Additive synthesis

Additive synthesis is a technique of audio synthesis which creates musical timbre.

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Since different instruments' timbre is composed of varying amounts of harmonics that change over time, with respect to a base tone, additive synthesis emulates this behavior similarly by creating a different amplitude envelope on each harmonic, as well as adding non-harmonic artifacts aiming to result in a realistic timbre recreation.

Related Topics:
Harmonic - Amplitude

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Usually this involves a bank of oscillators tuned to multiples of the base frequency. Often, each oscillator has its own customizable volume envelope, creating a realistic, dynamic sound.

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The concept behind additive synthesis may be recalled to discoveries by the French mathematician Joseph Fourier. Fourier discovered that discontinuous functions are formed by the summation of an infinite series. Following this, it was established that all signals, when represented as a mathematical function, can be composed as a sum of sine functions ( sin(x) ) of various frequencies. More rigorously, any periodic sound in the discrete time domain can be synthesized as follows:

Related Topics:
Joseph Fourier - Discrete time

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:s(n) = rac{1}{2} a_0(n) + sum_{k=1}^{k_{max}} a_k(n) cosleft( rac{2 pi f_0}{F_s} k n ight)-b_k(n) sinleft( rac{2 pi f_0}{F_s} k n ight)

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or

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:s(n) = rac{1}{2} a_0(n) + sum_{k=1}^{k_{max}} r_k(n) cosleft( rac{2 pi f_0}{F_s} k n +arphi_k(n) ight)

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where

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:a_k(n) = r_k(n) cos left( arphi_k(n) ight) ,, b_k(n) = r_k(n) sin left( arphi_k(n) ight) ,

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and F_s , is the sampling frequency, f_0 , is the fundamental frequency, and k_{max}

Related Topics:
Nyquist frequency - DC - Harmonic - Partial - Fundamental frequency

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A classic additive synthesizer was the Synclavier. The pipe organ may also qualify as an additive synthesizer because its pipes generate sine waves when blown, which are then added to each other to generate tones. More contemporary popular implementations of additive synthesis include the Kawai K5000 series of synthesizers in the 1990s and, more recently, software synthesizers such as the Camel Audio Cameleon and the VirSyn Cube.

Related Topics:
Synclavier - Kawai - 1990s - Software synthesizer - Camel Audio - VirSyn

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It has been shown in Wavetable Synthesis 101, A Fundamental Perspective, that wavetable synthesis is equivalent to additive synthesis in the case that all partials or overtones are harmonic (that is all overtones are at frequencies that are an integer multiple of a fundamental frequency of the tone as shown in the equation above). Not all musical sounds have harmonic partials, (e.g. bells) but many do. In these cases, an efficient implementation of additive synthesis can be accomplished with wavetable synthesis. Group additive synthesis is a method to group partials into harmonic groups (of differing fundamental frequencies) and synthesize each group separately with wavetable synthesis before mixing the results.

Related Topics:
Wavetable synthesis - Partial - Overtone - Harmonic - Fundamental frequency - Bell

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