Waldorf Rocket - Manual (Page 26)

Sound Synthesis Basics
Rocket User´s Manual 26
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
bow pulling the string slightly into one direction. At one
point, the string abruptly comes off the bow and swings
back to its original position. The bow is still moved and
so it catches the string again and the procedure is repea-
ted. The result is a waveform that looks like a sawtooth.
The same is true for a brass instrument. The string in this
case are the lips while the bow is the air. The lips are
moved by the air to a certain extent and abruptly move
back to their original position.
The Square Wave
The Square Wave is a pulse waveform with 50% pulse
width. This means that the positive part of the waveform
has the same length as the negative part. The pulse wave-
form can have other pulse widths as you will read later.
For now, we´ll talk about the square wave as a unique
waveform. The square wave consists of all odd harmo-
nics in which the magnitude of each harmonic descends
by the factor of its position. This means that the first
harmonic has full magnitude, the third harmonic has a
third magnitude, the fifth harmonic has a fifth magnitude
and so on. The following picture shows how the indivi-
dual harmonics build up the pulse wave:
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
+
+
+
.
.