From nwilson@morgan.com Tue Jan 17 13:35:38 1995
Date: Tue, 17 Jan 1995 12:17:11 -0500
From: Ab Wilson <nwilson@morgan.com>
To: Analogue Heaven <analogue@magnus.acs.ohio-state.edu>
Subject: Ring Modulator

Richard Klasic writes:
 > Excuse my totally dumb question. But can someone explain what a Ring 
 > Modulator is to me?

This will no doubt be one of many replies.

A ring  modulator has  two  inputs (lets call   them x and y) and  one
output. The output is  simply x multiplied by y.  So if the inputs are
two constant voltages the output will be their product. Also if either
input is zero then the output will be zero.

This is somewhat similar to a VCA except that a ring mod works in all
four cases with (+ve x, +ve y), (+ve x, -ve y), (-ve x, +ve y), (-ve
x, -ve y).

To understand why a ring  modulators are interesting  you need to know
one more   thing -   through   some bizarre feet   of  mathmatics this
multiplication has the following effects in the frequency domain. If x
and y are fixed frequency sine  waves then the output  will be the sum
and difference of these frequencies. eg for x=50Hz, y=50Hz, the output
is a 100Hz sine wave with a 0Hz (dc) component. For x=50Hz, y=75Hz the
output will be a mixture of a 25Hz sine and 100Hz sine.

If the inputs are not pure sine waves then the  output will consist of
the sums and differences of all the frequency componts of each signal.
So  for  x=3KHz  sawwave,  y=200Hz  sine the  output  will be  all the
frequency components of the original saw  shifted down 200Hz, plus all
the components  shifted up 200Hz. Since  these shifts are additions in
frequency   and not multiplications the  result   will no longer sound
harmonic because the partials of  the sound will  no longer be in tune
with the fundamental. This  is  the  first  and probably most   common
applicatino of a ring modulator - creating disonant, clangy timbres.

Now say x=1KHz sawwave and y=2KHz sawwave which has been passed though
a  low  pass filter  with  the resonance set very   high (but not self
oscilating)  so as to pick out  a narror band of  high harmonics.  The
output   will now be the  sum  and product  of  each  of the harmonics
selected by the filter with each of the harmonics of the 1KHz saw.  In
this case the frequencies of the input signals where a simple ratio of
each other so  the output will  still be harmonic.   The actual result
will sound similar to a formant filter since  the original single peak
in the response  will have been replaces  by multiple peaks -  one for
each of the sums and products.

Like most interesting synthesis techniques  ring mod takes quite a bit
of  tweaking to sound good.   It's not just  a case of  turning it on,
randomly moving a few sliders and then  asking whether the trendy term
is  acid or  hard trance   this  week.  That's probably   why it isn't
included in  more synths. I'm  a recent convert having only discovered
the prefiltering technique a few  weeks ago. It  came as one of  those
relevations. I now put ring mod up there  with FM and waveshaping as a
powerful  non-subtractive synthesis  technique  (the term constructive
seems appropriate).

	Ab.


From PPilgrim@teleglobe.ca Tue Jan 17 13:41:17 1995
Date: 17 JAN 95 11:39:33 EST
From: PPilgrim@teleglobe.ca
To: analogue@magnus.acs.ohio-state.edu
Subject: Re: Ring Modulator


Rick, 

 A ring modulator mixes two input signals and outputs two frequencies equal
 two the sum and difference of each input frequency. I believe the technical  
 term for this is an intermodulation generator. For instance, if
 you input 100Hz and 80 Hz, the output would be 20Hz and 180 Hz. In
 human terms, the output sounds "bell like" thus the name "ring" modulator.

 On my CS-60 the ringmodulator uses the audio signal as one input so it must 
 generate a second signal which it mixes with the audio signal (I never       
 looked into this). 
 
 It's a good tool to get metalic FMish sounds from an analog synth. Also
 you can get some great "weird" sounds for special percussive or theatrical
 needs.(especially B SciFi movies)

Philip Pilgrim


From media@pcnet.com Tue Jan 17 16:17:49 1995
Date: Tue, 17 Jan 1995 14:04:58 -0500 (EST)
From: Machine Media <media@pcnet.com>
To: Richard Klasic <rick@latlin.mednet.gu.se>
Cc: Analogue Heaven <analogue@magnus.acs.ohio-state.edu>
Subject: Re: Ring Modulator


> Excuse my totally dumb question. But can someone explain what a Ring 
> Modulator is to me?

When it comes to synths, I've asked even dumber questions. The last time 
I answered a question here, no one called me an asshole, so I'll continue :)

OK, a ring modulator is pretty simple. If you take a waveform and 
cross-modulate (multiply) it with a another simple waveform, creating a new 
waveform that does not contain either original waveform, that's 
ring modulation. The new waveform only contains harmonics at the sum & 
difference of the two original frequencies eg. if a 300hz tone is ring 
modulated by an 1100hz tone, you would get a new signal with 1400hz & 
300hz.  This is assuming that the original waveforms are simple (contain 
only their fundamental harmonic). If you take more complex waveforms, 
every harmonic multiplies every other harmonic, & so on.

Why is it called ring modulation?? Because it typically makes a "ringing" 
sound with all of these odd harmonics.

