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Tutorial about synthesis of sound: introduction to analogue synthesis (envelope generator) and theory on the synthesis of sound (filters).

Introduction to analogue synthesis - Envelope generator

A way of controlling signals within a synthesizer is by using a module called envelope generator (EG). When receiving an "on" gate signal, the envelope generator sends a new signal which can be used to control another module in the synthesizer. Analogue synthesizers usually have two envelope generators: one which controls the voltage controlled filter (VCF) and another one which controls the voltage controlled amplifier (VCA). In the first instance, the envelope modifies the timbre of sound over time by controlling the cut-off frequency of the VCF; in the second instance, the envelope modifies the amplitude (volume) of sound over time to create the natural dynamic movement of a sound. In the second chapter of this tutorial I covered the concept of ADSR envelope; in fact, the largest part of envelope generators work through the principle of ADSR (Attack - Decay - Sustain - Release).

In the following pictures we can see the ADSR controls present in the control panels of the MiniMogue VA (left) and the FreeMoog (right) virtual synthesizers. In the first instance, the ADSR control of the filter is labelled as Filter Contour while the ADSR control of the amplifier is labelled as Loudness Contour. In the second instance the control layout is quite similar but Release is implemented only as an on/off feature.

MiniMogue Luxus filter ADSR

FreeMoog filter ADSR

We will deal now with triggers and gates, the components which control how the signal is sent from the keyboard to the envelope generators. When we press a key in the keyboard a trigger sends a signal to the envelope generators, so these can start to shape the signal that the oscillators have started to generate. A gate is opened, which will keep the envelope acting as long as the key is pressed (sustained); then, when the key is released a trigger will close the gate. This means that the opening of a gate is related to Attack whereas its closure is related to Release.

As a practical example of this topic, let us imagine that we have programmed a pad sound in our synthesizer and adjusted in a certain way the envelopes for amplitudes and frequencies. When pressing a key in the keyboard the sound would start to grow in amplitude, due to the ADSR of the VCA, while at the same time the sound would start to get brighter (or any other effect which could have been programmed), due to the ADSR of the VCF. While keeping pressed the key the sound would remain sustained and when releasing it the sound would either stop or fade away, depending on the Release time. So, when a key is pressed the triggers will activate the OSCs, VCF and VCA all together to generate a sound which will remain active as long as the key is pressed.

Following a more technical approach the process can be explained like this: when a key is pressed on the keyboard, a signal informing about the corresponding pitch arrives to the oscillator bank; the combination of several oscillators create a certain waveform, which includes the corresponding pitch in its fundamental frequency and also a spectrum of harmonics (the harmonic series), necessary for the ability of extracting innumerable timbres from the waveform; then this raw waveform is directed to the filter bank, where part of the frequencies (harmonics) are removed or attenuated (subtracted) with the purpose of achieving a certain timbre, being the filter's ADSR envelope the responsible of modifying the cut-off frequency (timbre) over time; and, in the last stage, the waveform is sent to the amplifier, whose ADSR envelope will modify the amplitude of the sound over time.

In brief, a signal continuously flows from the oscillators to the amplifier, during a certain time on which it is modified according to the programmed parameters, generating so a complex waveform over time, which we call "musical note".

At this point we have a basic idea on how an analogue synthesizer works and how many possible sounds can be sculpted on it. To finish this chapter about analogue synthesis we will briefly review the basic components of an analogue synthesizer. To begin with, we have the oscillators, which are generators that receive a signal (input), generate a new signal (waveform) based on the input and then send the new signal (output); filters, which are modifiers that receive a signal (input) and then return a modified signal (output); and envelope generators, which are controllers that do not receive signals but just modify them by sending the corresponding parameters (output) to devices which create or, more often, modify signals (filters and amplifiers). The next chapters present additional knowledge on the physics which take place in the synthesis of sound.

Theory on the synthesis of sound - Filters

To begin with, let us see two additional types of filters which are not directly used for subtractive synthesis, but which can add features to music generation equipment.

