FM is a very versitile and simple synthesis technique. Invented by John Chowning and patented
by some company, FM works by rapidly changing the pitch of one oscillator by the output of another.
Yamaha-style FM is actually not frequency modulation but phase modulation: This produces similar sounds by
modifying the read position in one oscillator by the output of another.
Time for some terminology: the modulating wave is called.. oddly enough.. the modulator. The
wave that's being modulated is called the carrier. The oscillators are usually referred to as
So why should anyone bother with this? While we can get deep sweeping sounds with analog
(subtractive) synths or almost perfectly realistic tones with both sampling techniques and
physical modelling, the charm of FM is that it creates sharp semi-realistic instrument sounds
and unique synth tones. It produces a huge variety of tones: crisp slap basses, rich bell
tones, warm pads, keyboard tones that sound great when played as a complex chord, thick drums,
rubbery leads, and more.
FMHeaven (OS X, Windows): Like FM7
Ok, Let's Dig In
Let's start with only two operators. This makes it actually pretty easy to learn how to use FM.
Point #1: Multiple waveforms are easier to understand than multiple algorithms:
Everyone knows multiple waveforms from their other synths. But only these crazy digital
synths have all those different algorithms. Also, it is very hard to understand
what is happening when any parameter is changed when you have six or more operators all
But, for now we won't even use more than a sine wave. So, any cheesy FM synth will do.
The modulation setting, at least on the OPL2, is a multiplier. That is, it
multiplies whatever the note's frequency is by that number. So, if you play
a 100hz tone, a multiplier of 2 will be 200hz and 3 would be 300hz. Tricks
can be done with this-- If we add the operators instead of FMing them, we can
create chords using just one voice. First, notice the relationship between
200hz and 300hz. Since 300hz is halfway between 200hz and 400hz, it forms a
fifth interval. This is very useful in forming chords with few channels left.
If two of these are overlapped, chords such as full 7ths may be produced
using only two channels! For example, a C fifth and an E fifth overlapped
produce a C7 chord. As the modulation factors become higher, the possible
intervals become smaller.
Our First Voice: A Bass
FM does nice electric bass sounds surprisingly easily. Even if you can't do anything else with
FM, you should be able to do cool basses. Here we go!
Set both oscillators' attacks to be instantaneous and the decays kind of medium-slow, as you'd
expect a bass to decay. Ok. Now, set the carrier to full volume, and start with the modulator
at zero. When you play this, you should hear a nice sine-bass. This might actually be a little
hard to hear if you don't have a nice woofer or subwoofer. If you don't hear anything, it's
probably because the wrong oscillator is set to zero volume.
Now, turn up the modulator and keep playing notes. You'll hear that the sound gains sort of a
twang. In effect, turning up the modulator turns up the brightness of the tone. Turn it too
high and you'll start hearing those "blargh!" sounds that you got from every bewildered
videogame musician writing for an FM-based system.
Ok, so let's leave the volume of the modulator somewhere half-way so it sounds pleasant and
let's try something else.
Instead of having the modulation factor for the modulator at 1, set it to 2. It should now sound a little closer to a square than it did when it was
at 1. Below are the waveshapes and spectrums for 1:1 and 1:2 FM tones with a moderately loud modulator:
Now, we'll try something new:
Making Unpleasant Clanging Sounds
So, now that we've made a tone that's usable, let's see if we can scare the cat. Keep turning
the modulator's modulation factor up and the sound will produce a higher and higher pitched
clang. In addition, the sound should get a little thinner. Start turning the modulator's volume
up or down and the loudness (but not the pitch) of the clanging component will change. If we
leave the decays fairly long and turn the modulator volume down to a responsible level, this will
create bell-like tones. If you play another bell tone on top of it but slightly detuned, it will
sound a lot better. Using a fairly high modulation factor on the modulator and with a short
decay on both (with a shorter decay on the modulator than on the carrier) creates a nice marimba
Point #2: Modulator volume and modulation factor affect the brightness of the sound even though
they don't necessarily correspond to that. The modulation factor of the modulator in
a two-operator pair is partly responsible for determining how many high frequencies are
introduced into the sound, and the volume of the modulator describes generally how much
of that you want.
Scientists: If you want to see what happens to the frequencies in FM, look up bessel curves.
