This article is addressed both to psychologists interested in theories of pitch and timbre perception and to musicians interested in exploring pitch and/or timbral structures on a computer. A central assertion of the article is that these two enterprises are closely related and that both have been dominated by Fourier-analytic metaphors. I claim that Fourier analysis provides an inadequate model for both sound perception and computer analysis/synthesis of sound. In particular, it has led us to misconceive the relationship between musical pitch and timbre. Rather than modify or augment a Fourier-based perspective on these matters, I propose a different way of thinking about pitch and timbre that highlights their differences from one another and suggests different mechanisms for perceiving them. A view of musical pitch is summarized that treats pitches not as analyzable in isolation but as specifiable only with respect to a larger structure that, in Western music anyway, corresponds to a mathematical group. Following this, a view of musical timbre is summarized that links timbre perception with the dynamic processes by which sound is created, processes that are encountered and initiated outside as well as inside musical contexts and that never lead to the static-spectrum idealization of Fourier analysis except in degenerate cases. Implications of these views for creation of musical sounds by computer are also discussed.