June 23, 2004
Is music like language?
I've written before about Zipf's Law -- a concept invented in the early 20th century by the social scientist George Zipf. Zipf counted word occurence in hundreds of newspaper and magazine articles and found that while English has about 26,000 common words, over 90% of everything we say or write uses merely 2,000 of them. So if you plotted the most-common to least-common words on a graph, you'd see the first few spiking way up high, then quickly dropping down to an almost flat line as you get past the 2,000 most common words. A Zipf Curve looks like a ski slope.
Later on, the economist and sociologist Herbert Simon offered an explanation for this. He pointed out that words gain meaning the more they're used -- which gives the first few words in a text "first mover" advantage, since they're helping to define the topic under discussion. For example, I'm more likely to re-use words "occurence" or "meaning" in the rest of this article, while probably never using the word "lawnmower." That's part of how a text builds meaning: By introducing a few key words and repeating them, over and over again. (On a broader scale, that's probably how language evolved too, and possibly why the Zipf Curve exists.)
Anyway, a physicist recently decided to see if music behaves the same way. Damian Zanette of the Balseiro Institute studied the occurrence of notes in several pieces of music. Presto: They, too, had Zipf-Curve distributions. What's really interesting is when he compared the distributions in "pleasant" music -- like Mozart -- versus atonal, "difficult" music, like Schoenberg. As Nature reports:
The pieces by Bach, Mozart and Debussy all produced a relatively steep graph, suggesting a strong relationship between rank and frequency, and therefore a high level of meaningful context. In other words, if you have heard part of the piece, it is relatively easy to predict what kind of thing will come next. Zanette adds that jazz pieces he tested showed a similar pattern.
But the Schoenberg piece, one of the first truly atonal works, had a much flatter graph. This means that the piece does not have a set vocabulary of commonly used words that keep appearing. Instead, the size of the vocabulary increases at about the same rate as the length of the piece; new "words" are constantly introduced, while earlier ones are seldom repeated.
Posted by Clive Thompson at June 23, 2004 03:29 PM
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Clive: you must read "The Rules of the Game" by Eigen and Winkler. In 1975 2 German scientists sought to survey the relevance of Game Theory -- especially the idea of decision-making automata -- to EVERYTHING. This includes language and evolution and music.
It is full of nuggets like this:
In the 18th century some composers wrote down "create your own sonata" algorithms that involved dice and decision trees.
Moreover, each chapter concludes with a game that adapts the principles outlined in the preceding pages.
In any case, they try to demonstrate that even in Schonberg's way-outiest compositions there are perceptible patterns, changes and resolutions.
But let's think about this in the context of your article: The majority of persons appreciate a piece of communication that establishes what it is about right away (those "first-mover" words you talked about) and then returns to and expands upon those initial terms. However, some people appreciate more demanding rules in the games they play, or have trained themselves to handle a larger dataset, or to assimilate data over a longer period -- say a 2-minute long passage that directly correlates changes in pitch to a change in volume volume -- than the 8-note phrase that is the most common unit of musical discourse and perception.
The trouble is, the development of this ability has one friggin' steep learning curve.
This is why I follow Deluze and Guattari and think of experimental art as minority literature rather than avant-garde. It's cool that you are doing stuff that no-one has done before -- and stuff that only a tiny fraction of the population will appreciate. But please, don't kid yourself into thinking that you are ushering some bright new future that will sweep away all that has gone before, or that promises a new beginning for everything.
On the Jazz thing
Jazz is a conversation. What satisfying conversation heads off on new topics and introduces new terms every 2 seconds?
The study makes a pretty simple point, which is that atonal pieces lack pitch redundancy which makes it harder to "appreciate". Of course, that was the point, especially at that stage for Schoenberg's work, to push beyond the boundaries of tonality (which you could view as a fixed or limited pitch set). While these works lack the formality of the 12-tone system to come, it's still fully chromatic in a way that others (Wagner, Strauss, etc.) did before him, albeit still returning to the tonic for structural meaning. I do recall analytical discussions of this era of his work in grad school -- you can rationalize a lot of this era of Schoenberg in d-minor...if you really try.