This function describes the phenomenom. It'll show the amplitude of the sidebands
(added frequencies) at various modulation factors.
FM Trumpet and Clarinet
Now that we have a general feel for what a few of the parameters have done, we can recreate some
classic FM tones. Again, leave the volume of the modulator around halfway and set both
modulation factors to 1. If we play the sound low, it sounds like our original bass. Now, let's
decrease the amount of attack on both oscillators to mimic the attack on a real trumpet. If we
then play the resulting sound higher up, it does indeed resemble a trumpet. It's not a very
good trumpet sound, but it is reminiscent of that instrument. Try playing with other ratios, too.
2/3 is considered to be a clarinet sound. I think anyone trying
the classic FM examples hoping to get a tone usable in their music will be
disappointed pretty quickly-- these are more of a sort of proof of FM versatility than they are
pleasant instrument sounds.
Feedback is where the output of an oscillator is fed back and used as a modulator wave. I believe
in the Yamaha FM synths such as the OPL2 that feedback takes the last sample output by the pair and adds it into the carrier's modulation. This is useful because it simulates having more operators than
the synth actually has. In fact, a better FM trumpet than the classic example can be made using
just a self-oscillating FM operator. Feedback tends to make the sounds sharper (closer to a traditional saw or square) and,
if turned high enough, noise.
Point #3: Self-modulating operators, or feedback, can produce both sharp tones and noise.
Modelling Drums with FM
Initially, most people try to do a snare using nothing but noise. This doesn't work so well
because it lacks the body of the sound (the tone). In fact, it sounds like someone spitting.
So, to do a convincing snare, you need three things: noise, tone, and a strike sound. One
advantage of FM synthesis is that you can give the snare a little more pop than with conventional
additive synthesis. First, set the algorithm up so it looks like this:
As you can see, we have two modulating pairs (1&2, 3&4). The output of these are then added
(mixed) to create the final sound. If you are using something as cheesy as an OPL2 that only
does pairs, you can trigger two channels: one tone, one noise. Let's call operators 1&2 the
noise pair and 3&4 the tone pair.
For the noise pair, we'll set the feedback to maximum and both operators to full volume. This
should create something close to pure noise. To make the noise more pure and smooth, you can
increase the modulation factors. To make the snare rattle more, you can turn the modulator down
slightly (leaving the modulation factors at 1:1). Make sure that the modulator does not decay.
The tone is the fun part. We'll want a sinewave with a pop at the beginning. To do this,
set the modulator volume high and make it decay very quickly (within a couple dozen
milliseconds). The carrier should decay around the same rate as the carrier of the noise.
Now, play it back so that the tone of the snare is mid-range, around 300hz. You may have to
turn the noise component down a little so that it blends more smoothly, but if done right it
makes a convincing synth snare.
Most other drums can actually be done with just a pair. Let's try a hihat. First, set the
modulator's modulation factor high and crank the volume to full. Set the decays to what
you would expect a hihat to decay at. An open hihat can be done with a longer decay. Now,
put the feedback level to full. Slowly decrease the volume of the modulator until you hear
a nice clanging sound. One good thing about FM is that since the noise is generated off of
a sine, it is easy to do cyclic noise effects like this.
In an ordinary additive bass drum, you would have two components. One would be a sine wave that
slides down very quickly to provide the deep thump of the drum. The other is, like the snare,
a pop that calls the listener's attention to the start of the sound. Again, what's great about
FM form drums is the deep pop it can create. So, for the slide, you want to start at around 200hz
and slide down to around 60. It's nice to have a bass drum that slides down to a still-audible
level and fades there. Experiment with the pitch of the bass drum, see what you like. Now,
to add the pop, we'll add the modulating oscillator in at about half volume. This pop should
decay even faster than the snare's. We don't really want the listener to notice the pop, but it
should be long enough to add that extra punch. Playing with the modulation factor of the
modulator wave may yield better results.
Sometimes, pure sine waves just don't give you that tone you're after. But in FM, the other
waveforms don't tend to have a full range of frequencies in them (like in a subtractive synth).
