By Orrin Keepnews, Bill Grauer

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Extra resources for A Pictorial History of Jazz: People and Places from New Orleans to Modern Jazz

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An interesting phenomenon arises when the partials are related to more than one harmonic series. Consider the two sounds: (i) With partials at 600, 800, and 1000 Hz (ii) With partials at 800, 1000, and 1200 Hz 36 2 The Science of Sound Both have a clear virtual pitch at 200 Hz. The first contains the third, fourth, and fifth partials, whereas the second contains the fourth, fifth, and sixth partials. Sound example [S: 6] begins with the first note and ascends by adding 20 Hz to each partial. Each raised note alternates with a sine wave at the appropriate virtual pitch.

2 What Is a Spectrum? 19 fundamental (=first partial) second partial third partial magnitude fourth partial ... f 2f 3f 4f 5f frequency 6f Fig. 6. Vibrations of an ideal string and its spectrum. Because the string is fixed at both ends, it can only sustain oscillations when a half period fits exactly into its length. , as shown in the spectrum, which plots frequency verses magnitude. Guitar Pluck: Experiment Surely you didn’t think you could read a whole chapter called the “Science of Sound” without having to experiment?

This ambiguity of virtual pitch is loosely analogous to Rubin’s well-known face/vase “illusion” of Fig. 12 where two white faces can be seen against a black background, or a black vase can be seen against a white background. It is difficult to perceive both images simultaneously. Similarly, the virtual pitch of the fourth note can be heard as 215 when part of an ascending sequence, or it can be heard as 171 when surrounded by appropriate descending tones, but it is difficult to perceive both simultaneously.

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