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The sawtooth wave – Waldorf Nave User Manual

Page 56

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Sound Synthesis Basics

Nave User Manual

56

in recreating them electronically and building them into
a machine that could be used commercially. What they
implemented into his synthesizer were the still well-
known waveforms sawtooth and square. For sure, this is
only a minimal selection of the endless variety of wave-
forms, but Nave gives you exactly these waveforms at
hand.

Now, you probably know how these waveforms look and
sound, but the following chapter gives you a short intro-
duction into the deeper structure of these waveforms.

The Sawtooth Wave

The Sawtooth wave is the most popular synthesizer
waveform. It consists of all harmonics in which the mag-
nitude of each harmonic descends by the factor of its
position. This means that the first harmonic (the funda-
mental) has full magnitude, the second harmonic has half
magnitude, the third harmonic has a third magnitude and
so on. The following picture shows how the individual
harmonics build up the sawtooth wave:

Additive components of the Sawtooth wave

The sawtooth wave was thought as an abstraction of the
timbre of string and brass instruments. You can easily
understand that when you think of a violin. Imagine a

1

4

8

12

16

Frequency

Magnitude

Time

Amplitude

+

=

1st Harmonic

Magnitude 1

2nd Harmonic

Magnitude 1/2

3rd Harmonic

Magnitude 1/3

4th Harmonic

Magnitude 1/4

Harmonics

+

+

+

.

.