Klarinet Archive - Posting 000457.txt from 2004/06

From: Joseph Wakeling <joseph.wakeling@-----.net>
Subj: Re: [kl] "Tunes create context like language"
Date: Mon, 28 Jun 2004 10:40:00 -0400

John Dablin wrote:

>It contains a link to the original paper, which I haven't read
>
To put it on the list: the original paper is at
http://arxiv.org/abs/cs.CL/0406015 The "arXiv" is a scientific preprint
archive where many from physics, maths, computer science and biology put
preview versions of papers.

>I did think that it was a pretty bold claim to make based on analysing only three pieces of music.
>
>
I think the analysis performed is sufficiently "generic" that it seems
likely that it applies to a wide variety of music.

He looks at the number of occurrences of individual pitches as a
function of their "rank" (rank 1 meaning most frequently occurring
pitch, rank 2 second most frequent, ...) and shows that in all these
pieces it follows a particular function. By "pitch" he does not mean
merely note name (A, B, C, ...) but octave as well (this is not
explicitly stated but it's implicit in the ranges shown on his figures).

This is identical to an analysis of text performed by G. K. Zipf in the
1930s, looking at the number of occurrences of a word in a text,
compared to its rank---and the same function emerges in music. This
function is known as "Zipf's Law" and is one of the most well-known
functions among scientists dealing with complex systems and
interdisciplinary science.

The functions are all of the same type for all the different pieces, but
the exponent for atonal music---the Schoenberg---is significantly
different from the others. "Exponent" means basically a number which
controls the behaviour of the function without changing its fundamental
character.

What his analysis suggests is that in atonal work, the number of "new"
notes (i.e. notes not used before) grows at a much greater rate, as the
piece progresses, than in a tonal piece of music. This seems to me to
be consistent with our musical sense that tonal music operates in a much
more restricted "pitch space".

It does seem to me that the analysis needs to be considerably expanded
to take into account different types of modern music. For example, the
result above for Schoenberg might be a peculiarity of the sort of serial
music where all notes have similar "status", but it might not be so for
"free atonal" pieces like the Berio Sequenza IXa. The main problem here
is translating music into a form where the appropriate data can be
easily extracted. Zanette has used MIDI versions of the music to do his
analysis, where it's easy to extract the different notes in the piece.
Such MIDI data doesn't necessarily exist for a wide enough range of
music to be able to do an extensive enough analysis at present.

-- Joe

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