Article from UK Guardian

The following article appeared in the Manchester Guardian 11/27 and may
interest you and prompt comments, and thoughts from you: I, for one, would
like to know more - lucy@hour.com http://www.ilhawaii.net/~lucy Start of
article> My tiny fractal hand is frozen - Paul Parsons on the arithmetic than
runs from raga to ragtime,
from kabuki to country-style. SITAR OR the Spice Girls? Your ear can tell
the difference immediately but now science is catching up. Researchers in
Korea have new evidence that cultural differences in music can be
identified numerically, using the machinery of chaos theory. "Chaos" is the
emergence of wildly unpredictable behaviour from seemingly innocent
physics. It is an immediate feature of the world around us, cropping up in
quantum theory, astrophysics, and mathematical economics, as well as the
weather and even the timing of
a dripping tap. Despite apparent randomness, chaos is actually a
well-ordered phenomenon. It is caused by extreme sensitivity of a physical
system to its initial state, meaning that tiny differences become magnified
as the system evolves. Unpredictability arises because
we cannot measure the system accurately enough. This is why weather
forecasting is so hard. Chaos is sifted from randomness in systems by using
what is called "a phase portrait" - a diagram showing how the system evolves
from its starting state. scientists look for regions in the phase portrait
where the evolutionary from many initial states converge. These areas are
known as attractors. For a simple pendulum, the phase portrait is just a
graph if the
pendulum's position against its speed, and the attractor is a circle. But
as complexity increases,
the shape of the attractor becomes more convoluted. Chaotic systems have
fractal attractors. Fractals are disjointed shapes which have the same
appearance when viewed on many different length scales. their complex
structure creates the illusion of randomness. Fractal attractors are
classified by a number, the "dimension",
which increases the level of chaos in the system. Scientists have started
to look for phase portraits of speech and singing. "There is a tradition of
looking for fractal structure in music over the last decade or so" says Ian
Stewart of Warwick University, "in a sense trying to characterise the
'texture' quantitatively." While irregularities in
speech were thought to be produced by simple randomness, evidence soon
emerged that
they were,in fact, caused by chaos in the vocal system. Now a team headed
by Myeong-Hwa Lee, of Seoul national University, has studied the Korean
traditional song Gwansananyungma, the western song La Mamma Morta, and the
pure
note "Si". Plotting the volume of the sound on a phase portrait, they
established the dimension of
the attractor that each song converged to. Like the simple pendulum, the
pure note "Si" has a
roughly circular attractor confirming its single frequency and indicating
non-chaotic behaviour. La Mamma Morta, however , has a more complicated
attractor, with a mildly chaotic dimension of
2.5, while Gwansananyungma has a highly chaotic fractal attractor of 4.4.
It shows that the Korean song is more complex than its western number, which
Lee et al attribute to
the Korean vocal system and singing technique. More importantly, it shows
that voice patterns and
music can be quantified numerically. "All of this work will of benefit to
speech coding and other
technological uses," adds Lee. He now hopes the results, soon to appear in
the Journal of the Acoustical Society of America, will enable him to
construct a detailed mathematical model of speech. End of article>

lucy
http://www.ilhawaii.net/~lucy


SMTPOriginator: tuning@eartha.mills.edu
From: Carl Lumma
Subject: re: Bach? Puhleeze?
PostedDate: 30-11-97 23:15:04
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Ah, the old Bach chestnut...

I'll be back for the 9th annual Christmas Day "Microtonal Bach" radio
broadcast on WKCR 89.9 FM in NYC from 11 am to 3 pm. Perhaps
well-temperament is the origin of polymicrotonality?

Johnny Reinhard
Director
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@idt.net
http://www.echonyc.com/~jhhl/AFMM


SMTPOriginator: tuning@eartha.mills.edu
From: mr88cet@texas.net (Gary Morrison)
Subject: Spelling Checker
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