there are soft, delicate passages and also wild, fiery passages. The former given perhaps to the flutes and oboes and the latter to the trombones and tympani with the strings always present as a kind of substrate. This corresponds to Burke's classification of the beautiful and the sublime. If you are using an aesthetics that talks about beauty, then you also need the concept of the sublime, otherwise you can only talk about those soft flute passages and how beautiful they are and are at a loss for words to explain why that noisy and terrifying passage with the trombones and tympani is even in the piece.
I can describe the beautiful and sublime in terms of personal experience. I was once out hiking in the mountains on Vancouver Island and passed through some alpine meadows of wildflowers. Very beautiful! Then I climbed up a ridge that I thought was the peak. When I got to the top, as my head rose to the point where I could see past the ridge, suddenly I realized that I was on a mere foothill. Towering above me was a vast, massive crag that was the true peak: miles away and thousands and thousands of feet higher. That was the sublime: something great and astonishing and a bit fearful.
Here is the whole of Burke's book if you want to have a look.
The symphonies of Sibelius are not a bad place to look for an example of the sublime and beautiful in music: