Additive synthesis is evidently the first technique widely used for analysis and synthesis of audio in computer music [232,233,184,186,187]. It was inspired directly by Fourier theory [264,23,36,150] (which followed Daniel Bernoulli's insights (§G.1)) which states that any sound can be expressed mathematically as a sum of sinusoids. The `term ``additive synthesis'' refers to sound being formed by adding together many sinusoidal components modulated by relatively slowly varying amplitude and frequency envelopes:
and all quantities are real. Thus, each sinusoid may have an independently time-varying amplitude and/or phase, in general. The amplitude and frequency envelopes are determined from some kind of short-time Fourier analysis as discussed in Chapters 8 and 9) [62,187,184,186].
An additive-synthesis oscillator-bank is shown in Fig.10.7, as it is often drawn in computer music [235,234]. Each sinusoidal oscillator  accepts an amplitude envelope (e.g., piecewise linear, or piecewise exponential) and a frequency envelope , also typically piecewise linear or exponential. Also shown in Fig.10.7 is a filtered noise input, as used in S+N modeling (§10.4.3).
Additive Synthesis Analysis
Spectral Envelope Examples