Distortion 101

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.

Here's one that comes and goes every 200th of a second:

Let's add another one that comes and goes twice as often:


If these two forces are pushing and pulling on the same object - say... your eardrum - then that object is going to be pushed further when the two of them are moving in the same direction. When they're in opposition they're going to cancel out. So they can be considered one wave that looks something like this.

All pitched sounds can be thought of as being made up of sine waves like this. So when we mutilate our guitar signal by clipping it, we're changing the mixture of sine waves that make it up.

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 - the composite wave would look more 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 squared-off shape.

But don't take our word for it. Use this Java applet by Manfred Thole to experiment with the relationship between harmonics and waveforms. The sliders on the right add sine waves, while the ones on the left add cosine waves. These are sine waves that line up with each other at the peaks instead of the zero crossings.

It seems your browser can't do Java. Too bad. The applet would look like this:
Ugh! Even no images??

If you mess with this thing long enough, you'll deduce these truths:

When you add harmonics, with their amplitude diminishing as you go up the series, they form a wave with a sawtooth shape.

Use only odd-numbered harmonics (3rd, 5th, 7th), and you get a square wave.

Even-numbered harmonics (2nd, 4th, 6th) mess with the pulse width, often leading to a waveform that's not symmetrical from top to bottom.

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.

Curves can be described by mathematical equations, and there's an equation called the Fourier Transform that defines the relationship between harmonics and complex waveforms. This Java program is essentially a graphing calculator that plugs values into the formula. It plays the sound, too. Cool.

Here's the source code.

Is this cheating - to mix sine waves of different phase relationships? Observe that adding 2nd-order cosine waves sounds the same as adding 2nd-order sine waves. Our ears don't care about the phase of harmonics. This means that there are many different wave shapes that have the same harmonic content, and sound exactly the same.
  And what kind of distortion will give us even-numbered harmonics? Working with the sliders on the right hand side of the Java applet, you're not going to find any combination of even harmonics that looks like a wave you could get with clipping. But try adding 2nd harmonic with the 'a2' slider in the left-hand column. (This also adds a sine wave twice the frequency of the fundamental, it just starts off at a different point - it has a different phase relationship to the fundamental.) Look at that - looks like a wave that's had its feet loped off, but not its head. 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 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. That's where low frequencies push the high frequencies against the walls. They do this intermittently, and our ears hear the periodic smooshing and not smooshing as a whole other frequency. Not much controversy here; nobody seems to want this sound. Tubescreamers are popular as boosters to kick more signal into a tube amp, probably in large part because they cut the lows.
  Further reading:

R.G.Keen's Distortion 101. Covers the physics and a round-up of electronic techniques.

The Physics Classroom Lesson on sound waves and music.

Too often guitarists and manufacturers try to attribute the effect of an entire circuit to the behavior of individual components. It's not what parts you use, it's how you use 'em.
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 (like to say 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.

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