Intermodulation question -- discrete pickup sources vs. single pickup source

[midwayfair]

This came up last Sunday in talking with an engineer and a guy who was working on a hex pickup. The engineer suggested that you could run the hex through six different fuzz pedals and get no intermodulation even on complicated chords. I can't see a difference between playing thirds on one guitar or overdubbing a third on top of the root note on a different track, but maybe there's something that happens electronically as opposed to audio...ly .... auditorilly ... soundly .... braaaaaains what good's an english major anyway

Anyway: What's the score? Does something different happen inside the pedal than on different tracks or sources?

[Jazznoise]

Intermodular distortion is the results of non-linearities in a signal path causing the cosine partials to generate sum and difference signals. So while no system has NO IMD, running 6 parallel fuzz circuits would indeed avoid the noticably large amount you get with distortion pedals.

I'd miss it, honestly. Simple things like bending from one note into another are made magical by the beating generated by intermodular distortion.

[R O Tiree]

Surely, as soon as you mix down it will give you that same intermodulation? Even 2 disparate sources will give you those beat frequencies - shades of playing violin in my youth when they guy next to me just seemed incapable of tuning his instrument and I could hear the beat frequencies between him and the rest of the orchestra even on open strings.

[R.G.]

Your engineer friend is somewhat correct, somewhat not.

If you run a sine wave - that is, one and only one frequency - into any nonlinear process, the result will be the fundamental sine wave you put in, plus a number of harmonics of the original sine. If you call the sine's frequency F1, then you will get an output of some amount of F1, some amount of 2xF1, which the techie and musicology folks call F2, some amount of F3, some of F4, some of F5...

Each nonlinear process generates a different amount of each harmonic. Processes which operate on the positive and negative polarities equally will have only the odd harmonics, F3, F5, F7..., the even-number multiples of the original frequency being canceled. Any nonlinear process which affects positive and negative unequally will not achieve cancellation of the even multiples, so there will be some amount of **all** harmonics.

This is called "harmonic distortion". The human ear expects some harmonic distortion, and even likes some forms of it, or we would all hate fuzzes with a passion.

There is another kind of distortion. If you have a signal with two frequencies, Fa and Fb, and do anything nonlinear to the signal, you not only get out Fa, 2x Fa, 3x Fa,... as well as Fb, 2x Fb, 3x Fb, 4x Fb... but you *also* get Fa+Fb, Fa-Fb, 2x (Fa+Fb), 2x (Fa-Fb)... and Fa+/-(2xFb), Fb+/-(2*Fa)...

That is, it gets ugly. Lots of stuff that is musically unrelated to the original signals. Intermodulation more than vanishingly small sounds harsh and biting. Most people don't like and won't tolerate much of it willingly.

The idea behind a hex pickup is that an ordinary pickup produces the sum of all the strings at once, so you hear all of the strings that are not muted. Do a nonlinear process on that mixture, and you get both harmonic and intermodulation distortion. You can do much better on the intermod if you only hear one string. This is why single string runs sound sweeter than chords through a fuzz.

So if you always only had one string's signal, you would get rid of the intermodulation of the string signals. Great!!

But - (you knew there was a "but", didn't you?  ) string signals are not pure tones either. So picking up a single string with a hex pickup, fuzzing it, and then mixing the result with other strings does in fact get rid of all the Fa/Fb cross-product intermodulations in the output, and sound much less harsh. But you still have a single string signal that is not pure, has multiple signals in it, and not all of them are pure harmonics of the fundamental string vibration, for a number of reasons.

So yes, it helps. No, it will not get to zero intermodulation.

[midwayfair]

^ Thanks for the great explanations!

[WaveshapeIllusions]

So, to elaborate, playing a note on a single string through distortion will generate harmonic and intermodulation distortion? Since that note is not a pure sine wave all of its harmonics will result in IMD?

[R.G.]

Actually, I'd call that a simplification, not an elaboration, but that's right.
What was missing from my run down was the size of the distortion products.

A ring modulator is essentially pure intermodulation of two signals, and what comes out is only tenuously related to what went in.

A soft diode clipper may make 10 to 100 times less intermodulation distortion than a hard clipper. In really good hifi amps, the IM is much, much less than the THD.

Each nonlinear process has its own "signature" of the magnitudes of the products put out, and the amplitudes of the signals coming in have a big effect as well.

[drolo]

I'm still a bit lost as what the difference is between distorting the sum of all strings as opposed to distorting each one separately and then summing them. Wont they inter-modulate as well when the different distorted signals, with their individual harmonics are summed together. (please excuse my ingenuousness...)

