The synthesis techniques

n oIf we look at the spectrum of a complex sound, like a field recording or the sound of a voice or an instrument, we can appreciate the complexity of its time domain representation.

It contains many waveforms that add up to its final shape and sound. Some burst immediately with a fast attack and die quickly, some other decay slowly. We could take it as a model to reproduce through synthesis, but we will soon realise how lengthy and computational expensive would be the process of putting together independently all these waveforms together and their motion in time.

Additive Synthesis has been used, and in many circumstances is still used, to create many interesting sounds as, especially with nowadays computers, it can be performed more efficiently than before.

The idea of additive synthesis is that you can use oscillators like cycle~, rect~, saw~ that you have just seen in Max, adjust their progress over time with an envelope (you will learn more about it in Lesson 3), and sync them with many other sounds at the same time, thus creating a complex sound.

It is important to first start learning how to mix sound in Max and control their amplitude. The lesson on the multiplier object should address this topic.

Then, another technique allows creating more complex sounds from scratch just from two oscillators. That is the process of modulation.

With this process, we are able to excite (modulate) the amplitude or the frequency of a sound to obtain a more complex sound, containing not only one frequencies but two or more. There are several types of amplitude modulation, and many techniques for achieving frequency modulation.

Amplitude modulation

Once we know how to control the amplitude of a sound in Max, we can effectively use an oscillator to control it. An oscillator would cause the amplitude to vary regularly with time, sounding as a tremolo effect. When these variations are performed extremely quickly, at frequencies not achievable by hand, something happens to sound. New frequencies become audible, and they are predictable because they are always in mathematical relation to the frequency of the original modulated sound.

The oscillator which controls the main sound’s amplitude is called the modulator and, accordingly to how much its frequency is set and the difference with the main sound (the carrier)’s frequency, it produces two or more brand new frequencies.

Two main cases we have now: if the modulator is a bipolar signal, if the modulator is a unipolar signal.

Unipolar and bipolar signals

A signal is said bipolar when it oscillates between -1 and 1 passing through zero. It is said unipolar if oscillates between 0 and 1. This difference is important as they produce different results when used as modulators. In Max, a unipolar signal is obtained with phasor~, a bipolar with cycle~. In fact, any signal can be transformed in Max into the opposite with just a few calculations.

BIPOLAR SIGNAL MODULATOR

When using a unipolar signal as a modulator firstly a tremolo effect can be achieved, the classic oscillation of amplitude. This only if the frequency of the modulator is set reasonably low (4-32Hz).

When the frequency is set higher, the main frequency of the carrier will be lost and two other frequency will be perceived which are the exact sum and difference of the carrier and the modulator respective frequencies. Thus, a carrier of 1000 Hz, modulated at 1300 Hz will produce two frequencies: one set at 2300 Hz the other at 300 Hz.

BIPOLAR SIGNAL MODULATOR

When using instead a bipolar signal, three new frequencies are generated: the carrier is this time audible, and then again the sum and difference.

Frequency Modulation

The other big family of modulations is given by the frequency modulation, well known as FM. There are many techniques to achieves its effect, and I report here the main one mentioned by Curtis Roads in his Computer Music Tutorial.

The effect consists of two bipolar signals of which one is modulating not the amplitude but the frequency of the other. This produces sidebands in relation to the ratio between the carrier’s frequency and the modulator’s frequency.

To understand better FM, it is good to make a more practical comparison to AM just by thinking at them respectively as vibrato technique and tremolo technique.

If you ever played a string instrument, you must have noticed that a tremolo is a variation in volume, instead, a vibrato is a variation in pitch. FM works exactly like an incredible fast vibrato which can thus produce additional frequencies to the original carrier sound.

One important new element is though added: the modulator’s depth. If a vibrato is simply an oscillation of a signal around a fixed frequency, in our example a vibrato of 1000 Hz will oscillate below and above 1000 Hz, it is important to know how fast and how wide this vibrato will oscillate. The speed of the vibration is given by the already known modulator frequency, the range of the oscillation in pitch itself is given by the modulator’s depth. Just by adding this new element we could see how sidebands are created.

With integer numbers and an integer ratio between the carrier and the modulator we always have harmonic relations in the sequence of sidebands. In our case we will have: 1000 Hz, 2300 Hz, 3600 Hz on one side, and 300 Hz, 1300 Hz, 2900 Hz which is C, C+M, C+2M, C+3M, C-M, C-2M, C-3M…

The bigger the modulation depth, the lower the original frequency will sound, the more sidebands will become audible.

Subtractive synthesis

Subtractive synthesis is the last technique that completes this section. I will discuss it more in detail in later chapters when we will have already learned the filters. It is based in creating complex sound by processing, reducing, transforming a full broadband spectrum like that of white noise, isolating or putting in resonance individual frequencies or sections of it.