Now lets add tubular bells: A bell is a cup until it is struck. A metal 
cup full of air has alot of mechanical resistance against oscillating at 
any frequency other than its own resonance. Try blowing across a 
top of a glass. (what am I?? Mr. Science? ;) Frequencies that do not 
create nodes inside the bell aren't going to last very long. So, we ring 
the bell, and it wags back and forth, gee, just like a fast pendulum -- 
doesn't a pendulum have a specific frencency? So, we have the frequency 
of the "pendulum" cross modulating the nodal frequencies inside the bell, 
so the resulting frequencies are the sum & difference of these original 
frequencies. That's ring modulation :)

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From don@till.com Wed Jan 18 12:42:27 1995
Date: Tue, 17 Jan 1995 22:31:29 -0800
From: Don Tillman <don@till.com>
To: analogue@magnus.acs.ohio-state.edu
Subject: Re: Ring Modulator

   Date: 	Tue, 17 Jan 1995 12:17:11 -0500
   From: nwilson@morgan.com (Ab Wilson)

   A ring  modulator has  two  inputs (lets call   them x and y) and  one
   output. The output is  simply x multiplied by y.  So if the inputs are
   two constant voltages the output will be their product. Also if either
   input is zero then the output will be zero.

Ahh, correct and succinct.  

   To understand why a ring  modulators are interesting  you need to know
   one more   thing -   through   some bizarre feet   of  mathmatics this
   multiplication has the following effects in the frequency domain. 

The math is actually quite simple.  Remember in High School
trigonometry, when you weren't hanging out by the industrial arts wing
with the cool guys in those jackets, the equation for the cosine of
the sum of two angles?

  cos(a + b) = cos(a)cos(b) + sin(a)sin(b)

And since cos(x) = cos(-x):

  cos(a - b) = cos(a)cos(b) - sin(a)sin(b)

Add them together:

  cos(a + b) + cos(a - b) = 2 cos(a)cos(b)

The right half is multiplying to sine waves.  The left half is a pair
of sum and difference frequencies.  Piece of cake.

   Like most interesting synthesis techniques  ring mod takes quite a bit
   of  tweaking to sound good.   It's not just  a case of  turning it on,
   randomly moving a few sliders and then  asking whether the trendy term
   is  acid or  hard trance   this  week.  

[Direct hit!  Incoming, dive, dive.]

					   That's probably   why it isn't
   included in  more synths. 

Another reason is that it requires a lot of routing flexibility --
it's not always obvious what the best sources for the inputs ought to
be.  So it's best on a modular.

   Date: Tue, 17 Jan 1995 14:04:58 -0500 (EST)
   From: Machine Media <media@pcnet.com>

   OK, a ring modulator is pretty simple. If you take a waveform and 
   cross-modulate (multiply) it with a another simple waveform, creating a new 
   waveform that does not contain either original waveform, that's 
   ring modulation. The new waveform only contains harmonics at the sum & 
   difference of the two original frequencies.

This is a very mangled definition.  "Cross modulation"?  

   Why is it called ring modulation?? Because it typically makes a "ringing" 
   sound with all of these odd harmonics.

Uhhhhhhhhhhh, no.  It was called ring modulation long before
electronic music.  The name came from the earliest implementations,
consisting literally of a ring of diode tubes and three transformers.

   Now lets add tubular bells: A bell is a cup until it is struck. A metal 
   cup full of air has alot of mechanical resistance against oscillating at 
   any frequency other than its own resonance. Try blowing across a 
   top of a glass. (what am I?? Mr. Science? ;) Frequencies that do not 
   create nodes inside the bell aren't going to last very long. So, we ring 
   the bell, and it wags back and forth, gee, just like a fast pendulum -- 
   doesn't a pendulum have a specific frencency? So, we have the frequency 
   of the "pendulum" cross modulating the nodal frequencies inside the bell, 
   so the resulting frequencies are the sum & difference of these original 
   frequencies. That's ring modulation :)

Yuck, I count five blatent errors.

Bells have oodles of resonant frequencies, pendulums have one, and the
bell's frequencies are not harmonically related.  In that way the
sound of bells is similiar to the output of a ring modulator.  There
are very few other sources of sounds with those characteristics.

  -- Don

From don@till.com Wed Jan 18 19:07:12 1995
Date: Wed, 18 Jan 1995 14:25:29 -0800
From: Don Tillman <don@till.com>
To: analogue@magnus.acs.ohio-state.edu
Subject: Ring Modulator

More ring modulator tidbits...

Run a sine wave into both inputs of a ring modulator.  The output will
be a sine wave of twice the input frequency (sum frequency) with a dc
bias (difference frequency).  This only works with sine waves, for
obvious reasons.

Run a microphone into a ring modulator with an oscillator for the
other input.  Sing into the microphone.  Notice anything?  I mean
besides the fact that your voice comes out real strange.  It won't
feed back even if you're holding the mic right next to the speaker and
cranking it real loud.

Maestro used to make a ring modulator effects box that was
surprisingly popular with jazz electric pianists; both Jan Hammer
(w/Mahavishnu) and George Duke (Zappa) used them on their Rhoades'.
I'm pretty sure some member of the Don Ellis orchestra used one of
these too.

  -- Don






