I'd say that's a definite yes; one can learn a lot about music by listening to music   But I'm not so sure if I can stretch it to say that one's learning something about the physical universe through the musicality of the work, save that it's much more likely to trigger some sort of realization of some sort if it's aesthetically pleasing.

This seems to me to be undeniably true in the specific example of prolation canons communicating instantly the notion of nested self-similarity; but canons in general seem to fit into the world of tilings which are, well, as old as art itself really.

Loving the tuplets joke Alistair!

Alban Berg spoke of the finest music being the result of ecstacies of logic.

Definitely sounded like Kant to me.

I'll try to be as sensible as I can. I believe in what you're saying and I do think a musician can have a productive and fulfilling life without maths, nor indeed music theory or even notation. I offer the example of Charles Mingus. Mingus amungus.

However, notation is one logical step in the direction of rationalizing music. Pitch becomes a series of predetermined, accepted frequencies rather than a continuous band of all frequencies. Rhythmic values become a set of rational relationships: 1:1,3:4, 5:3, etc. rather than the (truly) irrational living rhythms of speech. Thus we can use notation to assure that a desired set of sounds can be produced and reproduced (as long as they employ the notatable pitches and rhythmic values), but we can't notate a primal scream or the rhythms of a speech by Malcolm X.

Naturally, notation can obscure the fact that the 'correct' or 'most musical' interpretation of almost all music requires these proportions to be regarded flexibly. Once we bear in mind this and other dangers, and don't overestimate notation, we suddenly have access to centuries of cultural artefacts that could not exist without notation.

Music theory is the next logical step in the direction of rationalizing music. "Harmony" becomes a series of predetermined, accepted pitch relationships rather than an undifferentiated morass of all possible simultaneous sounds. Meter becomes an increasingly complex set of accent hierarchies rather than the inflections and cadences of speech. Thus we can use music theory to explain how a desired set of sounds relate to one another (as long as they obey the theory), but we can't explain why music pleases us.

Naturally, music theory can obscure the fact that music which is not understood theoretically, or defies theory, is still music. Once we bear in mind this and other dangers, and don't overestimate music theory, we suddenly have insight into centuries of cultural artefacts that are linked more or less tenuously by common theoretical underpinnings. Sometimes very very tenuously

Mathematics is the next logical step in the.... catch my drift?

I am glad that someone (increpatio) mentioned Dmitri Tymoczko -- this is quite an apropos reference. Despite the monumental efforts of Tymoczko's research team, it remains to be seen whether their work will lead to any deeper insight or just be (d'apres increpatio) "having a reasonable amount of fun at the moment." As it is, Dmitri is a staunch defender of certain kinds of music making, and I can't help but expect that his research is motivated by a desire to "prove" that these kinds of music are somehow more "natural" and therefore pleasing than others. (If he's reading this, here is his chance to contradict)

It is for me a totally open question whether the purpose of rationalizing music is to explain pleasure, let alone whether that is actually possible. But Dmitri's work certainly is "fun"! Watch Chopin's E-minor prelude, op.28/4, move through three different kinds of musical "space" by following the links to the three movies at the top of this page: http://www.music.princeton.edu/~dmitri/ChordGeometries.html

I have a copy of Formalized Music, but have never really taken the trouble to study it in any detail, having been informed that quite a bit of the maths is pretty bunk (also, I'm very out of practice in maths myself - nearly 20 years ago when I was studying as an undergrad). If true, that might place doubts on whether the book really does do what it says on the tin. I'm interested to know why that above all was the thing that Xenakis wanted a wider reading audience to know about? Might it go hand-in-hand with the whole scientistic climate of the time that existed in various quarters (especially in the US, and the book was translated into English), a way of giving the work a type of cache in that manner?

Is 'unmediated' in particular necessarily always a positive thing? I don't think Xenakis's music sounds like that anyhow (nor am really sure what 'unmediated' music truly is).

As someone who did a maths degree but also plays the violin a lot, I guess I should have given the relationship between Maths and Music a lot more thought than I have.  As it happened, I got so annoyed with people always saying 'Oh Maths and Music go together' that I dismissed giving it a lot of attention.

Maths for me was a really easy thing - until I got to University when I had to do a lot of work (and didn't).  It was just intellectual.  Music on the other hand, was intellectual, emotional, spiritual and physical.  Looking at the equations for flow in a mathematical description of fluid moving is a very different experience from listening to, say, Mahler 2.

I have always thought of Maths and Music both as languages.  In maths, you translate a difficult problem in English (e.g. what happens to the fluid surface if you vibrate the side of a full beer glass at 440hz?) into 'Mathsese'.  Then you can solve it in maths (easy, or at least easier than doing it in English), and translate that back to English (you get circular ripples spaced 3cm apart, or whatever the answer is).

For music the translation is from the Composer's 'being' into 'the music' and into your 'being' - picking up stuff from editors, players and recording experts along the way.  The whole 'being' encompasing emotions as well as intellect and spirit.

But I wonder now if Maths could describe emotions, or spirit, or indeeed intellect.  Maths to me, and much of science is adicted to the physical world.  Cosmologists get ever more excited about learning what happened closer and closer to the big bang - but describe it only in physical terms when they talk about what their equations mean.  Perhaps there is only the physical - after all, all else is from the brain which is a physical thing......

Somehow though, I cannot step away from the feeling that music is more complete that maths, even if it (or perhaps because) is less perfect.

Tommo

I'm sure Xenakis would have agreed with that, although he wouldn't agree (and neither would I) that music and maths are both languages... they both use notations which are languages, and music obeys certain mathematical laws for the same reason* that everything else does (which also enables the use of mathematical tools in music of course), but otherwise mathematics is a matter of absolute truth, in so far as a result which is true (within a given axiomatic system) for me is also true for you and presumably for every other sentient being in the universe, while music, as we see every day on this discussion board, doesn't behave at all like that.

* though we don't and maybe can't know what this reason is!