Synthesis

What is synthesis? Broad definition: the combining of separate elements or substances to form a coherent whole. ( A nineteenth century French mathematician and physicist called Jean Baptiste Joseph Fourier, theorised that any periodic (repeating) waveform could be split into or constructed from multiple sine waves. In music, a synthesizer is a device which builds complex sounds by combining simple sound-generating building blocks known as oscillators, then modulating and processing them in a variety of ways. To understand how this works, we first need to understand a little about how we hear sound and the various ways it can be analysed.

Ways of looking at sound We can use a level meter to see a visual representation of a signal, but as the changes are so fast, this is only really useful in reading the volume of a signal. Instead, we can use an oscilloscope to analyse the changing level of a signal over time. This is often described as looking at the signal in the time domain. By zooming in very close to the waveform, it is possible to work out the frequency of the sound by observing it’s wavelength. Alternatively, a spectrum analyser (also known as Fast Fourier Transform or FFT analyser) can be used to look at changing levels across a range of frequencies in the frequency domain.

How we hear sound We perceive sounds with periodic (repeating) waveforms as having pitch, where as random, non-repeating waveforms are heard more as noise. Our brains tend to group frequencies which are whole multiples of each other together. When frequencies related in this way are played together they sound harmonious. This is why, for example, we recognise a C note played in one octave as being the same note when played an octave higher, since an octave implies a doubling of the frequency. The simpler the ratio between the two notes, the more consonant the interval sounds. Frequencies which do not divide so evenly are generally found to be less pleasant or inharmonious. Think of the beating, dissonant sound you hear between two notes when tuning an instrument. The pitch of a sound is determined by its base frequency, called the fundamental, where as its timbre is shaped by the sound’s overtones or extra harmonic content present over the top.

WaveformName 1Name 2Ratio Frequency example* Interval relationship Fundamental tone 1st harmonic-440Hz (A)1st 1st overtone2nd harmonic2:1880Hz (A)1st +1 octave 2nd overtone3rd harmonic3:11320Hz (E)5th +1 octave 3rd overtone4th harmonic4:11760Hz (A)1st +2 octaves 4th overtone5th harmonic5:12200Hz (C)3rd +2 octaves 5th overtone6th harmonic6:12640Hz (E)5th +2 octaves The harmonic series * Note: these frequencies/notes are not fixed and change depending on the fundamental. It is the ratios between the harmonics which are fixed.

Oscillators An oscillator is a device or program which generates a periodic waveform. These waveforms usually come in one of several common shapes, each with their own unique sound: Sine wave Square Triangle Sawtooth

Sine wave Sine waves are special in that they have no harmonic content other than their fundamental frequency. In other words, a sine wave represents a single frequency alone. As a result, we hear them as clear or ‘pure’ sounding tones.

Square wave As a rule, square waves contain only odd numbered harmonics. What this means is, if we were to look at one through a spectrum analyser, we would see that only the odd numbered harmonics in the harmonic series were present. So a square wave with a fundamental of 440Hz would not show anything present at 880Hz (the second harmonic), but a spike would be visible at the third harmonic of 1320Hz. These odd harmonics give the square it’s distinctive tone, often described as metallic sounding.

Triangle wave Like square waves, triangle waves contain just odd number harmonics. However, these harmonics are quieter in comparison and trail off much more sharply when looked at under a spectrum analyser. Their similarity in shape to sine waves, results in them sounding quite similar with a very dominant fundamental frequency. Their more angular shape adds extra harmonics to the sound, resulting in the added ‘buzzing’ quality.

Sawtooth wave Sawtooth, or ramp, waveforms contain both odd and even harmonics, resulting in a much harsher sound compared with a triangle waveform. A sawtooth waveform can almost be thought of like a cross between a triangle wave and a square wave, containing qualities of both. Inverse sawtooth wave-forms, so |\ |\ |\ instead of /| /| /|, also exist.

Additive synthesis Additive synthesis is one of the two most common methods of synthesis. It describes the method of adding together, or mixing, multiple sine waves to synthesize the target sound. It is for example, possible given enough oscillators to create an approximation of any of the standard waveform shapes by positioning additional frequencies where you would expect the extra harmonics to appear. The more sine waves used and the more care taken to accurately model the required sound, the closer the timbre will be to the target sound and the more the waveform will begin to resemble the modelled shape when viewed through an oscilloscope. An organ can be thought of as a type of additive synthesiser. As different stops are opened and closed, so different harmonics are added to the timbre.

Subtractive synthesis Subtractive synthesis is the other most common method of synthesis. In subtractive synthesis, harmonically rich waveforms are filtered to remove unneeded harmonics from the sound. Filters are essentially synth-speak for EQ or tone controls. It is for example possible to take an oscillator rich in harmonics like a square wave and filter the high harmonics out with a steep lowpass filter to make it approximate a sine wave in timbre and shape.