
For this
part of the tutorial, it is definitely best if you follow along with a
subtractive synth of your choice. I have provided some examples for each
part, but nothing beats learning the principles by actually
manipulating the sound and tweaking the controls yourself.
What is modulation?
"Modulation" is a fancy word for a very simple concept. To say that "A
is modulating B" just means that the behavior of A over time is
controlling the behavior of B over time. Envelopes are used to modulate settings of subtractive synths from the time when a note is struck to when it is released.
What is an envelope?
An envelope is a part of a synth which controls the behavior of
some characteristic of the sound that your synth produces from when a
note is first struck to when it fades out completely. Most subtractive
synths have at least three envelopes built in: an amp envelope, a filter envelope, and a modulation envelope.
Each of these envelopes typically has at least four controls, often
referred to as "stages" or "phases." These four controls are attack (A), decay (D), sustain (S), and release (R);
because of the abbreviations used for these four elements, envelopes on
subtractive synths are often called "ADSR envelopes." Now to explain
the function of each type of envelope:
Amp Envelope
When you play a note on your synth, the amp envelope controls the volume of the resulting sound over time. The attack
controls how long the sound takes to reach its highest volume once a
note is struck. A shorter attack time will give you a "punchier" sound,
while a long one will give you a sound that "fades in." The decay controls how long the sound's volume takes to drop down to the sustain volume. The sustain
volume is the volume maintained when you hold a note after the sound
has gone through the attack and decay "phases." How long the sustain
phase lasts depends on how you long you hold down the note(s) on your
synth. If you have the sustain set all the way at the top, the "held
note" volume will be the same as the "attack" volume.
If you
are following along with your own synth, try to imitate the volume
characteristics of each of the above files by adjusting the ADSR
controls on your amp envelope.

Sounds that typically have short or short-medium attack times are Synth
"stabs," keyboard sounds, basslines, any synth used in a "percussive"
manner, and some pad sounds. Sounds that typically have medium or long
attack times are synth "washes," noise sweeps, bass that gradually fades
in, and pads.
Filter Envelope
The filter envelope controls what the cutoff frequency of your synth's
filter does as a note is struck and then held. Here the attack setting
controls the amount of time that passes before the filter cutoff reaches
its highest frequency and the decay setting controls how quickly the
filter cutoff decreases after hitting its highest frequency. The sustain
setting controls the frequency of the filter as you continue to hold
the note down after the attack and decay phases have ended. The release
setting controls how quickly the cutoff frequency of the filter goes
from the sustain level back to nothing again. Here is an audio example
to give you some idea of what a filter envelope does:
ADSR filter envelope applied to a saw wave
In the above file, the filter envelope has a long attack time and a
short decay time, so it takes a while before all the frequencies are let
in, but then they get cut out quickly during the quick decay phase. The
sustain is at a medium level, so the filter is cutting out and leaving
in pretty even amounts of frequencies. The release time is short, so
once I let go of the note, the cutoff frequency drops right away.
Modulation (Mod) Envelope
Unlike the amp envelope and the filter envelope, the modulation envelope
can be "assigned" by you to control different settings on your synth,
and on some synths it can even control more than one setting at a time.
Typical parameters for the modulation envelope to control can include
the following:
Oscillator pitch: If you assign the mod envelope to the pitch of
an oscillator, the oscillator changes the pitch played from the time a
note is pressed to when it is released according to the ADSR model
explained above.
Oscillator mix: If you have more than one oscillator playing at
once, the "Mix" setting on the mod envelope can be used to vary the
volume levels of two or more oscillators relative to one another.
FM: Many subtractive synths allow you to use the frequency of one
oscillator to modulate another waveform; on the mod envelope, the FM
setting can be used to vary the level of frequency modulation over time.
FM will be discussed in the next part of this series.
A second frequency filter: Many subtractive synths have a second
frequency filter that acts upon the sound which results after the first
filter has been applied to the raw sound. With the mod envelope, you can
control the behavior of the cutoff frequency of this second filter.

