More on ring modulators and pitch shifters

Bryan T · Post by **Bryan T** » Wed Sep 09, 2009 12:30 am

Background
A bit of the theory of ring modulation. The ring modulator takes two signals as input and outputs the sum and difference of those signals. For example, if you input signal x and signal y, then the ring mod outputs signal x+y and signal x-y.

Some basic examples of what a ring mod does:

Ex. x=220 Hz, y=30 Hz.
x+y = 250 Hz
x-y = 190 Hz

Ex. x=220 Hz, y=220 Hz
x+y = 440 Hz
x-y = 0 Hz

Ex. x=220 Hz, y=440 Hz
x+y = 660 Hz
x-y = -220 Hz, which we hear as 220 Hz

Sometimes, the output sounds in tune, sometimes not. It all depends on how the audio and carrier frequencies relate. Because of this, ring modulators can produce all sorts of interesting sounds.

Still with me?

Pitch-shifting the audio and using it as the carrier
I started thinking about what happens when the carrier signal is a pitch-shifted version of the original signal. What happens with the sums and differences then? Lots of interesting things, but it took a bit of head-scratching to think things through.

Part of my initial confusion is that ring modulation works by adding and subtracting frequencies, but pitch shifting works by multiplying frequencies. I had to refresh my memory about how to work with ratios.

Ex. x = x, y = x (the carrier is the same as the audio signal)
sum = x+x = 2x
difference = x-x = 0
This produces an output an octave above the audio signal.

Ex. x = x, y = (3/2)x (the carrier is pitch-shifted a fifth above the audio signal)
sum = x + (3/2)x = (5/2)x
difference = x - (3/2)x = -(1/2)x => (1/2)x
The sum works out to be a major third an octave above the audio signal. 5/2 is equivalent to 5/4 when octave reduced. 5/4 is the just intonated major third.
The difference frequency is half the audio signal frequency, which is simply an octave below the original audio signal.

Ex. x = x, y = 2x (the carrier is an octave above the audio signal)
sum = x+2x = 3x
difference = x-2x = -x, which we hear as x
The sum works out to be three times the frequency. This octave reduces to 3/2, which is a just intonated fifth. So, the sum frequency is an octave and a fifth above the audio signal.
The difference frequency is the same as the original audio signal.

Ex. x = x, y = (4/3)x (the carrier is a fourth above the audio signal)
sum = (7/3)x
difference = -(1/3)x, which we hear as (1/3)x
The sum signal octave reduces to (7/6)x, which is a just intonated minor third, an octave above the audio signal.
The difference is equivalent to a perfect fourth above, but is in the octave below the audio signal.

Conclusion
So, what is this all about? What this means is that if you have a ring mod and a pitch shifter, then you should be able to get some interesting results by pitch shifting the audio signal and using that as the carrier. It is a way to have a 'tracking ring mod,' with repeatable (and predictable) results. Using a bit of knowledge about how to add two frequencies and make sense of the result, you can figure out how the sums/differences of any pitch-shifted interval relate back to the original audio signal.

Bryan

Bryan T · Post by **Bryan T** » Wed Sep 09, 2009 1:08 am

Also, pitch shifting the audio signal down instead of up will result in quite different results.

Bryan T · Post by **Bryan T** » Wed Sep 09, 2009 1:55 am

Here are some examples I worked out:

Pitch-shift / Sum / Difference
unison / octave / none
octave / octave+fifth / unison
fifth / major third+oct / octave below
fourth / minor third+oct / fourth, two octaves below
major 3rd / major second+oct / two octaves below
major 2nd / minor second+oct / three octaves below
major sixth / fourth+oct / fourth in octave below

octave below / fifth / octave below
fifth below / sixth / fourth, two octaves below
fourth below / minor seventh / two octaves below
major 3rd below / other minor seventh / minor sixth, three octaves below

Bryan T · Post by **Bryan T** » Wed Sep 09, 2009 12:56 pm

I'll try to record some examples to demonstrate.

patobrujo · Post by **patobrujo** » Wed Sep 09, 2009 3:26 pm

i found this really interesting... how about putting your signal in carrier in, and then carrier out in audio in. will this allow the RM to track the pitch of the incoming signal? is necesary to put the frecuency knob on a specific value? i'm a asking stupid questions?

mgrfgrmadness · Post by **mgrfgrmadness** » Wed Sep 09, 2009 3:29 pm

thank you for this, i understand ringmods so much better now
i love taking a split signal from a guitar and running one into the carrier in, and the other in the input, perfect octavia sounds

Bryan T · Post by **Bryan T** » Wed Sep 09, 2009 4:22 pm

patobrujo wrote:i found this really interesting... how about putting your signal in carrier in, and then carrier out in audio in. will this allow the RM to track the pitch of the incoming signal?

