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.
On the left, Voss and Clarke plot Log(frequency) on the x-axis, vs Log(loudness fluctuation power spectrum). The graphs are (a) Scott Joplin piano rags, (b) a classical radio station, (c) a rock radio station, and (d) a news and talk radio station. Below 1 Hz, the match to the reference 1/f graph is good. For (a), the signal was averaged over an entire recording. Joplin rags have a strong rhythm, so the power spectrum has a considerable amount of structure between 1 and 10 HZ. Below 1 Hz, we are detecting long-range correlations in the music, and the spectrum agrees well with 1/f. The rock graph (c) begins to flatten out on time scales longer than a single composition. Classical compositions tend to be longer; the data presented do not extend beyond the average length.
On the right is a similar plot for the pitch fluctuation power spectrum, a rough indicator of melody. The radio stations are (a) classical, (b) jazz and blues, (c) rock, and (d) news and talk, all averaged over about 12 hours. Again, the match with 1/f is good, though the talk station exhibits peaks at the time scale of a single sound, and at the time scale of the average time a person speaks..
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Voss extended this analysis other types of music, crossing cultural divides. On the left are pitch power spectrum plots for (a) Ba-Benzele Pygmies, (b) Japanese traditional music, (c) Indian ragas, (d) Russian folk songs, and (e) American blues. On the right are pitch power spectra for (a) Medieval music, (b) Beethoven's third symphony, (c) Debussy piano pieces, (d) a composition of R. Strauss, and (e) a comoposition by the Beatles. Again, the 1/f match is quite good.
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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.
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