Basics of sound
All sounds are composed of some combination of pure sine waves. Generally, a single "sound" will include a fundamental frequency, and any number of overtones. The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. An overtone is a natural resonance or vibration frequency of a system The frequencies of these overtones are either integer multiples of the fundamental frequency, or integer fractions thereof (subharmonics). Subharmonic frequencies are frequencies below the Fundamental frequency of an Oscillator in a ratio of 1/x This study of how complex waveforms can be alternately represented is covered in Laplace and Fourier transforms. In Mathematics, the Laplace transform is one of the best known and most widely used Integral transforms It is commonly used to produce an easily soluble algebraic This article specifically discusses Fourier transformation of functions on the Real line; for other kinds of Fourier transformation see Fourier analysis and
When natural tonal instruments' sounds are analyzed in the frequency domain (as on a spectrum analyzer), the spectra of their sounds will exhibit amplitude spikes at each of the fundamental tone's harmonics. Frequency domain is a term used to describe the analysis of Mathematical functions or signals with respect to frequency Familiar concepts associated with a Frequency are colors musical notes radio/TV channels and even the regular rotation of the earth Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system See Harmonic series (mathematics for the (related mathematical concept Some harmonics may have higher amplitudes than others. The specific set of harmonic-vs-amplitude pairs is known as a sound's harmonic content.
When analyzed in the time domain, a sound does not necessarily have the same harmonic content throughout the duration of the sound. Time domain is a term used to describe the analysis of mathematical functions or physical signals with respect to Time. Typically, high-frequency harmonics will die out more quickly than the lower harmonics. For a synthesized sound to "sound" right, it requires accurate reproduction of the original sound in both the frequency domain and the time domain.
Percussion instruments and rasps have very low harmonic content, and exhibit spectra that are comprised mainly of noise shaped by the resonant frequencies of the structures that produce the sounds. In Physics, resonance is the tendency of a system to Oscillate at maximum Amplitude at certain frequencies, known as the system's However, the resonant properties of the instruments (the spectral peaks of which are also referred to as formants) also shape an instrument's spectrum (esp. A formant is a peak in the Frequency spectrum of a sound caused by acoustic Resonance. in string, wind, voice and other natural instruments).
In most conventional synthesizers, for purposes of re-synthesis, recordings of real instruments are composed of several components.
These component sounds represent the acoustic responses of different parts of the instrument, the sounds produced by the instrument during different parts of a performance, or the behavior of the instrument under different playing conditions (pitch, intensity of playing, fingering, etc. ) The distinctive timbre, intonation and attack of a real instrument can therefore be created by mixing together these components in such a way as resembles the natural behavior of the real instrument. Nomenclature varies by synthesizer methodology and manufacturer, but the components are often referred to as oscillators or partials. Oscillation is the repetitive variation typically in Time, of some measure about a central value (often a point of Equilibrium) or between two or more different states A higher fidelity reproduction of a natural instrument can typically be achieved using more oscillators, but increased computational power and human programming is required, and most synthesizers use between one and four oscillators by default.
One of the most important parts of any sound is its amplitude envelope. ADSR envelope is a component of many Synthesizers samplers and other Electronic musical instruments. This envelope determines whether the sound is percussive, like a snare drum, or persistent, like a violin string. Most often, this shaping of the sound's amplitude profile is realized with an "ADSR" (Attack Decay Sustain Release) envelope model applied to control oscillator volumes. ADSR envelope is a component of many Synthesizers samplers and other Electronic musical instruments. Apart from Sustain, each of these stages is modeled by a change in volume (typically exponential).
- Attack time is the time taken for initial run-up of the sound level from nil (or blank sustainment) to 100%.
- Decay time is the time taken for the subsequent run down from 100% to the designated Sustain level.
- Sustain level is the steady volume produced when a key is held down.
