10.9 Musical examples

Curtis Roads - Eleventh Vortex (2001)

Curtis Roads, a pioneer of granular synthesis, composed some of the earliest and most influential music built entirely from grains. Eleventh Vortex is a dense cloud of thousands of tiny sonic particles, exactly the granular textures of this chapter taken to an extreme.

Aphex Twin - Equation (1999)

The track’s official title is not a word but a mathematical equation:

\[\Delta M_i^{-1} = -\alpha \sum_{n=1}^{N} D_i[n]\left[\sum_{j \in C[i]} F_{ji}[n-1] + F\mathrm{ext}_i[n^{-1}]\right]\]

The music itself hides a visual surprise: near the end, Richard D. James’s face is drawn directly into the spectrogram, visible only when you view the sound in the time-frequency domain. It is a playful demonstration that the spectrogram is a genuine, invertible representation of sound, and that spectral processing runs both ways.