Distortion - The Physics of Heavy Metal

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In the beginning, the guitar was a simple self-contained device comprising a source of audio-frequency vibration (strings), a method of amplification (sound box), all the gubbins necessary to keep the strings at the right tension and some glue to hold it all together. This configuration worked very well, but had two very important limitations: 1. it wasn’t very loud. 2. the soundbox sapped energy from the strings, severely limiting sustain. These limitations meant the guitar always played second fiddle to louder, bowed instruments such as, well, fiddles. The guitar was relegated to the role of backing instrument, except in very gentile circles where the audience was guaranteed to sit quietly and politely.

Luckily, this all changed with the invention of the electric guitar. The electric guitar was designed purposely to be used with an amplifier, which meant it could be as loud as you wanted it to be and could dispense with the built-in amplification and problems thereof. The guitar had finally been freed to be the lead instrument it always deserved to be.

As an electric guitar's sound spends a fair proportion of its journey from string to ear as a wiggly electric current in a wire, it presents a unique opportunity: it can be perverted electronically on its way. With the advent of the electric guitar, the guitar effects industry was spawned. Of all the effects created during the subsequent years, one stands out as being responsible for the emergence of several entirely new musical genres. Distortion, unlike most effects, which are deliberate attempts to make something sound like something else, is the result of a deliberate attempt to abuse the equipment. It is simply a consequence of pushing an amplifier (or speaker) harder than it is designed to go. Without it, we would not have rock, metal, or any of their hundreds of sub-genres.

The term distortion in an engineering context means any kind of corruption of the original audio signal. This could have a variety of causes, most of which would sound pretty damned awful. But we are concerned here with only one specific kind: harmonic distortion, known in various forms as clipping, fuzz, overdrive, dirty, crunch, grunge or any number of similar rock-and-roll terms.

Jimi Hendrix is often credited as the first guitarist to experiment with overdrive, though this is highly doubtful. However this entry is intended to cover the physics rather than the history, so we will not concern ourselves with that particular debate. The entry aims to explain the physical process involved in transforming the simple twang of a guitar string into the full-on, wall-to-wall blanket of noise at a death-metal gig.

Twang

When you pluck a guitar string, it vibrates. If you video this and slow the tape down, you’ll see the middle of the string swinging back and forth. This vibrational “mode” is called the fundamental, and the number of times it completes is back-forth cycle per second is called the frequency, which dictates the note you hear. For example, an open bottom E in standard tuning has a frequency of 82.4096 Hz, or cycles per second.

You may also be able to observe a second mode, whereby the centre of the string appears to be fixed in a particular plane, and the two lengths between the centre and the nut, and the centre and the string, swing back and forth. This is equivalent to another note, one octave up and slightly quieter. In fact, there are all sorts of vibrational modes that contribute various overtones to the note you’re trying to play. In practice, all natural sources of sound act in a similar way, and the only way of obtaining a “pure” tone is to use a synthesiser that’s specifically designed to produce one.

But for the purposes of explanation, lets assume there’s just the fundamental for the time being.

Jangle

If you could see such a pure tone as it’s converted to electrical current and sent down a wire to the amplifier, it would appear as a nice smooth sinusoid or sine-wave, with troughs and peaks separated in height by the voltage or amplitude, and successive peaks separated in time by the wavelength. The number of peaks passing per second is the frequency.

The amplifier will take this nice pure tone and make it bigger, before sending the bigger signal down another wire to the speaker, which converts it back to sound. The amplified signal looks exactly the same as the original but a bit taller. The sound wave you hear has exactly the same form as the electrical signal; it’s just travelling through a different medium.

So far we’ve taken a nice simple tone and made it louder. This will most likely sound like some ‘60s jangly guitar-pop band: fine for a those how like that sort of thing but a bit wet for your hardened rocker. Now we need to make it a bit meatier.

Gurgle

The next step is best explained by example. Suppose you have a simple amplifier capable of amplifying a signal 10 times; that is a gain of 10. In terms of the change to our sinewave, it makes it 10 times higher without changing the frequency. Suppose also that the amplifier circuits are powered from a 10V direct current (DC) supply1.

Given the tiny signals normally produced by guitar pickups, this is fine - feed the amp a 0.5V signal say, i.e. 0.5V between peak and trough, and you’ll get 5V out. All well and good, but still a bit George Harrison as opposed to Eric Clapton.

