Owner`s manual

CHAPTER 3 -
25
CHAPTER 3 -
The Craft of audio Synthesis
3.6.5.2.1
Ring Modulation
Whereas a VCA responds only to a positive-going signal at its amplitude-control input,
a ring modulator responds to both positive and negative levels at both of its inputs. Its
output is simply the product, arithmetically, of the two inputs. If you are new to audio
synthesis, draw a couple of signal graphs – it doesn’t matter what they are – on the
same timebase and vertical scale, and use a pocket calculator to work out the result of
multiplying the two signals together. That’s what a ring modulator does. (The expression
“ring modulator” describes the appearance of the analogue circuit design that’s required
for the multiplication.)
In the frequency domain, the difference between this and ordinary AM is only that the
carrier signal components are suppressed. Once again, if you work out the arithmetic, a
single-frequency carrier, modulated by a single-component program, generates a three-
component AM spectrum but only a two-component ring-modulation spectrum.
What’s useful about this? Well, since the carrier is almost always periodic (it comes from
an oscillator, right?), it has a harmonic spectrum.
Suppressing
this spectrum lets you hear
Suppressing this spectrum lets you hear Suppressing
just the sidebands, which can be completely enharmonic if you’re careful about the ratio
of the two input signal frequencies.
3.6.5.2.2
Frequency Shifting
It’s theoretically possible not only to suppress the original carrier, as in ring modulation,
but to isolate the lower and upper sidebands and make them available separately.
The arithmetic here is fascinating, because the end result (for once) is in one-to-one
correspondence with the input: for each component of the program signal, there is a
component in the output at C-p (or at C+p). In other words, the  nal spectrum has only as
many components as the original program did. This is called frequency shifting. Picture
the entire program signal spectrum shifted up or down by some  xed frequency.
The important thing to remember about this is that it’s not pitch shifting – which would
have to be accomplished by frequency multiplication – but
frequency
shifting. It’s an
frequency shifting. It’s an frequency
addition or subtraction process, and it
really
messes up any harmonic relationships that
really messes up any harmonic relationships that really
might have existed in the original spectrum.
3.6.5.3
Frequency Modulation
The spectrum resulting from amplitude modulation always has three components for
every one component of the program signal: the carrier itself, and two sidebands. In
Frequency Modulation,
however, the number of sidebands depends on the modulation
depth. It is possible from only two sine waves to generate a spectrum with dozens or
even hundreds of components. Modulating one sawtooth with another can produce a
spectrum so complex that it sounds almost like a noise generator. In such a patch, you
will usually reach for a  lter to take the edge off the resulting spectrum.
What happens is this: as the depth of modulation increases, the number of sidebands
does too, without limit. The additional sidebands come in at – guess what – integral
multiples of the program frequency.
For this reason, the most useful FM techniques involve only sine-wave carrier and
program signals.