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Auditory Perception

In the course of this book I have made extensive use of pictures. So why not also sounds? One issue—beyond the obvious fact that sounds cannot be included directly in a printed book—is that while one can study the details of a picture at whatever pace one wants, a sound is in a sense gone as soon as it has finished playing.

But everyday experience makes it quite clear that one can still learn a lot by listening to sounds. So what then are the features of sounds that our auditory system manages to pick out?

At a fundamental level all sounds consist of patterns of rapid vibrations. And the way that we hear sounds is by such vibrations being transmitted to the array of hair cells in our inner ear. The mechanics of the inner ear are set up so that each row of hair cells ends up being particularly sensitive to vibrations at some specific frequency. So what this means is that what we tend to perceive most about sounds are the frequencies they contain.

Musical notes usually have just one basic frequency, while voiced speech sounds have two or three. But what about sounds from systems in nature, or from systems of the kinds we have studied in this book?

There are a number of ways in which one can imagine such systems being used to generate sounds. One simple approach illustrated below is to consider a sequence of elements produced by the system, and then to take each element to correspond to a vibration for a brief time—say a thousandth of a second—in one of two directions.

So what are such sounds like? If the sequence of elements is repetitive then what one hears is in essence a pure tone at a specific frequency—much like a musical note. But if the sequence is random then what one hears is just an amorphous hiss.

So what happens between these extremes? If the properties of a sequence gradually change in a definite way over time then one can often hear this in the corresponding sound. But what about sequences that have more or less uniform properties? What kinds of regularities does our auditory system manage to detect in these?

A sequence of discrete elements and a possible corresponding waveform for a sound.

From Stephen Wolfram: A New Kind of Science [citation]