Monday, November 21, 2005

Reducing Music to Numbers

Music is vulnerable to math. As a system which can objectively be viewed simply as a set of twelve pitches - and, therefore numbers - music can have a virtually limitless variety of mathematical algorithms applied to it: The musical elements themselves do not prevent it. Or, even protest.

So much twentieth-century music is praised for it's arithmetical, mathematical, and geometrical exactitude. Why then, don't I like it? You can find unabridged aspects of math literally permiating the music of every great composer throughout all of music history; so why then does only the twentieth-century "atonal" stuff sound so abjectly lame to me?

Simple, really. In the music of the great composers whom I love, math was in the service of music: In the twentieth century, math started to rule over music. Math ruling over music is fundamentally... wrong.

Music has math in it - it's a kind of pure math in sound, in fact - but it's a math that is peculiar to music and other music-related natural phenomena. (Wait for it... here it comes!) The math that is directly related to the harmonic overtone series is the math of music and the music of math. We are dealing with a pre-existing mathematical system based on natural harmonic ratios: 1:1, 2:1, 3:2, 4:3, etc.

There are countless non-musical arithmetical and mathematical systems out there, and foisting them brutishly onto music can have almost no other possible result than to produce bad music. Non-music, even, in my view. No mater how robust the defense of whatever system is imposed on the musical elements, the end result must be... musical. The intellectual test for this is simple: If the system involved is within the sphere of the math that is directly related to the nature of sound, then there is a chance that the result will be musical, if not, no chance. But the acid test is even simpler: How does it sound? Eddie Van Halen said, "If it sounds right, it is right." I think this is overly simplistic on the one hand, but exactly correct on the other. I personally am willing to give composers the benefit of the doubt if they are incorporating the math of music, even if the piece does not speak to me individually. Hey, there are plenty of wildly popular and significant works from the common practice eras which do not speak to me, so who am I - pimple on the posterior of music that I am - to dismiss works that may be plenty communicative to some, and are based on musical mathematics, and yet don't say anything that I particularly want to hear? This goes back to my arguement that the now cannot ever hope to objectively predict it's place in history: Only history can do that after years of retrospect.

It seems to me that, for the most part, the objections of listeners to the majority of twentieth-century serialism has been shown to be sufficiently justified, and yet I think we are still far too close to the events time-wise to make any ultimate judgement on it. And, to be fair, asside from writing a serial fugue subject (Albeit one with obvious tonal implications), I also find that some aspects of atonality can be used as an effective resource within an overal tonal/modal context to suspend tonality, and to good effect. In fact, to far better effect than uncompromising and persistent atonality gives. The roots of this approach, by the way, go back to extended episodes of symmetrical structures like diminished seventh chords and augmented triads. That would be to at least the early Baroque, if not even further back.

Music has it's own will, and it's own agenda. In order to come to an understanding of it, you have to meet up with it on it's home turf and on it's own terms. The composer is the disciple, and music is the master. If you don't get that, you can't even get to square one, in this monk's humble opinion.

That certainly sounds hopelessly old fashioned and - perish the thought - Romantic, I'm sure, but this is what I have come to the conclusion is the actual, unvarnished truth of the matter.

When I hear contemporary critical reviews of music that describe the work under scrutiny as "uncompromising", I infer from that statement that the music is sadly saddled with some non-musical mathematical system or construct. I may not always be right, but experience has taught me that I more often than not... am. When I perilously assume that I won't like said "uncompromising" piece, my rate of accuracy approaches 100%.

Worse still, to me, is the old canard that says something to the effect of, "In the twentieth century, composers left the audience behind." Please. From my point of view, twentieth-century composers abandoned an audience that was still plenty hungry for new and different styles of music. The acceptance of increasingly "uncompromising" styles of jazz during the same time period would seem to me to qualify as solid anecdotal evidence of this.

Shillinger said that music with a "neutral pitch distribution" (Music that does not establish a pitch heirarchy and/or pitch axes) was objected to because it was fundamentally unnatural: "Audiences usually object to such music, and they are right to do so" (Quoting from memory, but I'm sure I have this essentially right). Now, Schillinger was lightyears ahead of me as a musical futurist, of that their can be no doubt, but the vast majority of his concepts - even if I wouldn't consider them for my own music - seem quite logical from a musical mathematics standpoint. I think this is key. At least a key, if not the key.

Yes, yes. Hoplessly old-fashioned. But, being a little old fashioned isn't always such a bad thing, is it Julianne?



"Not at all: I like old fashioned guys."

2 Comments:

Blogger Devin Hurd said...

The creativity of numbers has yet to really be plumbed. It sounds like you're objecting to the mechanically uncreative application of algorithmic procedure to music. Many serial works are painfully bad. The same can be said for a lot of tonal works and sometimes it's not the math that does it in even if it is cited as a major culprit (often correctly). Do bad tonal works fail for not being algorithmic enough?

The reality is that the math behind music is always there regardless whether the composer has consiously staked their aesthetic intent in it. The frequency ratios of just intonation are a prime example (pardon the pun). Every element of sound has a quantitative component and in the 20th century the mood turned toward hyper-rationalizing everything. I don't know if audiences have universally rejected everything that's come out of this impulse but I have seen them scurry away whenever the numerical trappings are exposed. Ultimately it is the quality of ideas that will survive as the hyperbole erodes away and leaves just the sonic traces behind. Perhaps people will warm up to some of Milton Babbitt's works once the memory of the "Who Cares if You Listen" essay is forgotten.

3:02 PM  
Blogger Hucbald said...

That's a point I failed to make clear, to be sure: Music, just by virtue of being music, always generates it's own math, whether the composer is aware of it or not.

And yes, Babbitt's "Who Cares...", uh, "diatribe" rubbed a lot of people the wrong way. Me included.

The pitfall, from my view, is that you can have beautiful and compelling mathematical formula, and try to shoehorn music into it, and it will fall flat as music a lot of the time. I first discovered this when I was writing BASIC programs that generated fractal melodies: The patterns in the numeric series were fabulously compeling, but it was not until I had tonal/modal filtering perameters added to the program that I got decent results. Even then, I can still do better by using a combination of intellect (Er... such as it is) and intuition.

Music is so malliable that nothing prevents any scheme from being applied to it, and that has lead to a lot of awful stuff that hardly anybody cares for, unfortunately. I mean, if you have to explain it for it to be appreciated, is it really functioning as music?

One of the reasons I like the mature Glass stuff so much is that his processes are quite transparent, slow to evolve, and easy to follow. Not to mention beautiful in an etherial way, as if it's tonality divorced from common practice syntax.

And, my reply to Babbitt will always be, "If you're not communicating, who cares if you compose?"

Thanks again, Devin. I always appreciate your point of view, and I'm beginning to think we agree more than I originally thought. Cheers.

5:40 PM  

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