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Tutorial about synthesis of sound: types of synthesis and introduction to analogue synthesis (oscillators).

Types of synthesis

Synthesis methods greatly vary throughout the vast range of synthesizers that have been developed since the colorful 1960s. With the advent of digital technology the complexity of synthesizers increased and new forms of generating sound appeared. The following paragraphs list the methods most commonly used for generating sound electronically; these are related to either analogue or digital technology, and may be associated to certain music genres as well.

- Additive synthesis: by adding together one or more basic waveforms and their harmonics, a complex waveform can be created. However, an enormous amount of harmonics are needed to create a simple sound and therefore this type of synthesis can be complex. The process of additive synthesis is also referred to as summing the waveforms and harmonics, a method which involves Fourier analysis, describing the representation of components of a sound's frequency as a sum of pure sinusoidal waves. An analysis of the components of sound's frequency is taken at a steady state to give an approximation of that sound's spectrum. As most natural sounds are spectrally dynamic, one single Fourier analysis could not possibly represent a sound in sine waves. By 'windowing', a Fast Fourier Transform (FFT) takes several of these approximations and strings them together to better predict a sound's spectrum over time.

- Subtractive synthesis: this method involves the generation of complex waveforms and a subsequent filtering of certain frequencies to achieve the desired sound. Therefore filters are crucial in subtractive synthesis, and the better they are and the wider the available range of them is the better the end result can be. Subtractive synthesis is the most common type of synthesis used in analogue, classic synthesizers from the 1970s.

- Frequency modulation (FM) synthesis: in this method the output of an oscillator (modulator) is used to modulate the frequency of another oscillator (carrier). These oscillators are called operators and FM synthesizers usually have four or six of them. Algorithms are predetermined combinations of routings of modulators and carriers. FM synthesis is not generally feasible using analogue oscillators so it has been usually digitally implemented, being the basis of the early generations of digital synthesizers, such as the Yamaha DX7 from the 1980s. FM synthesis can produce sophisticated and interesting sounds, being very good for creating metallic sounds.

- Physical modelling (PM or PHM) synthesis: this method simulates the physical properties of natural instruments or any sound by using complex mathematical equations in real time, requiring huge processing power.

- Linear arithmetic (LA) synthesis: this method takes short-attack sampled waveforms (PCM) and combines them with synthesized sounds that form the body and tail of the new sound. The sound is finally processed with filters, envelope generators and other systems.

- Wavetable synthesis: this method is used in certain digital synthesizers to implement a restricted form of real-time additive synthesis. This form of synthesis is fundamentally based on periodic reproduction of an arbitrary, single-cycle waveform. The distinction to other synthesis methods employing single-cycle waveforms is that multiple single-cycle waveforms are used while one or several wave modulators control the change between those multiple waveforms or mixtures thereof. Wavetable synthesis can be an efficient realization of additive synthesis in the case where all overtones are harmonic. However, unlike additive synthesis where each harmonic is generated and added together during the actual synthesis, in wavetable synthesis the waveform is precomputed from the harmonics and stored as wavetables that are later used during synthesis.

- Sample-based synthesis: this method uses pre-recorded digitized audio waveforms of natural or synthetized instruments. The waveforms are then stored in a memory and played back at varying speeds, corresponding to the notes played, and they usually have a looped segment which allows to play sustained notes. Using envelopes and modulators, these waveforms can be processed and layered to form complex sounds which can be often lush and interesting. The synthesizers which use this form of synthesis are widely known as samplers.

- Granular synthesis: in this method tiny events of sound, called grains or clouds, are manipulated to form new complex sounds. By using varying frequencies and amplitudes of the sonic components, and by processing varying sequences and durations of these grains, a new complex sound can be formed.

- Advanced vector (AV) synthesis: this method uses the combination and processing of digital waveforms. By using PCM samples, effects and filtering, stunning sounds can be created, from lush and evolving pads to strange stepped sequences. This type of synthesis was used in the Korg Wavestation synthesizer, which was fitted with a two-dimensional envelope, controlled through a joystick, and a wave sequencing system, which could play a sequence of PCM samples in a rhytmic and/or crossfaded fashion. The idea was to be able to crossfade two or more waveforms by using the joystick.

This simple introduction to the world of sound synthesis is intended just to open the mind for any further explanation, since this tutorial will cover only the method of subtractive synthesis, commonly used in analogue synthesizers (and for this reason also known as analogue synthesis). The study of this kind of synthesis is an excellent way of introducing beginners into the basic knowledge of sound synthesis. Understanding the components and functions included in any analogue synthesizer is fundamental for learning how to program our own sounds.

:: Introduction to analogue synthesis - Oscillators

As aforementioned, analogue (subtractive) synthesis involves the generation of complex waveforms and a subsequent filtering of certain frequencies to achieve the desired sound. Because of that, oscillators and filters are essential components in analogue synthesizers. To begin with, let us see how oscillators do work:

Usually, an analogue synthesizer will have more than one oscillator (OSC) and a low frequency oscillator (LFO). Obviously, the wider the set of oscillators is the larger the range of timbral possibilities is. An oscillator creates a single periodic waveform at a certain frequency; this is called a tone. The timbre of this raw tone depends on the type of waveform used and the pitch is given by the frequency. As it is easy to assume, oscillators work in the range of frequencies that the human hearing can perceive.

Apart from standard oscillators is the low frequency oscillator, also known as the modulation generator. Modulation is the process through which a waveform is used to alter or shape the properties of another waveform, which can produce dramatic changes in sound. The low frequency oscillator, which usually operates at a frequency below 10 Hz, outside of human hearing range, produces a waveform which is combined with the waveform produced by a standard oscillator; this greatly increases the timbral possibilities of an analogue synthesizer. Low frequency oscillators can be used as well for modulating another modules; for example, they might be used to cyclically adjust the volume level of a voltage controlled amplifier (VCA) up and down, creating so a tremolo effect on the sound.

At the beginning of this tutorial I explained the two basic characteristics which define a waveform: frequency and amplitude. It is easy to understand that frequency determines the periods of the waveform, which is the time that one cycle takes to complete. Having seen this, it is time to learn about another characteristic of waveforms, which is known as pulse width. Every waveform is formed by higher values (peaks) and lower values (valleys) that sequentially repeat on every cycle. What I have referred to as peaks in a wave are called pulses, and their width can be modified (modulated) in relation with the width (lenght) of periods. And obviously, what I am - graphically - referring to as width is actually time. The point of all of this is that altering this property of waveforms is useful as well for achieving additional timbral variations; this technique is called pulse width modulation (PWM) and is widely present in analogue synthesizers.

Let us see now two pictures that show the oscillator banks of two different virtual synthesizers built after well known classics: the MiniMogue VA (left) and the Arppe2600 VA (right). We can see the LFO section in the oscillator bank of the MiniMogue VA and the pulse width sliders in the oscillator bank of the Arppe2600 VA. In this latter we can see how the oscillators are labelled as VCO (Voltage Controlled Oscillator); in more modern synthesizers this is often replaced by the label DCO (Digitally Controlled Oscillator).

MiniMogue Luxus VST oscillator bank Arppe2600 VA VST oscillator bank

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