For instance, a synth might have a sine and then a bunch of sine-derived waveforms. A synth
that I'm writing features a squarewave, but it's a dull squarewave because modulating by a full
one creates nasty high tones. Introducing non-sine-related waveforms into a sound generally
makes it into a synthier tone. For instance, if I make my modulator a saw, the sound takes on
a saw-like tone (in a less predictable way than a subtractive synth). Some FM synths, such as
the DX7, only have sine waves, but also include six operators. These operators can be added
together to create a new waveform before being used as a modulator or carrier for FM.
Point #4: Subtle and complex waveforms have a not-so-subtle effect on the resulting sound in FM.
The Importance of Chorus
So. by now, you're probably saying, "Alright, FM does a bunch of different tones, but half of
them are so thin!". Well, nobody got anywhere with a synth without a little bit of detuning!
So, for those high up FM tones, double up the output and detune it a little. It doesn't even
have to be the same tone-- a softer version of the same thing (or even using fewer oscillators)
can do the trick too. This helps make all sorts of convincing ensemble tones. For example,
a decent brass ensemble sound can be done with a few buzzy FM tones with trumpet-like attacks
On some synthesizers, the modulator can be detuned from the carrier. This creates a rougher tone
and is useful to add grit to otherwise crisp timbres, such as for wind instruments.
Point #5: Don't forget about layering and detuning as with other synths
3+ Operator Configurations
Cascading operators can be used to produce a much more complex timbre
than is possible with any 2-operator configuration. I always think
of this configuration for string-related tones. For example, the
first modulator can be used as a pluck sound which modifies the
tone of the last pair. Rich timbres such as slap basses may be
created if the first modulator is high enough and does not die off
quickly. Pitched noise effects or fuzz effects may also be created
if the first operator set is used to create feedback noise.
On an OPL2/3 or a Yamaha TX81z, we have the luxury of multiple waveform types.
However, on many others such as the FB-01 or the famed DX7, there is only a
sine-wave. This is not necessarily a handicap though because multiple
waves can be added before being used as a modulator! The effect is that of
an "additional spectrum superimposed on the original" (Moore, Elements of
Computer Music, p.330).
Remember that a low number of harmonics are necessary for an additional FM
waveform: Various classic waveforms can be made with as few as three
oscillators. One advantage of doing it with multiple oscillators instead of
with a flat waveshape is that each oscillator can be enveloped independently.
One possibility is that higher harmonics could die off more quickly.
The OPL Waveform Types
The OPL waveforms are not pure classic waveforms such as a square or saw.
They are derived from sine-waves. For example, waveforms 1-3 are made by
reading the sine table in different orders. Waveform 1 is just half of
the sine cycle with the second half left blank. Waveform 2 plays the
first sine half twice in a row. Finally, waveform 3 is a quarter of a
sine cycle followed by a quarter cycle left blank. The abrupt chopping
of the cycle in waveform 3 makes it the sharpest of the four OPL2
A formant group is a region in the frequency spectrum that emphasizes a specific tone and its surrounding frequencies. This is typically seen as a hump-like shape on the frequency graph which centers on a particular frequency. In FM, a similar shape may be created by placing the carrier's pitch above the modulator. As the carrier's
modulation factor is increased, the center of the formant shifts. For example, let's say we start at a 2:1
ratio giving the following frequencies:
|Frequency (Hz)||262||523||785||1047||1308||1570||1832||etc |
At 2:1, the top 3 frequencies are 262, 523 and 785. At 3:1, the top frequencies are 785, 1047 and 1308. As I
shift up to 4:1, the top frequencies are 1308, 1570 and 1832.
So, what are these useful for? It turns out that if you were to look at the spectrums for instruments
or speech, you would notice that they can be broken down into formant groups. They can then be synthesized by
adding together multiple formant groups!
A similar example shown in Snd
As a non-linear synthesis technique, frequency modulation is not band-limited. What this means is that it can
produce waves which contain frequencies too high for a given sampling rate. When a signal contains a frequency
that is this high, it produces unexpected tones. This phenomena is called aliasing. Say we take a sine wave
at a frequency close to the maximum allowed. As we increase the pitch, the frequencies heard actually drop in
pitch as they wrap over the maximum frequency! An alternate name for this behavior is foldover.
What this all means is that a sound which is extremely sharp may not sound the same in different sampling
rates. For example, great cyclic noise effects such as the hihat below may be created with a high modulator.
However, if this sound is played back with a different sampling rate, it will likely sound different.