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Most composers who use mathematics to construct music do not intend it to be heard. Tom Johnson does. When he performed his piano cycle "Counting Keys" in Cologne in 1986 he began each piece by counting out its structure in numbers so that the audience could follow the logic of the music. A particularly appreciative member of that audience was John Cage. One might wonder what the famous advocate of indeterminacy could find interesting in this exactly determined, highly predictable music, until one considers his favourite definition of art as the imitation of nature in her manner of operation. Much of what we see in nature, whether flowers, sea-shells, ice-crystals or patterns of growth and decay, is determined by mathematical processes.