Repitition of
notes in music create semantic meaning
Everfelt 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."
