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Sound Synthesis Tutorial

:: Types of synthesis

Different types of synthesis methods can be found on the vast range of synthesizers that were and are constantly produced. With the advent of digital technologies, synthesizers have increased in complexity and new forms of generating the sound have appeared. Let's see some of the newer and older methods of generating sound electronically:

- Additive synthesis: by adding one or more basic waveforms together 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 complicated. The process of additive synthesis is also referred to as summing the waveforms and harmonics, a method that adopts Fourier analysis, describing the representation of a sound's frequency components as a sum of pure sinusoidal waves. An analysis of a sound's frequency components 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, the filters are crucial in subtractive synthesis and the better the filters and the wider the choice of them available, 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 analog oscillators, so generally it has been 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 prerecorded digitized audio waveforms of real or synthetic instruments. The waveforms are then stored in memory and played back at varying speeds for the corresponding notes played, and 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 that can often be lush and interesting. The synthesizers that 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 is 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 kind of synthesis was used in the Korg Wavestation synthesizers, that were fitted with a two-dimensional envelope, managed through a joystick, and a wave sequencing system, that 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 just intented to open a bit the mind for any further explanations, 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 the beginner 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. Let's see firstly how oscillators work:

Usually an analogue synthesizer will have more than one oscillator (OSC) and a low frequency oscillator (LFO). Obviously, the larger the equipment of oscillators, the larger the timbral possibilities. An oscillator creates a single periodic waveform at a certain frequency, or what is the same, a tone. The timbre of this raw tone will be different depending on the type of the waveform and the pitch is given by the frequency. As is easy to assume, these oscillators work in the range of frequencies that the human hearing can perceive.

Separated from the standard oscillators is the low frequency oscillator, also known as the modulation generator. Modulation is the process by which a waveform is used to alter or shape the properties of another waveform, which in the case of sound synthesis can produce dramatic changes in sound. So the low frequency oscillator, which usually operates at a frequency below 10 Hz, out of human hearing range, produces a waveform that is combined with the waveform produced by a standard oscillator, greatly increasing the timbral possibilities. Low frequency oscillators can be used to modulate another modules as well, for example, they might be used to move the volume level of a voltage controlled amplifier (VCA) up and down, creating a tremolo effect on the sound.

In the beginning of this tutorial I explained the two basic characteristics that 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 the width of the pulses can be modified (modulated) in relation with the width (lenght) of the periods. And obviously, what I am - graphically - referring to as width is actually time. The point on 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 it is widely present in analogue synthesizers.

Let's 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), which are available for download in this website. You can notice the LFO section in the oscillator bank of the MiniMogue and the pulse width sliders in the oscillator bank of the Arppe2600. See how in this last one, the oscillators are labelled as VCO (voltage controlled oscillator); in more modern synthesizers this is often replaced by DCO (digitally controlled oscillator).

MiniMogue Luxus Oscillators Arppe2600 Oscillators

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