We have already mentioned inverse-FFT synthesis as a means of greatly decreasing the cost of additive synthesis relative to a full-blown bank of sinusoidal oscillators. This section summarizes a number of more specialized methods which reduce the computational cost of additive synthesis and are widely used.
For periodic sounds, the sinusoidal components are all harmonics of some fundamental frequency. If in addition they can be constrained to vary together in amplitude over time, then they can be implemented using a single wavetable containing one period of the sound. Amplitude shaping is handled by multiplying the output of the wavetable look-up by an amplitude-envelope generated separately [186,167]. Using interpolation (typically linear, but sometimes better), the table may be played back at any fundamental frequency, and its output is then multiplied by the amplitude envelope shared by all harmonics. (The harmonics may still have arbitrary relative levels.) This form of ``wavetable synthesis'' was commonly used in the early days of computer music. This method is still commonly used for synthesizing harmonic spectra.G.8
Note that sometimes the term ``wavetable synthesis'' is used to refer to what was originally called sampling synthesis: playback of sampled tones from memory, with looping of the steady-state portion to create an arbitrarily long sustain [165,27,107,193]. This book adheres to the original terminology. For sampling synthesis, spectral phase-modifications (Chapter 8) can be used to provide perfectly seamless loops .
The basic idea of group-additive synthesis [130,69] is to employ a set of wavetables, each modeling a harmonic subset of the tonal components making up the overall spectrum of the synthesized tone. Since each wavetable oscillator is independent, inharmonic sounds can be synthesized to some degree of approximation, and the amplitude envelopes are not completely locked together. It is important to be aware that human audio perception cannot tell the difference between harmonic and inharmonic partials at high frequencies (where ``high'' depends on the fundamental frequency and timbre to some extent). Thus, group-additive synthesis provides a set of intermediate points between wavetable synthesis and all-out additive synthesis.
Further Reading, Additive Synthesis
Nonparametric Spectral Peak Modeling