Introduction to Computer Music: Volume One

7. What are wave shapes and spectral content? | page 2

Most acoustic instruments not in the ‘noise’ category produce some combination of fundamental and harmonic partials. Bells are a category of sound that produces inharmonic partials, so called, because they do not correlate to the harmonic partials above.

The collection of frequencies produced by a waveform are prime contributors to its spectrum (pl. spectra). For a periodic waveform, the shape of the wave determines not only the frequency of the partials, but also their relative strength, another important factor of timbre.

In the 18th Century, a mathematician named John Baptiste Fourier determined that:

1) all complex periodic waves may be expressed as the sum of a series of sinusoidal waves
2) that these waves are all harmonics of the fundamental and
3) that each harmonic has its own amplitude and phase (which we have not discussed yet).

With the advent of computers and digitized audio data, it has become routine to perform Fourier analysis on existing sound to break it down into its component frequencies along with their specific amplitudes. It has also become commonplace to 'reverse engineer' this process and create complex timbres by carefully mixing sine waves in a process called additive synthesis, practiced masterfully by composer Jean Claude Risset amongst many others.

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