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Additive synthesis is a technique of audio synthesis which creates musical timbre. For other uses, see Music (disambiguation). ...
In music, timbre, or sometimes timber, (from Fr. ...
The timbre of an instrument is composed of multiple harmonics or partials, in different quantities, that change over time. Additive synthesis emulates such timbres by combining numerous waveforms pitched to different harmonics, with a different amplitude envelope on each, along with inharmonic artifacts. 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 that changes over time. This article is about the components of sound. ...
It has been suggested that pulse amplitude be merged into this article or section. ...
A numerically controlled oscillator or digitally controlled oscillator (DCO) is an electronic system for synthesizing a range of frequencies from a fixed timebase. ...
Theory
The concept behind additive synthesis is directly related to work done by the French mathematician Joseph Fourier. Fourier discovered that periodic functions are formed by the summation of an infinite series. Following this, it was established that all periodic 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: Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. ...
Discrete time is non-continuous time. ...
![s[n] = frac{1}{2} a_0[n] + sum_{k=1}^{k_{max}} a_k[n] cosleft( frac{2 pi f_0}{F_mathrm{s}} k n right)-b_k[n] sinleft( frac{2 pi f_0}{F_mathrm{s}} k n right)](http://upload.wikimedia.org/math/8/7/3/873b1a57717bee700d9cf9a0300f648a.png) or ![s[n] = frac{1}{2} a_0[n] + sum_{k=1}^{k_{max}} r_k[n] cosleft( frac{2 pi f_0}{F_mathrm{s}} k n + varphi_k[n] right)](http://upload.wikimedia.org/math/6/f/c/6fc94d9b9af576203814bafd7f98711b.png) where ![a_k[n] = r_k[n] cos left( varphi_k[n] right) quad b_k[n] = r_k[n] sin left( varphi_k[n] right) ,](http://upload.wikimedia.org/math/d/a/2/da2ed65cf15fb963ff7b7e8f65c3837d.png)
and Fs is the sampling frequency, f0 is the fundamental frequency, and kmax < floor(Fs/(2 f0)) is the highest harmonic and below the Nyquist frequency. The DC term is generally undesirable in audio synthesis, so the a0 term can be removed. Introducing time varying coefficients rk(n) allows for the dynamic use of envelopes to modulate oscillators creating a "quasi-periodic" waveform (one that is periodic over the short term but changes its waveform over the longer term). The Nyquist frequency, named after Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system. ...
Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ...
Additive synthesis can also create non-harmonic sounds (which have non-periodic waveforms) if the individual partials are not all having a frequency that is an integer multiple of the same fundamental frequency. With time-varying and general (not necessarily harmonic) frequencies of fk[n], (the instantaneous frequency of the kth partial at the time of sample n) the definition of the synthesized output would be: This article is about the components of sound. ...
An overtone is a sinusoidal component of a waveform, of greater frequency than its fundamental frequency. ...
Vibration and standing waves in a string, The fundamental and the first 6 overtones The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. ...
In signal processing, for a sinusoidal signal is called the angular frequency (usually radians/second) and is the frequency (usually in hertz or cycles/second). ...
![s[n] = frac{1}{2} a_0[n] + sum_{k=1}^{k_{max}} a_k[n] cosleft( frac{2 pi}{F_mathrm{s}} sum_{i=1}^{n}f_k[i] right) - b_k[n] sinleft( frac{2 pi}{F_mathrm{s}} sum_{i=1}^{n}f_k[i] right)](http://upload.wikimedia.org/math/f/4/8/f48c4622d0597caa04c0c226f0d8fa76.png) or ![s[n] = frac{1}{2} a_0[n] + sum_{k=1}^{k_{max}} r_k[n] cosleft( frac{2 pi}{F_mathrm{s}}sum_{i=1}^{n}f_k[i] + varphi_k[n] right)](http://upload.wikimedia.org/math/b/0/6/b0631c948074d08dfd5809b3387c9ffb.png) where - .
