Voss and Clarke

Many electronic devices are known to exhibit 1/f noise.

As a graduate student at Berkeley, Richard Voss was studying this problem, using signal-processing equipment and computers to produce the power spectrum of the signal from a semiconductor sample.

When one sample had burned out and another was being prepared, Voss plugged his signal-analyzing equipment into a radio and computed the power spectrum.

Amazingly, a 1/f spectrum appeared.

Voss changed radio stations and repeated the experiment - another 1/f distribution.

Classical, jazz, blues, and rock all exhibited 1/f distributions.

Even radio news and talk shows gave (approximate) 1/f distributions.

These results are reported in Voss and Clarke.

Here are two sets of examples. Click the pictures for details.

Many examples of Western music - meaning music of Europe and North America, not cowboy music - exhibit 1/f behavior. Music from several cultures - African, Japanese, Indian, and Russian - and a range of times - Medieval through the Beatles - exhibit 1/f behavior.

Voss uses these observations eloquently to bring closure to one of the classical Greek theories of art.

The Greeks believed art imitates nature, and how this happens is relatively clear for painting, sculpture, and drama.

Music, though, was a puzzle.

Except for rare phenomena such as aeolian harps, few processes in Nature seem musical.

Voss uses the ubiquity of 1/f noise to assert music mimics the way the world changes with time.

To emphasize how this is a time fractal, we mention that the correlation of a note with the previous ten notes is the same as the correlation with the previous 100 notes, and is the same as the correlation with the previous 1000 notes, ... . There is a self-similarity of the correlations.