- Comb filter: this filter has a number of band reject (notch) filters at certain distances (delays); it is not intended for attenuating any part of the signal but for adding a delayed version of the input signal to the output (basically, a very short delay whose lenght and feedback can be controlled). The delays are so short that only their effect on the sound, rather than the delays themselves, can be heard. The lenght of the delays is determined by cut-off frequency whereas the feedback is controlled by resonance. In a practical sense, this type of filter is used for creating effects such as chorus or flange, typically present in the output section of analogue synthesizers.

- Parametric filter: this filter, also known as parametric equalizer, controls three parameters on the signal: frequency, bandwidth and gain. It allows to select a range of frequencies (bandwidth) for being attenuated or amplified (gain), as well as the desired amount of attenuation or gain. Any frequencies outside the selected bandwidth are not altered. Parametric filters cover the range of frequencies commonly used in music production (0 Hz to 20 kHz) and their precision is determined by the number of bands that they have (each band being in fact an individual filter). As parametric filters group multiple filters they allow for more complex filtering applications, being possible to use them for creating dynamic effects over time when an ADSR envelope linked to them allows to control the bandwidth parameters.

Now it is time of dealing with the aforementioned concept of resonance, which is also referred as emphasis or Q. If we look at the pictures above we can see the knobs labelled as Emphasis which are present in the filter banks of the MiniMogue Luxus and FreeMoog virtual synthesizers; and if we look at the pictures included in the previous chapter we can see a slider labelled as Resonance in the VCF of the Arppe2600 VA virtual synthesizer. That previous chapter explains about the slope caused by the delay that analogue filters experience when cutting off frecuencies. The range of frequencies where the slope climbs is called the transition band and the boost of that range of frequencies is called resonance, as the following graphic shows.

Resonance in a filter

Resonance occurs when sound in the pass band near the cut-off frequency is sent back to the filter as it comes out, creating so a feedback effect. The amount of feedback affects the volume of these frequencies, as well as the timbre of the sound. Which practical use could we make out of this hump on the slope? Altering the resonance of a filter along with the cut-off frequency can create incredible sounds as, for example, a self oscillation effect which would generate an audible - and screaming - sine wave. Some other undulating sound effects related to sine waves (such as shrieks, sirens or throbs) are possible, especially if a low frequency oscillator is assigned to the filter's resonance. Another trick involves using a high resonance to highlight the higher harmonics of a low frequency (bass) sound, which adds presence to the sound; it is also possible to do the opposite, by using a low resonance to highlight the lower harmonics of a high frequency (treble) sound.

If we look again at the pictures above, we can see the knobs labelled as Contour Amount (in the MiniMogue Luxus) and Amount Of Contour (in the FreeMoog). Filter amount (contour amount) determines how sensitive the filter's cut-off will be to control from the envelope generator; the higher the amount the larger will be the range of frequencies the filter allows to pass. This is just the amount of modulation that the filter's envelope generator applies on the cut-off point.

To put an end to this chapter, I will explain the difference between passive filters and active filters. This knowledge is not really essential for the practical utilization of a synthesizer but it enhances the understanding of how a filter does work.

- Passive filters derive their power from the input signal, so they have no power of their own until a signal passes through them. In this case, the amplitude response and phase response of a filter are crucial in determining the relationship between what enters the filter and what exits it; this is called the transfer function. The basic transfer functions have been explained in the previous chapter about filters and the concept of phase will be covered in the next chapter.

- Active filters use active components, such as amplifiers, placed between the transfer functions implemented on the filter, designed to improve its performance and predictability while avoiding the need for inductors, which are typically expensive in comparison to other components. An amplifier also prevents the load impedance of the following stage from affecting the characteristics of the filter, and can have complex poles and zeros without using a bulky or expensive inductor. The shape of the response, the quality factor and the tuned frequency can often be set through inexpensive variable resistors. In some active filter circuits a parameter can be adjusted without affecting the others. However, there are some limitations when using active elements: available active devices have limited bandwidth, so they are often impractical at high frequencies, while amplifiers consume power and inject noise into the system.

The largest part of analogue synthesizers have active filters and the diverse designs of amplifiers are a reason whereby analogue synthesizers from different manufacturers have a distinctive sound.

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