Advanced Search

Music is comprised of sound waves. Waves can be modeled mathematically using a Fourier series. So, could we then write music in terms of mathematics by using a Fourier series to represent the sound waves? Would it be worthwhile to do so? Would it have any benefit over traditional music notation?

Music is composed of sound waves, but that's only part of the story. A Fourier analysis would run the risk of including too much information, overlooking the fact that there can be very different interpretations of the same piece. It might be possible to fudge that point. (After all, compression schemes rely on Fourier analysis, but don't include every detail.) The real point is that to be useful, musical notation has to be something that musicians can efficiently read. To make the case that Fourier analysis would be useful for that purpose would be a pretty heavy lift, I suspect. Compare: it would be possible to give a Fourier analysis of a speech in a play, at least as performed by some actor. But I'd be willing to bet that any actor would find it a lot easier just to have the words written down. Musical notation, like written words and dance notation, is able to do its job precisely because it vastly, massively underspecifies the full detail of what any performance will actually be like. The point...

Say there is a music band whose members engage in frequent illegal/immoral acts, e.g. drunken driving, drug use, prostitution, rape, assault, etc. I want to buy their latest album, but I know that the money they receive from me will end up fueling their criminal behavior. Knowing this, is it wrong for me to buy the album?

You've given some good reasons for not buying the album. And since it's hard to make the case that you need this particular album, the reasons seem pretty strong - strong enough to convince me, at least. That said, there's a larger and harder issue here, and I'm guessing you may have it in the back of your mind. Many of us spend money at businesses whose practices we really wouldn't approve of if we let ourselves think about it. Perhaps they buy goods from sweat shops. Perhaps they have despicable labor practices. Without pretending that this does justice to the matter, a couple of issues strike me. One has to do with thresholds and balances. At what point are the practices of a business "bad enough" or insufficiently offset by the value of what they provide (including employment) that I should stop patronizing them? And how strong are my obligations to inform myself? I may know that business X has some very nasty practices. I might decide to patronize business Y instead, but the only...

How would a person who believes that musical works are universals account for instances of musical works which seem to imply that each performance of the same piece is always different, not only in the sense that all performances are different interpretations of the same score, but taking the examples of the arab "maqam", the indian "raga" or western jazz music, in which improvisation and sometimes a radical "mutation" of the work plays an important role, not accidental but essential to the performance of that work? Victor G.

Any performance of a musical work will always differ in some ways from other performances. And universalist theorists know that. What's required is that the performance nonetheless have the characteristics that the relevant universal call for. (Or have enough of them; we'll set issues about imperfect performances aside.) So suppose the universalist would say something like this: there's something that makes a performance even of a work that allows for accident or improvisation a performance of one work rather than another. Whatever that is tells us which universal the work corresponds to. It may just be that in some cases, the pattern that the work "is" may be more abstract. Whether that's fully adequate is harder to say. But it's the obvious way to deal with the sort of worry that you raise.

It is generally accepted that certain intervals in music sound "harmonious", i.e. 3rds, 4ths and 5ths. Why is this so? Why do these certain intervals constitute a pleasant sounding harmony, as opposed to jarring, dissonant intervals like 2nds and 7ths? I do not believe it is a matter of taste - most people, even those with no musical training will uniformly identify a harmony as harmonious (or in tune) or dissonant (or out of tune, I suppose). However, I am open to being disproved on this point.

It's an intriguing phenomenon. And it turns out, so I gather, that it's not confined to humans. Various animals differ in their responses to what we label consonant and dissonant intervals. Why this should be isn't something that a philosopher, as such, is in a good position to say. It clearly has some physiological basis and seems to have something to do with the phenomenon of "beats" (something you can actually experience as pulses when two high-pitched notes that differ slightly in pitch are played together.) One study I discovered (by Jonatan Fishman et al. of Albert Einstein medical college) looks at the neural correlates of dissonance in macaques and in humans. If you're able to follow the neurophysiological details (I'm not) you can have a look at the link. There are also references to earlier work. There are still some things left over that a philosopher might want to puzzle about. One is the sort of thing that physiology might straightfowardly help us understand: why is it that...