source file: mills3.txt Date: Sun, 30 Nov 1997 13:48:30 +0100 Subject: Article from UK Guardian From: Charles Lucy 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? 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