This
part and the next part will examine "the practice": what the typical
buttons, knobs, and sliders on a subtractive synth do to a sound. I hope
to provide a starting point for developing your ability to hear a sound
and "reverse engineer" it, and of course for designing your own patches
from scratch. In this particular installment, I will briefly explain
the meaning of the following terms and their relevance to patch design:
oscillator, tuning / detuning, polyphony, filter, resonance, and
"opening up."
Oscillators
An oscillator -- often abbreviated "Osc" and sometimes "VCO" for
"Voltage-controlled Oscillator" -- generates the basic waveform(s) of a
subtractive synth. The number of oscillators on a given subtractive
synth is usually from around two to six. The character of a finished
sound will vary drastically according to what waveform(s) your
oscillator(s) is generating. Some synths allow you to choose from a
large number of different waveforms for the oscillator to generate, and
some even allow you to draw or load your own waveforms and play them.
Many synths give you the ability to fine-tune the pitch(es) played by
the oscillators in terms of "cents." A "cent" is a tiny pitch difference
of just 1/100th of a semi-tone (the musical interval from a note to its
flat or sharp). Detuning refers to a process in which two or
more oscillators are used to make a sound and one oscillator is pitched
higher or lower than the other. This creates a sort of "vibrato" or
"chorusing" effect when two or more waveforms of slightly different
frequencies interact and bounce off of one another. It is the basic idea
behind the famous "supersaw" sound, which in its widely-known JP-8000
incarnation used seven sawtooth waveforms detuned from one another.
Basic detuning example
The above file plays a single sawtooth waveform followed by two sawtooth waveforms detuned from one another by thirty cents.
Polyphony
Polyphony is the number of notes that a synth can play simultaneously. Many early synths were monophonic;
they could only play one note at once. Most modern synths allow you the
option of setting their polyphony number. In terms of softsynths, the
polyphony setting is part of what determines the "upper limit" of a
synth's CPU usage; a synth patch set with a relatively low polyphony
number will be less likely to overload your CPU simply because it will
not allow you to play enough notes at once to do so.

Filters
A filter is a part of a synth which attenuates ("cuts out")
certain frequencies of the waveform generated by the synth's oscillator.
Which frequencies are cut out will depend on the type of filter and the
cutoff frequency of the filter.
The four most common types of filters are:
Lowpass (LP): Cuts out all the frequencies above the cutoff frequency.
Highpass (HP): Cuts out all the frequencies below the cutoff frequency -- the inverse of lowpass.
Bandpass (BP): Cuts out all the frequencies below and above a narrow "band" of frequencies.
Notch: Cuts out all the frequencies within a narrow band and lets all others through -- the inverse of bandpass.
Basic examples of what these filters do to a sound:
A raw sawtooth waveform
A sawtooth waveform with a lowpass filter
A sawtooth waveform with a highpass filter
A sawtooth waveform with a bandpass filter
A sawtooth waveform with a notch filter
The resonance setting on a filter allows you to increase the
volume of the frequencies near the filter's cutoff frequency. When you
increase the resonance on a filter, the sound will often seem to
"squeak" or "bubble," depending on the cutoff and filter type you have
set for the patch. Resonance can be manipulated to achieve some pretty
neat-sounding effects, as in the following file:
Two examples of high resonance
The first part of the file shows what happens to a sound when the
resonance is increased gradually. The second part is an example of what
happens when a sound has a constant high resonance setting but the
filter cutoff is moved up and down.
It should be noted that the term "cuts out" is not entirely accurate
when talking about what filters do, since filters are never "perfect" at
eliminating all the frequencies above or below a certain point. Imagine
running pure noise (all frequencies playing at equal volume) through a
low pass filter; a graph of the frequencies in the resulting sound would
look something like this:
As you can see, the filter causes the frequencies of a sound to have a
"sloping" behavior rather than a strict "on / off" one. The steepness of
the slope is dictated by the strength of the filter, which is specified
in terms of "dB." A 24 dB filter makes a steeper "cutoff slope" than a
12 dB one, which in turn makes a steeper slope than a 6 dB one. The
steepness of the volume slope created by the filter is called the Q factor. Most modern subtractive synths allow you some degree of freedom in setting the strength of the filter.
When people talk about a filter "opening up," they mean that it is
letting more frequencies through as time goes on. The term "opening up"
is usually used in the context of a lowpass filter whose cutoff
frequency is getting higher and higher. The sound should be very
familiar to you from many trance songs, which often use filters that
gradually (or suddenly) open up in order to increase the tension or
energy at some point in a track. Here is an example I made today:
Two examples of a lowpass filter opening up
The first part of the file is an example of a lowpass filter gradually
being opened up. The second part leaves the filter closed but then opens
it suddenly at different points to create short "stabs;" even though
the whole second part consists of just one note, an impression is
created of a background noise and another, more intense noise bursting
through to the foreground.
I hope you have enjoyed reading this part and that it has given you some
ideas for sounds or at least some food for thought. If you believe that
I have made any errors or glaring omissions in explanation, please tell
me. In a day or two I will write and post the third part of this
series.
Part Three will deal with modulation, envelopes, LFOs, and FM.

