[sdiy] Harmonic effect of rectification

[Richie Burnett]

In general when you put a complex signal through a non-linearity you get both
harmonics and "cross products" (also known as inter-modulation products)
produced.

So if your input signal contains three frequencies a, b, c.  The output of the
distorting thingy will likely contain harmonics of the form:

2a, 3a, 4a, 5a, etc...
2b, 3b, 4b, 5b, etc...
2c, 3c, 4c, 5c, etc...

and also "Sum" cross-products of the form:

a+b, b+c, c+a

and "Difference" cross-products of the form:

a-b, b-c, c-a

Even for just 3 frequencies present in the input, the output is already a rich
soup of frequency components.

If a, b and c are all related by simple fractions, then the sum and difference
frequencies will also fall on this scale.  However, if a, b and c are in complex
ratios, then at least some of the sum and difference frequencies will sound
horribly discordant.  That's why power chords sound okay through distortion
pedals.

The inter-modulation aspect of the distortion also explains why you can feed two
similar high frequencies into a distortion box and hear a new lower frequency in
the output.  This isn't a harmonic, what you're hearing is a difference product
due to inter-modulation.

-Richie,


> For the non-mathematicians, the quick answer is that you have a monophonic
> note going to a severe distorter like a rectifier, you get higher multiples
> of the same frequency.
>
> But if you have a number of different frequencies in the signal - like a
> chord - then you get a very non-harmonic bunch.