[earthtonesaudio]

If anyone wants to hear this effect for themselves you don't need a hex pickup, just a sound card and Audacity (free) or any multi-track recording software.


Step 1: record a fuzzy chord normally.

Step 2: record the same chord, only this time record just one string at a time; each string gets a new track.

Step 3: compare the sound of the single-track chord with that of the six-track chord.

[Jazznoise]

Surely, as soon as you mix down it will give you that same intermodulation? Even 2 disparate sources will give you those beat frequencies - shades of playing violin in my youth when they guy next to me just seemed incapable of tuning his instrument and I could hear the beat frequencies between him and the rest of the orchestra even on open strings.

You're confusing Beating and IMD. IMD often causes beating as the partials generated may only be cents or Hz apart. So while the presence of IMD might be deduced by peceived beating, the presence of beating does not itself correlate to the presence of IMD. It's merely an indicator that partials of similar but different frequency are present. Correlation does not imply causation, and all that. 

I'm still a bit lost as what the difference is between distorting the sum of all strings as opposed to distorting each one separately and then summing them. Wont they inter-modulate as well when the different distorted signals, with their individual harmonics are summed together. (please excuse my ingenuousness...)

Just like you can get various amounts of clipping, you get various levels of IMD. A ring mod, as said, is pure IMD. An octave fuzz is probably the next largest. Then standard clipping circuits, compression etc. etc.

[R.G.]

I'm still a bit lost as what the difference is between distorting the sum of all strings as opposed to distorting each one separately and then summing them. Wont they inter-modulate as well when the different distorted signals, with their individual harmonics are summed together. (please excuse my ingenuousness...)

Imagine that (1) each string produces a pure sine wave and that (2) the mixer is perfectly linear, not doing any distortion itself, and (3) the same fuzz/distortion is applied either to each string separately or all strings mixed.

Distorting each string separately can produce only harmonics of that string. The high E string distorted all by itself (call this Fe) can produce only Fe, 2xFe, 3xFe..., all of which are musically related to the original Fe.

Similarly, the G string can produce only Fg, 2xFg, 3xFg... if it's distorted by itself.  Mixing the products of the two distortions you get Fe and its harmonics, Fg and its harmonics, but NO (Fe+/-Fg) or harmonics of that.

If you first run Fe and Fg into the mixer, you get (Fe+Fg). When you distort that, you get Fe and its harmonics, Fg and its harmonics, but also Fe+Fg, Fe-Fg, and harmonics of both (Fe+Fg), (Fe-Fg), and harmonics of Fe, Fg, and the cross products of their harmonics with each other.

It's this last series of (Fd-Fg) and the cross products that you cannot have in distortion before mixing.

The human ear LIKES multiplicative and exponential things. F + 2xF +3xF + 4xF... sounds good.
The human ear does not like add-and-subtract processes. F1+F2 is OK. F1-F2 is the sound of a ring modulator, and sounds strange. F1 +/- (n*F2) is ugly.

[drolo]

Hmm i see, I'm going to fire up my looper and listen to what it does  (or just listen to some Queen record..)
I will try to find an example of what such a guitar actually sounds like. intriguing..

[FiveseveN]

I will try to find an example of what such a guitar actually sounds like.

Pages with info and sound samples:
http://v6overdrive.com/samples.html
http://www.matthiasgrob.org/pEE/sndhist.htm
http://www.youtube.com/watch?v=Wzda9Ij4Un4
http://www.carmi.se/misterstarshine/Projects/7/
http://www.roland.com/V-Guitar/processing.html (see GR-D distortion)
http://music-electronics-forum.com/t13930/ (discussion)
etc.
I've fiddled with this kind of thing myself and now that the subject has resurfaced, might give it another go.

[drolo]

Thanks for the links,

on the V6 page the samples sound very different than what i had imagined. Very synth ..ey ..
I can see it being useful in some situations as well as not too nice in some others (like some samples demonstrate ..)

that guy scared me a bit ...
http://www.youtube.com/watch?v=Wzda9Ij4Un4

[FiveseveN]

Yes, the resulting sound might be described as "synthy" or unnatural, because we've become accustomed to the "normal", IMD'd drive tone. Some crosstalk could probably help here.
I think Roland pretty much nailed it with the GR-D: http://www.youtube.com/watch?v=Q4o3lAxPd3g
Or maybe we should leave the guitar alone and just play keyboards already  .

