Are Undertones a Reality?

[thehallofshields]

I was playing around with a Bazz Fuss build tonight, and I noticed, when I played staggered 5ths, I got a sort of OC-2 sounding Thump.

It made me think how often people mention that rare fuzzes like the Percolator, Bosstone, etc. do unpredictable transient 'Octave Down' effects. I always thought this was just imagined.

Of course, I've read Mark Hammer explain Inter-modulation and how we get the Sum and Difference. It got me rethinking it.

So my questions are:

(1) Are Harmonic Undertones Possible?
(2) Does Inter-modulation account for 'Phantom Octave Down' heard in Distortion Effects?
(3) Which types of clipping arrangements are more likely to produce said effects?

[thehallofshields]

Some sample math of a Power-Chord.

A4 = 440.00hz
E5 = 659.26hz

Difference = 219.26hz, A3 = 220.00hz - Wow. Simple Octave Down
Sum = 1099.26, C#6 = 1108.70 - Ugh... Somewhere flat of an Octave + Major Sixth

Wow pretty simple...

Okay Octaves

A4 = 440.00hz
A5 = 880.00hz

Difference = 440.00hz - Okay nothing new there.
Sum = 1320.00hz, E6=1318.50 - Just sharp of 2 Octaves + Fifth. Nice.

An Inverted 5th (or a 4th)

E4 = 329.63hz
A4 = 440.00hz

Difference = 110.37hz, A2=110hz - Holy... that's almost a perfect 2 Octaves Down!
Sum = 769.63hz, G5=783.99 - Alright, we're flat of an Octave + Minor 7th... A little odd.

[Keppy]

1) Yes. Check the video below at 50sec for an example, or click this link. http://youtu.be/ubaoVzWe14M?t=50s
http://youtu.be/ubaoVzWe14M

2) Yes, at least partially, although some of these effects have such a pronounced bottom octave that I think there's more to it in some cases. The effect in the video above mixes a filtered signal with a plain fuzz.
3) Clipping arrangements that generate even-order harmonics:
Even order harmonics: 2nd=octave, 4th=2octaves
Odd order harmonics: 3rd=octave+P5th, 5th=2octave+M3rd
The even order harmonics make your math work. The odd ones don't really work unless the even ones are present as well. The most common method of emphasizing even-order harmonics is simple asymmetrical clipping, but that doesn't really create the obvious octave effect. The Harmonic Percolator is supposed to emphasize even-order harmonics, but I haven't worked out how.

[induction]

I built a harmonic jerkulator and percolator in one box, with clipping options of Si, Ge, and none. The percolator with Ge clipping very clearly gives sub-octave for single notes on the sixth and 5th strings between frets 3 and 12, as long as you pick softly. Harder picking kills the octave. The jerkulator doesn't give octaves anywhere on the fretboard, with any picking strength, as far as I can tell. So,

1) It's absolutely a real phenomenon
2) Probably not in this case, because it works on single notes.
3) Ge hard clipping, in this case. I don't know if that's a universal truth, though.

[ashcat_lt]

A4 = 440.00hz
E5 = 659.26hz
...Sum = 1099.26, C#6 = 1108.70 - Ugh... Somewhere flat of an Octave + Major Sixth

In my book, that's an Octave+Major Third

Do be careful, though, that you're not confusing the fundamental with an octave down effect.  A lot of dirt pedals tend to "speak" an octave up from the lowest notes.  Between high-passing and a prominent first octave harmonic, I think a lot of tend to think of the E string as being  higher than it really is.  When the fundamental actually speaks, it tends to come across as very bassy, and I can see where it might be confused in certain contexts with an octave down effect.

[blackieNYC]

True about the fundamental.  Listen to an 80 Hz sine wave.  Some folks don't think that could come out of a guitar.
Undertones - I built a Bosstone, and put a mosfet boost in front.  I got these occasional distracting octave down bursts - obnoxious only because they were so very intermittent.  Some friendly forum advice didn't help so naturally, I tried to bring out the octave downs. Life gives you lemons, make lemonade and whiskey sours. If I put my Ge Fur Face in front, with everything cranked, trebled rolled back at the gtr, I get a suboctave AND a slightly weaker 4th or 5th below that, jumping around between each other one at a time as the note rings out.  Didn't know you could get those.

[teemuk]

Yes, people generally obsess too much about the fundamental. My guitar plugged to spectrum analyzer displayed second, fourth and fifth harmonic stronger than the fundamental (and lesser, yet prominent amount of third) and only when vibration of the string started to decay did the amplitude of harmonics > 4th begin to decay. Basically, fundamental and second harmonic always had about the same amplitude. That said, most guitar amps - and especially all kinds of distortion effects - try to tame down all fundamentals of lower strings notes because in distorted tone these are nothing but "mud and farting". Usually it's about amplifying the harmonics and letting our brain do the job of reconstructing the fundamental from that data. We don't always neccessarily even hear it, at least not in full amplitude vs. other harmonics. Besides, it would be extremely boring if guitars outputted only sine waves.

[thehallofshields]

Okay so asymetric clipping is more likely to produce octave-down. This happens without Intermodulation?

But are we actually altering the waveform so something happens every other cycle, or is the brain filling in the Octave-Down because of something going on with the harmonic series?

[Transmogrifox]

But are we actually altering the waveform so something happens every other cycle, or is the brain filling in the Octave-Down because of something going on with the harmonic series?

It is possible that something happens every other cycle with a fuzz.  Often when you have a DC bypass cap on something like a BJT gain stage, and asymmetrical clipping, you end up getting something like a dirty envelope follower at the emitter.  This phenomena (dynamic clipping threshold) is some of what is attributed to the sound of tubes.

Pushed to an extreme with an input with the right fundamental it can be imagined this would pulsate between shut-off and amplification at a rate causing something different to happen on consecutive cycles of the input signal, creating lower frequency noises than the input's fundamental.

As such the gain of that stage is in some vague sense a relaxation oscillator in which the relaxation rate is dependent upon both input signal amplitude and input frequency.  The dependence is probably not neatly related by multiples of input frequencies.  I suppose this is one part of the reason fuzz is so nasty sounding (I mean "nasty" in a good way -- this is the nasty we like in a good fuzz)