User Guide

624 Appendix Synthesizer Basics
The picture below shows a sawtooth wave with the filter half closed (24 dB/Fat). The
effect of the filter is somewhat like a graphic equalizer, with a fader set to a given cutoff
frequency (the highest frequency being fed through) pulled all the way down (full
rejection), so that the highs are damped. With this setting, the edges of the sawtooth
wave are rounded, making it resemble a sine wave.
The wave length here is not really higher, but the zoom setting is.
Fourier Theorem and Harmonics
“Every periodic wave can be seen as the sum of sine waves with certain wave lengths
and amplitudes, the wave lengths of which have harmonic relations (ratios of small
numbers).” This is known as the Fourier theorem. Roughly translated into more musical
terms, this means that any tone with a certain pitch can be regarded as a mix of sine
partial tones. This is comprised of the basic fundamental tone and its harmonics
(overtones). As an example: The basic oscillation (the first partial tone) is an “A” at
220 Hz. The second partial has double the frequency (440 Hz), the third one oscillates
three times as fast (660 Hz), the next ones 4 and 5 times as fast, and so on.
You can emphasize the partials around the cutoff frequency by using high resonance
values. The picture below shows an ES1 sawtooth wave with a high resonance setting,
and the cutoff frequency set to around 60%. This tone sounds a duodecima (an octave
and a fifth) higher than the basic tone. It’s apparent that exactly three cycles of the
strongly emphasized overtone fit into one cycle of the basic wave: