Owner`s manual

14
CHAPTER 3 -
The Craft of audio Synthesis
CHAPTER 3 -
3.2.2.2.1
Harmonic Series
The spectral view of any periodic signal has components at simple multiples of the signal
frequency. For example, suppose we examine a sawtooth wave at a frequency of 110Hz.
It will have components at 110, 220, 330, 440, and so on.
A simple number sequence like this is called a
harmonic series.
It is interesting to think
about musically; the smaller numbers in the series all form simple musical intervals:
octaves,  fths, fourths, and thirds.
Most musical instruments generate harmonic spectra. Some have more, some have
fewer harmonics, and there are wide spectral variations even within a single instrument
depending on how it is played. In general, whatever the actual spectral components are,
they will always form a harmonic series.
In audio synthesis, you will use oscillators to generate pitched tones that have a harmonic
spectrum.
Spectrum = the sine-wave component of a signal
Increasing Power
Increasing Pitch
1 2 3 4 5 6 7 8 9 10
@250Hz
sine
wave
saw
tooth
guitar
string
immediately
after pitch
just before
dying out
1/8
pulse
wave
(octaves)
middle C
250Hz
A harmonic series is composed of
numerically equal frequency intervals,
and that means decreasing pitch intervals
Increasing Power
Increasin
g
Frequenc
y
N 2N 4N 8N 16N 32N 64 128 256 512 1024
1 2 3 4 5 6 7 8 9 101112
The first couple of octaves’ worth of a harmonic
series make useful musical intervals: octaves, 5ths,
4ths, 3rds and so on. Beyond the 16th, they get too
close together to sound good.
Increasing Power
Increasin
g
Pitch
ANY ANY*2 *3 *4 *8 *16
octave
8
5th
maj
3rd
min
3rd
Pick any frequency; the multiples of that are a harmonic
series. A, B, and C are all harmonic series.
Increasing Power
Increasin
g
Pitch
C
B
A
etc.
2Khz 4K 6K 8K
etc.
100Khz 200
250Hz 500
1250
1500
1750
750 1K 2K
300 400