I don't think it works like that.

is necesary to put the frecuency knob on a specific value?

The frequency knob doesn't do anything when you are using an external carrier.

Bryan T · Post by **Bryan T** » Wed Sep 09, 2009 4:23 pm

mgrfgrmadness wrote:thank you for this, i understand ringmods so much better now

No problem. I was inspired by the discussion yesterday.

i love taking a split signal from a guitar and running one into the carrier in, and the other in the input, perfect octavia sounds

Yep, that's a great effect.

Bryan T · Post by **Bryan T** » Thu Sep 10, 2009 12:04 am

Here's a quick audio demo of using a pitch shifter on the carrier signal to have a tracking ring mod:

http://bryantysinger.com/tempaudio/trackingRM.mp3

Some comments: I used a very simple sound on the Little Phatty, with a single oscillator and a simple waveform. I think that lets you hear the purity of the notes. I used an Alesis Ineko for the pitch-shifting. It is pretty cool - it has a lot of character - but isn't the most accurate or non-glitchy of pitch shifters. It also has a fairly audible delay when pitch-shifting.

I think you can do an awful lot with this kind of processing. Using a more complex wave form gives some really cool sounds, as does adding the second oscillator on the Little Phatty. Having an LFO control the Mix on the Ring Mod is a great way to add some motion to the sound.

I think you could do a lot with a better pitch shifter, such as the Eventide Pitch Factor. If you used one with expression pedal control you could morph between two settings for some really sick sounds.

Bryan

DontBelievetheHype · Post by **DontBelievetheHype** » Thu Sep 10, 2009 6:58 am

A few months ago I tried this with my dry into the audio input, and the HOG set to +1oct going into the Carrier in... and noticed no difference that just using the HOG mixed with dry signal.. Ill have to give this a shot again and try sending dry into the audio/carrier in's, as well as some different intervals; I must have been doing something wrong.

The Radium King · Post by **The Radium King** » Thu Sep 10, 2009 11:37 am

use the hog in step bend mode with just the fundamental on as the carrier in, and send the dry signal to audio in. now the carrier will track the input, with a pitch offset set by the expression pedal. given that the hog will take cv inputs, try using an lfo, envelope follower or envelope follower controlling the lfo, to modulate the carrier.

ps, pato - the internal carrier wave in the ring mod is a voltage controlled oscillator (controlled by the frequency knob) that is connected to the ring mod circuit. when you connect an external carrier (ie, plug your instrument into the carrier in jack) the vco is disonnected fromt the ring mod circuit. it is, however, still sending it's info to the carrier out jack. so if you were to then plug the carrier out into the audio it, your ring mod would be working in reverse - the instrument is now the carrier and the carrier is now the instrument. i think that, sonically, it would sound just the same ?!?

Bryan T · Post by **Bryan T** » Thu Sep 10, 2009 4:57 pm

patobrujo wrote:i found this really interesting... how about putting your signal in carrier in, and then carrier out in audio in. will this allow the RM to track the pitch of the incoming signal?

I tried this. What you get with the Mix on 0 is just the carrier signal, determined by the setting of the Frequency knob. As you turn up the Mix you start to hear the sum/difference tones with the signal that you are sending to the Carrier input.

It is an interesting way to generate a drone and then introduce ring modulation of that drone.

Bryan

patobrujo · Post by **patobrujo** » Fri Sep 11, 2009 11:15 am

Bryan T wrote:
patobrujo wrote:i found this really interesting... how about putting your signal in carrier in, and then carrier out in audio in. will this allow the RM to track the pitch of the incoming signal?
I tried this. What you get with the Mix on 0 is just the carrier signal, determined by the setting of the Frequency knob. As you turn up the Mix you start to hear the sum/difference tones with the signal that you are sending to the Carrier input.

It is an interesting way to generate a drone and then introduce ring modulation of that drone.

Bryan

Yes i tried this too, not what i expect but an interesting effect either way...