- Release time is the time taken for the sound to decay from the Sustain level to nil when the key is released. If a key is released during the Attack or Decay stage, the Sustain phase is usually skipped. Similarly, a Sustain level of zero will produce a more-or-less piano-like (or percussive) envelope, with no continuous steady level, even when a key is held. Exponential rates are commonly used because they closely model real physical vibrations, which usually rise or decay exponentially. A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value
Although the oscillations in real instruments also change frequency, most instruments can be modeled well without this refinement. This refinement is necessary to generate a vibrato. Vibrato is a musical effect produced in singing and on musical instruments by a regular pulsating change of pitch, and is used to add expression and vocal-like qualities to
Overview of popular synthesis methods
Subtractive synthesizers use a simple acoustic model that assumes an instrument can be approximated by a simple signal generator (producing sawtooth waves, square waves, etc. The sawtooth wave (or saw wave) is a kind of Non-sinusoidal waveform. A square wave is a kind of Non-sinusoidal waveform, most typically encountered in Electronics and Signal processing. . . ) followed by a filter which represents the frequency-dependent losses and resonances in the instrument body. An audio filter is a type of filter used for processing Sound signals. For reasons of simplicity and economy, these filters are typically low-order lowpass filters. The combination of simple modulation routings (such as pulse width modulation and oscillator sync), along with the physically unrealistic lowpass filters, is responsible for the "classic synthesizer" sound commonly associated with "analog synthesis" and often mistakenly used when referring to software synthesizers using subtractive synthesis. Pulse-width modulation (PWM of a signal or power source involves the Modulation of its Duty cycle, to either convey information over a Oscillator sync is a feature in Synthesizers One Oscillator will restart the period of another oscillator so that they will have the same base frequency Although physical modeling synthesis, synthesis wherein the sound is generated according to the physics of the instrument, has superseded subtractive synthesis for accurately reproducing natural instrument timbres, the subtractive synthesis paradigm is still ubiquitous in synthesizers with most modern designs still offering low-order lowpass or bandpass filters following the oscillator stage. In Sound synthesis, physical modelling synthesis refers to methods in which the Waveform of the Sound to be generated is computed by using a Mathematical
One of the newest systems to evolve inside music synthesis is physical modeling. This involves taking up models of components of musical objects and creating systems which define action, filters, envelopes and other parameters over time. The definition of such instruments is virtually limitless, as one can combine any given models available with any amount of sources of modulation in terms of pitch, frequency and contour. For example, the model of a violin with characteristics of a pedal steel guitar and perhaps the action of piano hammer . . . physical modeling on computers gets better and faster with higher processing.
One of the easiest synthesis systems is to record a real instrument as a digitized waveform, and then play back its recordings at different speeds to produce different tones. This is the technique used in "sampling". Most samplers designate a part of the sample for each component of the ADSR envelope, and then repeat that section while changing the volume for that segment of the envelope. This lets the sampler have a persuasively different envelope using the same note. . See also: Sample-based synthesis. Sample-based synthesis is a form of audio synthesis that can be contrasted to either Subtractive synthesis or Additive synthesis.
Synthesizer basics
There are three major kinds of synthesizers, analog, digital and software. An analog synthesizer is a Synthesizer that uses analog circuits and Analog computer techniques to generate sound electronically A digital synthesizer is a Synthesizer that uses Digital signal processing (DSP techniques to make musical sounds A software synthesizer also known as a softsynth or virtual instrument is a Computer program for Digital audio generation In addition there are synthesizers that rely upon combinations of those three kinds, known as hybrid synthesizers.
There are also many different kinds of synthesis methods, each applicable to both analog and digital synthesizers. These techniques tend to be mathematically related, especially frequency modulation and phase modulation.
- Subtractive synthesis
- Additive synthesis
- Granular synthesis
- Wavetable synthesis
- Frequency modulation synthesis
- Phase distortion synthesis
- Physical modeling synthesis
- Sample-based synthesis
- Subharmonic synthesis
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