Tunes create context like language: Maths shows why tonal music is easy listening.

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Tunes create context like language

Maths shows why tonal music is easy listening.
19 June 2004
Philip Ball

Nature: Link: http://www.nature.com/nsu/040614/040614-11.html

Full Text:
Ever felt as though a piece of music is speaking to you? You could be right:
musical notes are strung together in the same patterns as words in a piece
of literature, according to an Argentinian physicist.

His analysis also reveals a key difference between tonal compositions, which
are written in a particular key, and atonal ones, which are not. This sheds
light on why many people find it so hard to make sense of atonal works.

In both written text and speech, the frequency with which different words
are used follows a striking pattern. In the 1930s, American social scientist
George Kingsley Zipf discovered that if he ranked words in literary texts
according to the number of times they appeared, a word's rank was roughly
proportional to the inverse of its frequency. In other words, a graph of one
plotted against the other appeared as a straight line.

The economist and sociologist Herbert Simon later offered an explanation for
this mathematical relationship. He argued that as a text progresses, it
creates a meaningful context within which words that have been used already
are more likely to appear than other, random words. For example, it is more
likely that the rest of this article will contain the word "music" than the
word "sausage".

Physicist Damian Zanette of the Balseiro Institute in Bariloche, Argentina,
used this idea to test whether different types of music create a semantic
context in a similar fashion.

The key in which a piece of music is written is one factor that influences
which notes are more or less likely to come next. The repetition and
elaboration of particular melodic phrases is another.

>From Bach to Schoenberg

To measure these effects, Zanette analysed four different compositions: J.
S. Bach's Prelude Number 6 in D; Mozart's first movement from his Sonata in
C (K545); Debussy's Menuet from the Suite Bergamasque; and the first piece
from Schoenberg's Three Piano Pieces, Opus 11. Each is a solo piano piece,
but they all differ in style and period.

Zanette counted the frequency of different notes in each piece (taking into
account both the pitch and the length of the note), and plotted that against
their rank, as Zipf did with texts.

All of the pieces showed a text-like distribution, especially for the
higher-ranking notes. But the strength of the relationship varied, as
indicated by the slope of each graph, published on the preprint server
arXiv1.

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.

Although all of the piano pieces have a text-like property, the atonal
composition has less structure and less context; it is like a story whose
characters are constantly changing.

Unfamiliar flux

Zanette says the finding implies that the reason many people find it
unsatisfying to listen to atonal music is not simply because its harmonic
and melodic structures are unfamiliar, but because the meaning or context of
the piece is constantly changing.

"That doesn't mean Schoenberg's music is not comprehensible," Zanette
cautions. Indeed, Schoenberg himself wrote that the goal of the composer is
to produce comprehensibility. Zanette points out that the sequence of notes
is only one of the ways to create context in music. It could also be
produced rhythmically, for example.

He suggests that to appreciate atonality, we may need to look for coherence
in different aspects of the composition.

"It's very good to start having these scientific bases for understanding
music", says Brazil-based composer Heather Jennings. "They provide a fresh
perspective on musical theory."

References

1.    Zanette, D. H.. Preprint, http://xxx.arxiv.org/abs/cs.CL/0406015
(2004).

? Nature News Service / Macmillan Magazines Ltd 2004