Growl

But most practical guitar amplifiers have at least two stages. First there is a small, low-power amplifier known as the pre-amp, intended to boost the guitar's tiny signal to a high enough level that it won't get swamped by noise inside the amp. Then there are one or more high-power stages, collectively known as the power amp, which boost the signal to the levels needed to drive the speakers.

Lets say our pre-amp has a gain of 3, and the power amp 10. The 0.5V signal from you guitar is boosted to 1.5V by the pre-amp, and then the power amp valiantly tries to boost this to 15V. But it can’t. Regardless of what you stick into it, the maximum output has to be between 0 and 10V, as that’s all the power supply has given it. 10V is the absolute limit of “headroom” available.

The nice sine-wave rises as far as the limit, in this case 10V, and then flattens off. The top of the peak is clipped off, giving rise to the term "clipping". At this point we have just overdriven the amplifier, and are starting to sound like more a '70s garage-punk band.

Grunge

Now it gets technical. Why does a clipped signal sound like it does? Well, you no longer have a sinewave. It now has sharp corners and a flat top, and is starting to look a bit like a square wave2. Mathematically, this square wave can be described by its Fourier series - a series of sine or cosine3 waves of frequency 1f, 2f, 3f, and so on. The first component is known as the fundamental or first harmonic, and subsequent components as second harmonic, third harmonic and so on.

Without going into the maths, imagine trying to completely fill in the square wave shape with a series of sine and cosine waves, one at the fundamental frequency, then another at twice that, then three times, and so on until the area under the square wave is completely filled in. This is not merely a mathematical curiosity - this is exactly what comes out of the speakers. Your single tone has been converted into a single tone plus a load of harmonics - giving rise to the term harmonic distortion.

Musically, the second harmonic is an octave higher than the first, the third harmonic is a perfect fifth above the second, the fourth is a fourth above the third and two octaves above the first, and so on. All the extra notes produced are harmonically-related, which is why it doesn’t sound like a discordant racket. Well, not usually anyway, as we shall see.

As you overdrive the amp more and more, the pulse gets squarer, its sides get steeper, and you need higher and higher frequency harmonics to fill it in. Therefore the more severe the distortion, the more components are present and the more high-end the sound becomes. Many of the highest components will disappear though, partly because your gear is incapable of reproducing them and partly because your ears are incapable of hearing them, particularly if you've been to a lot of metal gigs.

Kerrang

If you play two notes at once you get two complete sets of all these harmonics. Some of these will interact with each other to form additional components, known as intermodulation products. When you play two notes, f1 and f2, intermodulation products tend to appear at the sum and difference of the two, i.e. f1-f2 and f1+f2. When you factor in all the harmonics, the number of components present increases exponentially with the number of notes played, and generally, all components are harmonically-related in some way. We now have a power chord, or Kerrang, as it’s sometimes known.

Crank the preamp up as far as it’ll go and you’ll get something akin to white noise: somewhere between I’ve Got a Fuzzbox and the Jesus and Mary Chain. Meaty, but still not very metal.

But thankfully it doesn’t end there. Lets abandon our view of the signal as amplitude plotted against time, and instead look at the frequency domain - a view of amplitude against frequency. You’ll need a spectrum analyser to show this in real-time, so just imagine it instead. The original tone, if pure, would look like a single spike at the tone frequency with height corresponding to amplitude.

The distorted tone would look like a series of spikes at f, 2f, 3f and so on with amplitude reducing each time. Now factor in your power chord, and the fact that your guitar doesn’t produce a pure tone in the first place - and in place of the discrete spikes you’ll start to see a whole general mish-mash covering a wide range, or band, of frequencies. It might look more like a rather spiky, gothic-looking hill than a series of telegraph poles.

The area under this curve - the area of the hill - dictates the overall power of the signal. As you can imagine, the area of the hill is a lot bigger than the area of the original spike. So there is a lot more power in the signal. The reason that a full-on metal guitar sounds more powerful than a clean one is because it is - the amp uses more power to produce it.

An Aside - The Two Finger Chord

Interestingly, the physics of intermodulation distortion dispels the myth that rock guitarists only know one chord. Given high levels of distortion and the resulting intermodulation, a chord needs to be kept simple to ensure that it still sounds like a chord. Try strumming a full six-stringed minor-seventh with full-on distortion, and you’ll get so many different and unrelated components that it’ll sound like a recording of Concorde taking off played through a broken speaker. This would not phase many punk guitarists, who are often keen just to make as much noise as possible, but metal guitarists will stick to a two-or-three-note chord comprising only octaves and fifths, thereby ensuring that only the desired frequencies appear. The two-string chord has absolutely nothing to do with lack of ability. Honest.

