### Additive Synthesis (Early Sinusoidal Modeling)

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:(11.17) |

where

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 [166] 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).

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Additive Synthesis Analysis

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Spectral Envelope Examples