For me (and I was never a theorist, nor would I claim to be one if you tied me to chair and whipped me...nuh-uh) I don't think the pitches are the central component of "appreciation" or what makes "difficult" music "difficult". It ain't all about the pitches, not to ears like ours that have grown up with a wealth of recorded music and electronic sounds. There are tons of work prior to Schoenberg, and popular music since, that roil about the entire chromatic -- think of the most angst ridden scenes in romantic opera, think about most advanced jazz, even the wildest of sample/mixed hip-hop -- but since they still return, structurally, to a chord or key that is based upon the standard diatonic, or a regular beat, people are better able to "appreciate" it. Something like "Yeah, ok, that was a wild break, but now I know where we are (cue drum solo)."
The works of Schoenberg's pupil, Anton Webern, takes it to the next level, also disrupting any sense of rhythm and conventional structural periodicity -- and leaving a listener without a leg to stand on, if she is approaching the work within the scope of Western/Classical music. Personally, I love the challenge of having to figure it out myself.
And, to the sense of music "as conversation". Of course, music can serve lots of purposes, and we're most used to it functioning in a narrative manner (that's a Western bias, of course. I simply can't figure out the Japanese aesthetic, for example, in movies or children's books). Cage questioned that in a meaningful way, but left little room to build on. Again, it's simply what you want to get out of it -- talking to a crazy person (who changes topics every 2 seconds) can be terrifying and fascinating. At least as "art", you're a safe consumer of said craziness. As much as I enjoy that chaos, I wouldn't want it driving the cab. Or as a spouse!
Damn, Clive, can't I change this timestamp so it won't seem like I've just blown off a morning of work?
Ahahahah! I think you're stuck with the Eastern Standard Time stamp. I'll forward that post to your boss right now.
Killer points all around. Erik, indeed, I gotta read that stuff -- and the distinction between an avant-garde and experimentation is both completely apt and badly misunderstood by practitioners of the art, as well as their critics. Jason, yes, I think the return-to-center moment is most important in giving a work of music a sense of human-like shape; you can do all manner of weird stuff so long as you resolve to the 1st of the scale in which you began.
If you are always pressing the envelope, you will suffer many paper cuts.
Clive
Part of the problem with the web and why people are ignorant of its workings is YOU and your kind) and your attitude.
Why the hell should I HAVE to learn more about the working of the web or even computers to be ablr to use what I own. Yes if I bought the damn thing and its software , why the hell should some asshole geek like your self be able to write into the contract that he "will monitor your surfing, or even control your computer remotely...".
If I take my car into the mechanic does then have the right to place into his contract that he can monitor where I drive and even control my car remotely (with electronics today both are technically possible)?
So according to YOUR esteemed logic, I must learn EVERYTHING there is to know about cars, engines, electronics, transmissions, etc.
And you should learn everything there is to know about how women think because one of them may take you for a ride through court? Oh, and you should also learn to know everything there is to know about thelaw too.
Great logic geek.
Time will come that people like myself get fed up enough with the viruses, spyware peopel that we will start supporting legislation with incredible controls on your guys. SO much for freedom.
What will it take for folks like you to get to "know even a little bit" about what the rest of the world out here really wants in computers.
You don't read the license agreement how can you even "think that real people would"?
what? what the hell are you talking about chuck? point well taken. you do have every right in the world to choose to be as ignorant as you wish. Godspeed.
Leave Clive alone. Go back to reading Rod and Reel Illustrated.
reminds me of other smarties who tried to formulate esthetic theories in terms of mathematical relationships.
like george david birkhoff, who ambitiously applied power laws to theories of music, art, etc. he calculated aesthetic enjoyment as the quotient of complexity and order. a kind of orderliness coefficient.
max bense took birkhoff as a departure point and applied information theory to derive an 'information esthetics'. for him, the esthetic experience remained an experience of orderliness, the perception of regularities within a context, as one moves from initial perceived input/detail to a larger conceptual pattern.
so the enjoyment of an esthetic experience comes in perceiving a balance between those expected formal regularities, and the stimulating novelty of deviations from the formal pattern.
so the best music, in the parlance of signal theory and power laws, rests somewhere between brown noise (overly predictable) and white noise (too irregular or random) -more in the 'pink noise' range. just the right balance of expectation and surprise. see: adlibs, happy accidents, and charlie mingus improv.
as it turns out, the allman brothers 'whipping post' live at fillmore east, ranks highest in birkhoff's calculations for 'esthetic effect', with a coefficient of 0.92!
Okay, that is totally wild about "Whipping Post". I always knew I liked that song!
(By the way, the Rod and Reel joke made me laff.)
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