If fk[n] = k f0, with constant f0, all partials are harmonic, the synthesized waveform is quasi-periodic, and the more general equations above reduce to the simpler equations at the top. For each non-harmonic partial, the phase term φk[n] can be absorbed into the instantaneous frequency term, fk[n] by the substitution:
![f_k[n] leftarrow f_k[n] + frac{F_mathrm{s}}{2 pi}left( varphi_k[n]-varphi_k[n-1] right)](http://upload.wikimedia.org/math/9/a/2/9a2c93c051f1a66cda5321bf63f2c4bc.png) If that substitution is made, all of the φk[n] terms can be set to zero with no loss of generality (retaining the initial phase value at s[0]) and the expressions of non-harmonic additive synthesis can be simplified (with the additional elimination of the DC term) to ![s[n] = sum_{k=1}^{k_{max}} r_k[n] cosleft( frac{2 pi}{F_mathrm{s}}sum_{i=1}^{n}f_k[i] + varphi_k[0] right)](http://upload.wikimedia.org/math/0/e/d/0ede40becc17997773dc870b9f45d473.png) . If this constant phase term (at time n=0) is expressed as ![varphi_k[0] = frac{2 pi}{F_mathrm{s}}sum_{i=-infty}^{0}f_k[i]](http://upload.wikimedia.org/math/4/8/3/4835e9b5695984f27e20d45aeb2a6f1f.png) , the general expression of additive synthesis can be further simplified: ![s[n] = sum_{k=1}^{k_{max}} r_k[n] cosleft( frac{2 pi}{F_mathrm{s}}sum_{i=-infty}^{n}f_k[i] right)](http://upload.wikimedia.org/math/a/6/6/a66c80b57c865a6853c7535648daa392.png)
Additive synthesizers A classic additive synthesizer was the Synclavier. Certain organ pipes, which create sinusoidal waves (mostly flute pipes) can be combined in the manner of additive synthesis. However, pipes, which generate other types of wave forms (for example square wave generating clarinet stops)are not suited to this purpose. 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, Image-Line Morphine, the VirSyn Cube, White Noise WNAdditive, and the ConcreteFX softsynth Adder. Another instrument with this capability is the Hammond organ, which uses nine drawbars to control the harmonics. The Hammond was invented in 1935 as a substitute for the much bulkier and expensive pipe organ. Synclavier I The Synclavier System was an early digital synthesizer and sampler, manufactured by New England Digital. ...
The Kawai Musical Instruments Mfg. ...
The Kawai K5000 is a digital synthesizer set manufactured by Kawai around 1996 available in three different versions. ...
A software synthesizer, also known as a softsynth or virtual instrument is a computer program for digital audio generation. ...
Calculated spectrum of a generated approximation of white noise White noise is a random signal (or process) with a flat power spectral density. ...
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. Wavetable synthesis is used in digital musical instruments (synthesizers) to produce natural tone-like sounds. ...
An overtone is a sinusoidal component of a waveform, of greater frequency than its fundamental frequency. ...
Approximate harmonic overtones on a string An overtone is a natural resonance or vibration frequency of a system. ...
This article is about the components of sound. ...
Vibration and standing waves in a string, The fundamental and the first 6 overtones The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. ...
A bell is a simple sound-making device. ...
Wavetable synthesis is used in digital musical instruments (synthesizers) to produce natural tone-like sounds. ...
Additive resynthesis As demonstrated by software such as SPEAR, it is possible to analyse the frequency components of a recorded sound and then resynthesize a representation of the sound using additive techniques. By calculating the frequency and amplitude weighting of discrete partials in the frequency domain (typically using a fast Fourier transform), an additive resynthesis system can construct an equally weighted sinusoid at the same frequency for each partial. The Fast Fourier Transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. ...
Because the sound is represented by a bank of oscillators inside the system, a user can make adjustments to the frequency and amplitude of any set of partials. The sound can be 'reshaped' - by alterations made to timbre or the overall amplitude envelope, for example. A harmonic sound could be restructured to sound inharmonic, and vice versa.
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