When guitarists refer to 'distortion', they mean what's technically called harmonic distortion. This is what happens when a gain stage is asked to create a bigger version of a signal than it has the capacity for. As the signal gets too big for the device's boundaries, its head and feet get clipped off. This changes the shape of the waveform, which of course makes it sound different.
To understand how the sound is effected, we need to understand a bit about the correlation between the shape of a wave and harmonics.
And what are harmonics? Actually, harmonics and waveforms are two ways of describing the same sound. Sound is vibration, and we can describe complex vibration either by plotting change in position over time (drawing it as a curve), or by thinking of the complex vibration as a combination of simple vibrations. The simplest periodic vibration is a sine wave.
If we take a sine wave that comes and goes 200 times a second, and mix it with other sine waves that cycle twice as often, three times as often, four times as often... the result is a more complex wave.
These additional waves are called harmonics.
In the case of sound waves, the coming and going is the squishing and stretching of air. When two waves are pushing at the same time, the air gets extra squished. If one wave is squishing while the other is stretching, they tend to cancel each other out.
It's a little easier to grasp this if you watch it in action. Click the ADD button below and observe how the harmonic pushes and pulls at the fundamental sine wave.
All pitched sounds can be thought of as being made up of sine waves like this. So when we re-shape a complex waveform, it's the same thing as changing the mixture of sine waves that make it up. It's useful to think of it as a mixture of harmonics, because that view correlates with how humans hear, and with harmony.
If we took our fundamental sine wave, and added one that comes and goes three times as often - which would be called the third harmonic - we'd get get something like this:
Hm... looks kind of like what would happen to the sine wave if it was subjected to the kind of clipping displayed at the top of the page.
Odd-numbered harmonics (the 3rd, 5th, 7th, etc.) push the composite waveform towards a square wave.
So when we neatly square off the tops and bottoms of a signal, we add odd-numbered harmonics. There'll be plenty of high-order harmonics, because it takes harmonics that are a lot higher in frequency than the fundamental to put tight corners in a waveform. Or looking at it the other way around, if you put tight corners in the waveform, you're going to hear high-order harmonics. A bipolar transistor biased for maximum headroom does just that, because it chops off the heads and feet of the wave very abruptly. Some other devices don't chop things off quite so neat. They exhibit soft clipping – they start to round off the heads and feet as they approach the device's limits. So the harmonics are closer in frequency to the fundamental, and sound more like part of the same tone.
Now what about even-numbered harmonics? In that first interactive picture we added second harmonic, but that didn't result in something that looked like a wave you could get with clipping. But if we shift the phase of that second harmonic (the point at which it starts)...
Look at that - looks like a wave that's had its head loped off, but not its feet. That's definitely doable. So asymmetrical clipping creates even harmonics.
Do we want to add even harmonics? Let's take on that controversial issue. Even sounds better, right? Tubes produce even, transistors produce odd, right? Wrong! Wrong!
Okay, there is some truth to those statements, in some contexts. In the world of high fidelity, audiophiles point out that triode tubes (that's preamp tubes to us) tend to produce more 2nd harmonic than 3rd, and bipolar transistors the opposite. But these guys are talking about tiny amounts of distortion - well less than 1% THD. And they're using their amps to play back recordings of... what do those guys listen to on those things, anyway? This is totally irrelevant to the world of guitar distortion.
The holy grail of guitar overdrive is thought by many to be the distortion that goes on in a tube power amp. All the classic guitar amps have push-pull output stages which, due to their symmetry, only generate odd harmonics. Transformers also tend to create odd harmonics when overdriven. Crank those amps all the way up, and they produce even and plenty of odd harmonics, and we love them for it. Just don't play your Esquival records through one.
Furthermore, the gadgets that produce the most even harmonics are probably those vintage transistor fuzz boxes that rectified (chopped off the entire bottom half of) the signal.
The fact is that both even and odd harmonics are important to getting a good guitar sound, and both can be generated with either tubes or transistors.
Whoops. We were going to keep this about phenomena, not technologies. Sorry...
Most of what makes an overdriven component sound the way it does, then, is how it shapes the corners that it adds to the wave, and whether it treats the bottom and top half the same way.
Intermodulation is another distortion that's pretty important to guitarists. We get intermodulation because the signal we're distorting is not a sine wave - it's full of all sorts of different frequencies to begin with. Especially when we play chords with ninths, thirds, sixths and sevenths. The lower frequencies intermittently smash the higher ones against
the walls, which causes new patterns, at frequencies that aren't multiples of the original signal.
SYMMETRICAL SOFT CLIPPING
Spectrum after clipping
IM distortion is ugly, because it adds frequencies that are out of tune. So audiophiles hate it, and engineers devote their lives to eliminating it. Guitarists generally want to minimize it too, though ugliness is a color that can be nice to have in your palette. Guys who like to bend a distorted double-stop are using IM for effect. And if we ever got rid of it completely, a lot of players would complain that the sound didn't have enough "hair".
But most of the time we do want to minimize IM distortion, and one thing that helps is to reduce bass before the distortion. (Tubescreamers probably became popular as boosters more because of the way they cut bass than because of the way they distort.)
The phenomena we've described above have to do with a single act of clipping. I bring this up because, when we get into bickering about tubes and transistors, I'm going to make the point that in the classic tube guitar amps that we all know and love, the distortion does not take place all at one point.
Imagine what lovely mutilations we could commit if we did things like hard clip just the top peaks, flip the poor bastard over, and then soft clip it. Or mix in an upside-down bit of signal that's gone off to some other part of the circuit and had some other godawful thing done to it. Or reduce the amplitude of the big, slow undulations in the wave, so we can get in there and smoosh up the little wiggly parts.
For us here at Blackstone Appliances, this is the fun part. ∎
Is this cheating – to shift the phase of the harmonic?
The interesting thing is: Our ears don't care about the phase of harmonics. So there are many different wave shapes that have the same harmonic content, and that sound exactly the same.