Subtractive
synthesis is probably the most commonly used method of synthesis in
electronic dance music. It is used by famous hardware synths such as the
JP-8000, Nord Lead, and Access Virus, and much-used softsynths like
z3ta+, Vanguard, and Albino. It is often the first sort of synthesis
that new producers have a chance to play around with, and one that a
great many producers use to produce "bread and butter" sounds for
tracks, such as the "supersaw" and a huge number of keyboard and bass
sounds. But how does this synthesis method actually work?
The basic idea behind subtractive synthesis is very simple, and is
hinted at by the word "subtractive": take a raw, harmonically rich unit
of sound -- called a "waveform" -- and manipulate component frequencies,
change pitch, dynamic properties, and (sometimes) timbre by using the
knobs and sliders on your synth. Each of these terms could use some
explanation, which I will give. But first it's time to say a little bit
about tones, timbre, and how they relate to the mathematical properties
of sound waves -- I know, boring, but it's good to know and might make
things less confusing later on.
Frequencies, Pitches, Harmonics, and Partials
All waves, including sound waves, have high points (peaks) and low points (troughs). The frequency
of a sound wave (or any kind of wave) is the number of times per second
that the sound wave repeats itself -- how long it takes to move from
trough to trough or peak to peak. Pitch is, for our purposes, the
same thing as the frequency of a sound: if a sound wave has a high
frequency, you will perceive it as "high-pitched," and if it has a low
frequency, you will perceive it as "low-pitched." The frequency of a
sound wave is measured in Hertz (abbreviated "Hz"). Nearly any
given sound you hear will contain lots of individual waves with
different frequencies -- these combine to give the sound its distinct
character -- and a sound's fundamental frequency is the frequency of the lowest frequency wave contained within the sound.
A harmonic is a whole number multiple of the fundamental
frequency of a sound; as an example, 880 Hz would be the "second
harmonic" of 440 Hz, since 440 * 2 = 880; then 1320 would be the "third
harmonic," and so on. A partial is a fractional or decimal
multiple of the fundamental frequency of a sound; 660 Hz would be a
"partial" of 440 Hz. Sounds that people call "rich" have a lot of
harmonics and sometimes partials present along with the fundamental
frequency: this is what gives them their unique, attractive, or
"interesting" character. [1]

What is a "waveform?"
[Note: a very useful tool to use in following along here is Native
Instrument's Absynth, because it allows you to edit your own waveforms
and view the effects on the harmonics of a wave (and vice versa).]
A waveform is the "basic" sound you start out with when you construct a
patch from scratch on a subtractive synth. The four "classic" waveforms
are the following:

What does the shape of each waveform represent? The shape represents two
characteristics on the following graph: the y-axis of the graph is
amplitude (one half the vertical distance from a wave's peak to its
trough) and the x-axis of the graph is time:

The four waveforms pictured above each have a characteristic "sound" (or
"timbre") that results from the harmonics contained in them. Both the
square and saw waves are especially rich in harmonics, making them ideal
building blocks for "lead" sounds that can catch the listener's
attention. Here are the four classic waveforms being played on Reason's
Subtractor synth:
Sine - Triangle - Square - Saw
Now, after this long introduction you are probably thinking, "Okay,
fine, but when are you going to tell me the stuff that will actually
help me in designing a synth patch?!" Soon, soon! The next installment
of this series will cover oscillators, filters, envelopes, and all the
other good stuff that will allow you to create nice patches for
subtractive synths.
NOTES
[1] It is useful to think of all non-sine waves as the sum of a
bunch of sine waves, each one having a different frequency (usually, but
not always, an integer multiple of the fundamental frequency). That is,
waves such as saws and squares can be thought of as a number of sine
waves all interacting with one another; this "summing of waves" concept
is the basis for additive synthesis, but that is getting off-topic...