Modulation Synthesis

Lecture Slides

A series of images of the lecture slides...

Links to online documentation

FM resources

Here are a couple of links to interesting stuff about Frequency Modulation:

CLM stuff you should look up

  • definstrument (how to define a CLM instrument)
  • oscil (a sinewave oscillator)
  • env (a piecewise linear envelope)
  • outa (basic one channel output)
  • with-sound (how to get everything working)
  • the run loop

CM stuff you should look up

Here is the dictionary where all of Common Music functions and macros are documented.
  • hertz (converts from anything to frequencies)
  • keynum (converts from anything to key numbers)
  • note (converts anything to note names)
  • pick (pick a random argument - and see pickl as well)

Modulation Synthesis

Ring Modulation

Amplitude Modulation

Simple Frequency Modulation


  • A very simple ring modulation instrument (ringmod.ins)
  • A very simple ring modulation instrument with wavetable oscillators (ringmodw.ins)
  • A very simple amplitude modulation instrument (ampmod.ins)
  • A very simple amplitude modulation instrument with wavetable oscillators (ampmodw.ins)
  • A very simple frequency modulation instrument (fmmod.ins)

Here are a bunch of fm instruments, mostly coming from the clm area ("/usr/share/common-lisp/source/clm/"). You should explore, there's a wealth of information and examples hiding there...


The eternal "fm bell". Here is the header of the instrument and a short description of its parameters:

(definstrument fm-bell (start-time duration frequency amplitude 
			amp-env index-env index
                        (degree 0.0)
			(distance 1.0)
			(reverb-amount 0.005))

Mandatory parameters

starting time in seconds
duration of the note in seconds
frequency of the note in Hertz
amplitude of the note (between 0 and 1)
amplitude envelope. A list of time-value coordinates that determines the evolution of loudness over time. The time values are relative and are scaled to the duration of the note (for example I usually use a time axis that stretches between 0 and 1).
modulation index envelope. A list of time-value coordinates that determines the evolution of modulation index over time. The modulation index controls the "brightness" of the sound (the higher the index the brighter the resulting sound).
modulation index. The scaler for the index envelope.

Optional parameters

angle in degrees from where the sound is coming from in a stereo rendition. "0" is left and "90" is right; "45" is right in the middle of the stereo field.
distance in feet from where the sound is coming from.
amount of reverberation added to the sound. For this to work you must have a reverberator loaded and the with-sound call has to specify it.

Some random with-sound's

doesn't sound like a bell...

  (with-sound()(fm-bell 0 4 440 0.1 
                        '(0 0 0.05 1 0.2 0.4 0.8 0.2 1 0)
                        '(0 0 0.02 1 0.2 0.2 0.8 0.1 1 0)
so let's tweak envelopes a bit...

  (with-sound()(fm-bell 0 4 440 0.1 
                        '(0 0 0.002 1 0.2 0.4 0.8 0.2 1 0)
                        '(0 0 0.001 1 0.1 0.08 0.8 0.01 1 0)
maybe try a duller bell?

  (with-sound()(fm-bell 0 4 440 0.1 
                        '(0 0 0.002 1 0.2 0.4 0.8 0.2 1 0)
                        '(0 0 0.001 1 0.1 0.08 0.8 0.01 1 0)
but with a different envelope and a lower frequency it's not a bell any longer... (but sounds like the typical fm wow)

  (with-sound()(fm-bell 0 4 78 0.1 
                        '(0 0 0.3 1 0.4 0.9 0.8 0.2 1 0)
                        '(0 0 0.35 1 0.38 0.9 0.8 0.01 1 0)


A drum simulation. Here is the header of the instrument and a short description of its parameters:

(definstrument fm-drum (start-time duration frequency amplitude index 
                        (high nil)
                        (degree 0.0)
                        (distance 1.0)
                        (reverb-amount 0.01))

Mandatory parameters

modulation index.

Optional parameters

"t" introduces an upwards glissando in the end of the note (the glissando function is a constant hardwired into the instrument, it could be made a parameter, of course).

Some example with-sound's

  (with-sound ()
              (fm-drum 0 1.5 55 .3 5 nil)
              (fm-drum 2 1.5 66 .3 4 t))


A very nice gong simulation. Here is the header of the instrument and a short description of its parameters:

(definstrument gong (start-time duration frequency amplitude
                     (degree 0.0)
                     (distance 1.0)
                     (reverb-amount 0.005))

Mandatory parameters


Optional parameters


Some example with-sound's

  (with-sound () (gong 0 3 261.61 .6))

Fm violin

A generic and very versatile fm instrument created by Bill Schottstaedt. A nice example of multipurpose coding. Almost everything has reasonable defaults but can be changed. If you examine the code you'll see another feature common to good instruments. The key parameters are defaulted to the value of special (global) variables. That opens the possibility of globally changing the behaviour of a bunch of notes by just encasing them in a "let" with redefinitions of those global variables. Here is the header of the instrument and a short description of its parameters (which has plenty off):

(definstrument fm-violin
  (startime dur frequency amplitude 
   (fm-index                   fm-violin-fm-index)
   (amp-env                    fm-violin-amp-env)
   (periodic-vibrato-rate      fm-violin-periodic-vibrato-rate)
   (random-vibrato-rate        fm-violin-random-vibrato-rate)
   (periodic-vibrato-amplitude fm-violin-periodic-vibrato-amplitude)
   (random-vibrato-amplitude   fm-violin-random-vibrato-amplitude)
   (noise-amount               fm-violin-noise-amount)
   (ind-noise-freq             fm-violin-ind-noise-freq)
   (ind-noise-amount           fm-violin-ind-noise-amount)
   (amp-noise-freq             fm-violin-amp-noise-freq)
   (amp-noise-amount           fm-violin-amp-noise-amount)
   (noise-freq                 fm-violin-noise-freq)
   (gliss-env                  fm-violin-gliss-env)
   (glissando-amount           fm-violin-glissando-amount)
   (fm1-env                    fm-violin-fm1-env)
   (fm2-env                    fm-violin-fm2-env)
   (fm3-env                    fm-violin-fm3-env)
   (fm1-rat                    fm-violin-fm1-rat)
   (fm2-rat                    fm-violin-fm2-rat)
   (fm3-rat                    fm-violin-fm3-rat)
   (fm1-index                  fm-violin-index1)
   (fm2-index                  fm-violin-index2)
   (fm3-index                  fm-violin-index3)
   (base                       fm-violin-base)
   (frobber                    fm-violin-frobber)
   (reverb-amount              fm-violin-reverb-amount)
   (index-type                 fm-violin-index-type)
   (degree                     nil)
   (distance                   1.0)
   (no-waveshaping             nil)
   (denoise                    fm-violin-denoise)
   (denoise-dur                .1) ;used to be .5 
   (denoise-amp                .005)

Mandatory parameters


Optional parameters

fm-violin-fm-index 1.0
overall modulation index.
fm-violin-amp-env '(0 0 25 1 75 1 100 0)
amplitude envelope.
fm-violin-periodic-vibrato-rate 5.0
periodic vibrato frequency (periodic vibrato is a triangular wave).
fm-violin-random-vibrato-rate 16.0
random vibrato rate (random noise added to the vibrato).
fm-violin-periodic-vibrato-amplitude 0.0025
amplitude of the periodic vibrato.
fm-violin-random-vibrato-amplitude 0.005
amplitude of the random vibrato.
fm-violin-noise-amount 0.0
add index and amplitude noise (internal movement of the sound).
fm-violin-noise-freq 1000.0
bandwidth of the index and amplitude noise.
fm-violin-ind-noise-amount 0.0
index noise amount
fm-violin-ind-noise-freq 10.0
bandwidth of index noise.
fm-violin-amp-noise-amount 0.0
amplitude noise amount
fm-violin-amp-noise-freq 20.0
bandwidth of amplitude noise.
fm-violin-gliss-env '(0 0 100 0)
glissando envelope (pitch envelope)
fm-violin-glissando-amount 0.0
scaler for the pitch envelope.
fm-violin-fm1-env '(0 1 25 .4 75 .6 100 0)
index envelope for first modulator
fm-violin-fm2-env fm-violin-fm1-env
fm-violin-fm3-env fm-violin-fm1-env
fm-violin-fm1-rat 1.0
modulator / carrier frequency ratio for first modulator.
fm-violin-fm2-rat 3.0
fm-violin-fm3-rat 4.0
fm-violin-base nil
kind of interpolation to be done between envelope points.
fm-violin-frobber nil
fm-violin-reverb-amount 0.01
reverberation amount.
fm-violin-index-type :violin
fm-violin-denoise nil
whether to try to reduce quantization noise in envelopes.
fm-violin-index1 nil
modulation index for the first modulator.
fm-violin-index2 nil
fm-violin-index3 nil

