Virtual Taps

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.

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I'm Clive Thompson, the author of Smarter Than You Think: How Technology is Changing Our Minds for the Better (Penguin Press). You can order the book now at Amazon, Barnes and Noble, Powells, Indiebound, or through your local bookstore! I'm also a contributing writer for the New York Times Magazine and a columnist for Wired magazine. Email is here or ping me via the antiquated form of AOL IM (pomeranian99).

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