Two pitches on one distorted electric guitar versus the two pitches on separate distorted guitars

Just from practical experience it seems the former (two pitches on one distorted electric guitar) is nosier than the later (the two pitches on separate distorted guitars.) I don't know this is actually the case, but it seems so.

An example could be playing a passage in thirds around middle to high range. On one guitar those thirds seem to get very muddy and noisy. But if the parts are on separate guitars it seems less noisy.

Can someone elaborate on what happens in those two scenarios in terms of electric signals and acoustics? If there isn't really a difference, that would be helpful to know too.

Re. two separate guitars: I was thinking two separate speakers or two separate recorded tracks.

Intermodulation (IM) or intermodulation distortion (IMD) is the amplitude modulation of signals containing two or more different frequencies, caused by nonlinearities or time variance in a system. The intermodulation between frequency components will form additional components at frequencies that are not just at harmonic frequencies (integer multiples) of either, like harmonic distortion, but also at the sum and difference frequencies of the original frequencies and at sums and differences of multiples of those frequencies.

Distortion can be seen as another word for (or the result of) the non-linearity referred to in that quote. When you make a change in the input signal, you get a disproportionate change in the output signal - as you'll know, that's how distortions work, and that's non-linearity.

The sum and difference frequencies generated from the sinusoidal components of a single note are mostly closely related to the original note's components. When you distort two notes separately, that's all you get - each note with its own sums and differences.

However, if you distort a signal containing two notes mixed, you also get a load of other frequencies generated that represent the sums and differences of the components of each other's sums and differences. Depending on the pitches and spectra of the two notes, these may well be less closely related to the frequencies of the components in the original notes, which can cause the sound to be 'rougher'.

This is one of the the main reasons for the use of power chords in rock - a distorted open fifth creates relatively few messy, 'unrelated' frequency components.

topo Reinstate Monica's answer is much better, but I'll leave this here anyway.

From a signal processing perspective, you're looking at two different scenarios:

• (1) : distort(guitar1 + guitar2)
• (2) : distort(guitar1) + distort(guitar2)

There are two operations here: "+" and "distort". Out of these two, "+" is a linear, and "distort" is a non-linear operation. Distortion, by definition, cannot be undone: it means destruction of at least some aspects, some information in the original signal. When you play two different simultaneous notes into the same guitar amplifier, it's like scenario 1 - the signals are first summed and then the sum is distorted in the amp. But if you have a separate amp for each note, it's like scenario 2 - each signal is first distorted, and then the two distorted signals are summed linearly in the air.

For the linear summing operation, you can in theory get the original signal back with a reverse operation (subtraction).

• Sum(AB) = A + B
• A = Sum(AB) - B

But for the nonlinearity, the distortion, there isn't necessarily any way to reverse the operation and get a non-distorted clean signal back. For example, if the distortion is a simple clipper that saws off tops and bottoms of the sine waves - how do you undo? What if the input signal was like that to begin with and not nice round sine waves?