[Jazznoise]

I'd like to add that IMD isn't inherently bad but complex. Playing 220 and 440 hz, an octave, gives us extra 220 and some 660 which is the octave and a 5th. Playing a 10th, such as 220 and 554.366 Hz gives us 334.366 and 774.366 which gives us roughly a 5th, flat a few cents, and a b7 minus a few cents. Actually, I'm fairly sure by just temperment the new 7th is more in tune than a standard ET one. Obviously harmonics may clash as strings don't have a perfect harmonic series in the real world and complex intervals get pretty crazy, but we tend to make ourselves hear that which appears to be a pattern. This is why FM synthesis or a Timpani works at all, the fundamental is really an illusion. We get over it.

There's a reason a Hendrix chord sounds how it does when it's distorted and it's this stuff.  We hear in many ways and for many reasons. Log scales using 12 TET is what we're used to, but that's more cultural than innate. Sitting down and distorting sine waves on a synth in various intervals and compound intervals can give you a good understandong of this, as well as ways to use it. Different temperments will also give you radically different results, for complex tones especialy.

[earthtonesaudio]

Here's a question for the IMD aficionados: how would one go about maximizing it?  Is there a way to have chords go in and *only* intermodulation distortion come out?  What about single notes?

[R.G.]

Here's a question for the IMD aficionados: how would one go about maximizing it?

The communication biz has the terms:
Double sideband, suppressed carrier is nothing but the sum-and-difference products of deliberate intermodulation. The simple model is a ring modulator, some forms of which were used in early DSSC.
A more extreme version of this suppressed one of the two side bands and only sent either the higher or lower sideband; in radio parlance this is single sideband (or SSB). It's good for radio because the power used sending it is sending ONLY the information, not wasted on things like the carrier. Think poorly aligned citizen's band radio, or CB leaking into an AM radio. Duck quacking.

In music, we'd likely go for ring mod.

Note that all of these use "the signal", a composite of what you want to send, modulated by, or modulating, a fixed carrier wave. This will be important in the next answer.

Is there a way to have chords go in and *only* intermodulation distortion come out?

Not that I know of. All nonlinear processes tend to make some THD, except in the special case where you have two signals and modulate them to make DSSC or SSB, and then one of them is separate from the other.

A chord is already a mixture of signals, and when you do a nonlinear process on a mixture, you get the intermodulation of the mixture. No good way I can think of at the moment to make zero THD and all IM.

If you had two pickups separately, you could use one for the signal and one for the carrier and intermodulate them to get DSSC of the two with each other. Don't know how that works with six, though. And I can't think of a good way to separate the components of a chord other than crossover bands or per-string pickups.

What about single notes?

Gotta have two separate things to intermodulate without HD. Same problem as chords, just smaller mixtures of harmonics.

Maybe it could be done, but nothing I can think of at the moment. Ring mod is hard enough to make musical.

[Paul Marossy]

A ring modulator is essentially pure intermodulation of two signals, and what comes out is only tenuously related to what went in.

I have a nice sounding ring modulator (not my design) that's kind of based on the Maestro Ring modulator. I love it. It's fun to feed it with a distortion pedal following a wah pedal. Like most things that have some amount of intermodulation going on, it sounds great for single note stuff and various double stops, but not so great with chords.

When I first heard the original EH P.O.G. I thought it was fantastic and had to get one. There's no intermodulation (that you can obviously hear), you can play full chords and sound something like a pipe organ. I like how you can get a few different octaves going for each note and it doesn't get nasty sounding like a regular octave pedal would. Of course it has some kind of microprocessor in it to accomplish all that, and it does a pretty good job.

One other circuit I've messed with recently, which I am reminded of for some reason, is the Harmonic Percolater. It has a distinctive sound that sounds a bit to me like intermodulation distortion, but looking at it on the scope it actually looks like crossover distortion. The two at times can sound somewhat similar, but intermodulation distortion is way uglier sounding than crossover distortion is (although that sounds pretty bad if it's a significant amount).

Anyway, I think it might be possible to do something that gets the intermodulation down to something reasonable with a hexaphonic pickup system, but I think a microprocessor would have to be involved.

[Jazznoise]

Here's a question for the IMD aficionados: how would one go about maximizing it?  Is there a way to have chords go in and *only* intermodulation distortion come out?  What about single notes?

Simplest solution would be self modulation, such as running the same signal as both modulator and carrier in a Ring Mod. For single notes that's always going to give you an octaving effect. Phase shifting one signal to another will create interesting differences that aren't obvious without doing some maths. If anyone has Max or CSound try ring modding one sawtooth to another, and then dry it with an allpass or even a small delay. I'm a little surprised no one has capitalisd on this yet.

I've tried building a transformless ring mod with silent carrier and external modulation and it's not so easy.  Hoping those Opto Fets we discussed in another thread might do the job, we will see.