Some example with-sound's

For a compilation of examples on how the fm-violin can sound load the fmviolin.clm file. The 20 Mbyte soundfile created by loading fmviolin.clm into lisp after compiling and loading both v.ins and jcrev.ins is at /usr/ccrma/web/html/courses/220b/lectures/1/examples/fmviolin.snd (this will save you some time since the soundfile take quite a long time to be created). Start a copy of "snd" and load the file in it to play the example. Please be aware that for this example to work you will also have to compile and load a reverberator (jcrev.ins). If you want to play with the lisp code inside fmviolin.clm I strongly suggest you take apart the file and create a small with-sound for each example you are interested in... the whole soundfile is almost 20Mbytes long.

Fm voice

Chowning's fm voice instrument.

(definstrument fm-voice (beg dur pitch amp
                         vowel-1 sex-1
                         ampfun1 ampfun2 ampfun3
                         indxfun skewfun vibfun ranfun
			 dis pcrev deg vibscl pcran
                         skewscl ranpower glissfun glissamt)

Some example with-sound's

(let ((ampf '(0 0 1 1 2 1 3 0))) 
   (with-sound (:wait t) (fm-voice 0 1 300 .8 3 1
           ampf ampf ampf ampf ampf ampf ampf
           1 0 0 .25 1 .01 0 ampf .01)))

Music examples

Water Music by Bill Schottstaedt.


Turenas by John Chowning.



Roads: When was Turenas composed?

Chowning: It was completed in the spring of 1972. The compositional work spanned several years, however. I was involved with writing the spatial manipulation programs for some time, and Turenas made extensive use of that experimentation. It's hard to say when a composition begins if research is tied so intrinsically to a work. The piece evolved over a period of years, and I finally finished it after I concluded that I had enough of the music-gestural control over the computer.

Roads: Turenas is based on the frequency modulation (FM) sound synthesis technique, a technique based on your own research. How is FM used in Turenas?

Chowning: FM is something I stumbled upon in the mid-1960s. It turned out that one could, in a sense, "cheat on nature." By modulating the frequency of one oscillator (the carrier) by means of another oscillator (the modulator), one can generate a spectrum that has considerably more components that would be provided by either of the two alone (Chowning 1973).

There's another important aspect. FM provides a simple way to get dynamic control of the spectrum, which is one of the aspects of natural sounds that was very difficult to reproduce with analog synthesizers. So FM is a synthesis technique that is useful or not depending upon the type of control one desires. It turns out to be quite widely used, and its usefulness is that it provides a few handles onto a large timbral space.

In Turenas, I used only the FM technique for generating the tones. I used it in both a harmonic series mode and a noisy inharmonic series mode, with transformations between the two. One of the compositional uses of FM was in timbral transformation. This was often coupled with spatial manipulation. As the sounds crossed the space they underwent a timbral transformation.

Roads: How was this accomplished?

Chowning: There were a number of techniques. Sometimes there were very slow transformations from harmonic series timbres to other harmonic series timbres -- from rich double-reedy sounds to flutelike sounds. In that case, there was a gradual change in modulation index. Other kinds of transformations in the piece had to do with changes from harmonic to inharmonic spectra or the inverse, through a gradual change in the carrier-to-modulator (c:m) ratio.

(excerpted from an interview with Chowning by Curtiss Roads)
Stria by John Chowning.


Phone by John Chowning.


©2000-2005 Fernando Lopez-Lezcano. All Rights Reserved.