The Science of Synthesis - Part 2

A single wave produces a single tone known as the fundamental frequency, which in effect determines the pitch of the note. When further sine waves that are out of phase from the original are introduced, if they are integer multiples of the fundamental frequency they are known as 'harmonics'. Harmonics make the sound appear more complex.

A single wave produces a single tone known as the fundamental frequency, which in effect determines the pitch of the note. When further sine waves that are out of phase from the original are introduced, if they are integer multiples of the fundamental frequency they are known as 'harmonics'. Harmonics make the sound appear more complex.

Otherwise if they are not integer multiples of the fundamental they are called 'partials', which also contribute to the complexity of the sound. Through the introduction and relationship of these harmonics and partials an infinite number of sounds can be created.

The harmonic content or 'timbre' of a sound determines the shape of the resulting waveform. It should be noted that the diagrams shown below are simple representations, since the waveforms generated by an instrument are incredibly complex which makes it impossible to accurately reproduce it on paper.

In an attempt to overcome this, Joseph Fourier, a French scientist, discovered that now matter how complex any sound is, it could be broken down into it's frequency components and, using a given set of harmonics, it was possible to reproduce it in a simple form.

To use his words, 'Every periodic wave can be seen as the sum of sine waves with certain lengths and amplitudes, the wave lengths of which have harmonic relations. This is based around the principle that the content of any sound is determined by the relationship between the level of the fundamental frequency and its harmonics and their evolution over a period of time. From this theory, known as the Fourier theorem, the waveforms that are common to most synthesizers are derived.

Addition of sine waves to create a square wave

Addition of sine waves to create a Sawtooth wave

Addition of sine waves to create a triangle wave

Here concludes the second part of this post, if you want to know more about acoustic science, please read Rick Snoman's Dance Music Manual (Second Edition) Toys, Tools and Techniques.