Philosophers talk about emotions as having objects. If you are angry, you are angry about something or at someone. If you are sad, you are sad about something, the same with happy. They contrast object-directed emotions with moods, which don't have an object. Moods are things like cheerful or gloomy feelings that do not relate to anything in particular. This is a simplification, of course. Here is an article with more detail--see especially section 3 on emotions and intentional objects.
What does this have to do with music? We sometimes talk about music as being sad or happy. There is an anecdote about Schubert that applies. He had played at a salon in Vienna and afterwards someone came up and asked him why his music was always sad. He replied that all music is sad. Perhaps true of Romantic music, but certainly not of Classical or Baroque music. I want to propose that music is neither happy nor sad, nor does it really depict other ordinary emotions. The reason is those objects: music has no object. If there is a piece of music that is slow, languorous, gloomy, we may well talk about it as being 'sad', but it is sadness without an object, therefore a mood, not an emotion. Wagner called the first movement of Beethoven's string quartet in C# minor, op 131, the saddest thing in all music. Here it is:
If it is truly sad, then why do we enjoy listening to this and similar music? I think the answer is that it is only 'sad' by metaphor. This, and all music without any text, is really only 'about' musical beauty. We enjoy beauty in music. Sometimes that beauty comes in slow, languorous forms and sometimes it comes in bright, sparkling forms. Here is the very next movement of the quartet:
Similarly, there is no such thing as 'angry' music: music doesn't make us angry and composers are not angry when they write it. This is why I am always a little leery of attaching much importance to biographical details as a guide to what a piece of music 'means'. Music, again, music without text or lyrics, doesn't mean anything in the usual sense. Perhaps I should say "most music" because there are some interesting exceptions. Sometimes composers have been known to code meaning into a piece through the use of either notes that refer to someone or something, or to construct music with some numerological significance. This is interesting, of course, but it is essentially an extra-musical ploy or reference.
One famous example is Shostakovich's coding of his own initials into several pieces. When speaking the names of the notes in German, E flat is 'es' and B natural is 'h'. Therefore DSCH stands for Dmitri Shostakovich and corresponds to the notes D, E flat, C and B natural. Here is the opening of his Eighth String Quartet, which is permeated with this figure:
Bach did the same at the end of the Art of Fugue with a new subject using the notes BACH. Another example from Bach is the first fugue, in C major, from the Well-Tempered Clavier that uses a subject of exactly 14 notes. B = 2, A = 1, C = 3 and H = 8 for a total of 14. One musicologist claims that the Mass in B minor, also by Bach, uses numerology as well. There are, apparently 2345 measures in the whole piece and the only repeated music, the Dona nobis pacem, is based on a theme that begins with the 2nd, 3rd, 4th and 5th scale degrees. Well, maybe... In any case, these coded references are essentially non-musical and while they may be significant, it is something apart from the fundamental musical structure.
But music can have a dramatic effect on us, making us tap our foot, move our head, breath more heavily, even tingle with goose-bumps. How does it do this? I don't think we really know, though in a neurological lab at McGill University, they are looking at the brain to see if they can find out. I think I prefer to think of it as a mystery: how mere vibrations in the air, impinging on our ears, can have such a profound effect.
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