Owner`s manual

CHAPTER 3 -
17
CHAPTER 3 -
The Craft of audio Synthesis
3.4
How Signals and Sounds Go Together... Sort Of
Signal activities, being entirely physical kinds of things, are easily nameable, measurable,
catalogable, countable. Sounds, as we pointed out above, are not quite so easily
domesticated. The music and other sounds that we listen to correlate in several well-
established ways with the signals around us; but the correspondence is not simple. There
are always surprises.
3.4.1
Signal Frequency and Audible Pitch
This is probably the best-established and most reliable correspondence. It dates all the
way back to Pythagoras, the Greek philosopher who 2500 years ago worked out that
halving the length of a vibrating string made the pitch rise by one octave.
3.4.1.1
How Adding Pitches Means Multiplying Frequencies
The range of audio frequencies
– of human hearing, in other words – is
conventionally stated to be 20Hz to
20KHz. And when you think linearly, it
sounds tragic to learn of someone, say,
who can only hear up to 10KHz. But in
the realm of human pitch perception,
such a person has kept 90% of his
hearing range: from 10KHz to 20KHz is
just one octave out of the 10 we hear.
This is a
really important fact
in
really important fact in really important fact
audio synthesis; you will encounter
it over and over again, in every
patch you create. It governs much
of the arithmetic of generating and
controlling spectral distributions and patches:
4
Equal
pitch
intervals require exponentially increasing frequency increments;
4
Equal
frequency
increments make a harmonic series. In a harmonic series, as we go
frequency increments make a harmonic series. In a harmonic series, as we go frequency
up the series we get smaller and smaller pitch intervals.
A harmonic series is composed of numerically
equal frequency intervals, and that means
decreasing pitch intervals
Pitch b
y
octaves
Frequency in cycles / seconds
0 1 2 3 6 7 8 9 10
middle C
Each division
is one octave.
To add an octave, you have
to multiply F x 2.
20Hz 40Hz 78Hz 156Hz
312Hz
625Hz
1250Hz
2500Hz
5KHz
10KHz