Wall of Noise

Now, the next thing we need to consider is the shape of the frequency spectrum. If it rises gradually from the left, peaks in the middle and then tails off to the right, in a Ben Nevis fashion, it’ll probably sound a bit rubbish. The reason for this is a truly great guitar sound needs has two key characteristics: seriously meaty bass frequencies - the ones at the bottom - that cause the floor to shake, and loads of high frequency harmonics - at the top end - giving attack and clarity.

A preponderance of middle will make the sound dull and wooden. Middle is the natural enemy of the rock guitar and needs to be suppressed. You want to filter out the middle, creating two hills with a valley in between. A sound with loads of bass and treble but no middle is referred to as “boom and fizz”, or “scooped”, referring to the shape of the spectrum.

However, everything has its limits. Kill the middle part of the spectrum entirely and your guitar might sound great in the bedroom, but will be all but inaudible against the sonic backdrop of a live band, where your bass is competing with the bass guitar and the high end is competing with the cymbals. Live, you’ll need to selectively boost the middle portion again for the guitar to cut through.

Another Aside - The Tube Amp

Most rock guitarists still prefer the ancient technology of valves or vacuum tubes instead of much smaller and more-reliable solid-state transistors. The valve is said to produce a “warmer” sound. The reasons for this are numerous and complex, but relate to the different way that tubes and transistors boost certain frequencies, particularly when in distortion.

The transistor will probably amplify your sound more accurately and consistently, but metalheads aren’t especially interested in accuracy. The tube amp starts to behave less linearly when driven to its limit - that is, the output is no longer exactly input-times-gain. If we return to our clipped sinewave, instead of cutting off abruptly at the limit, the tube amp will start to cut off just before the limit, giving a slightly rounded edge to the signal and reducing the very high frequency harmonics. This is called soft-clipping and will allow you to pile on the distortion beyond levels that would overwhelm the original tones of the chord using a transistor amp.

The term “overdrive” was coined originally to refer to the practice of driving the tubes just beyond their rated limit, i.e. just into the non-linear region, which gives a very slight soft fuzz effect. These days overdrive usually refers to a sound that is less distorted than, well, distortion: more Status Quo than Slayer.

Tube amps also tend to accentuate even harmonics slightly more than odd, and transistor amps the other way round, although it is debatable whether the human ear can actually detect this difference.

There are a lot of myths regarding valve amps, most probably originating from the fact that they used very different circuit designs in the early days. Valves present a higher impedance to the speaker, and their output response will tend to vary as the speaker impedance varies. Valves also use far higher supply voltages, with the practical consequence that the power supplies are less sophisticated, and tend to allow the mains supply frequency through to intermodulate and “colour” the sound. Nowadays of course amps are designed specifically to produce the most desirable sound and the differences are less-well defined.



While tube amps are definitely preferred amongst professionals, they are not ubiquitous. Dimebag Darrell4 of Pantera and latterly Damageplan famously always used transistor amps, proving their usefulness even with the heaviest bands around.

Beyond a Broken Speaker

Dave Davies of the Kinks famously obtained a very crude fuzz effect by slashing his speaker cone with razor blade. Today’s extreme metal guitar sounds rely on careful selection of guitar pickups and effects units, pre and power amplifiers, careful control of compression and clipping, spectrum shaping and even consideration of the acoustics of the venue to ensure the correct frequencies propagate to the correct places.

Some Nu Metal and Emo bands have gone even further by taking the wall-of-noise, sanitising it and taming it for use as and when it suits them. Some might say they have gone too far, but that is a matter of taste, and tastes change over time.

Nearly forty years of development has seen distortion develop from simple hardware abuse to one of the sound engineer’s finest arts. Yes, you can buy an amp off the shelf that’ll appear to recreate Machine Head’s wall-of-noise in the bedroom, but to scale this up to gig volume without destroying the sound still takes a great deal of skill.

So the next time that your parents declare your favourite music to be an unsophisticated racket, make sure you put them straight.

1The amp will contain circuitry to convert AC mains to the DC supply for the electronics, but we don’t need to worry about that.2Like a turret, for the non-technical.3The same, but shifted left by a quarter wavelength, or more correctly phase-shifted by -90 degrees.4RIP - he was shot onstage in 2004.

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