Odd vs Even Harmonic Distortion (What’s The Difference?)

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  • What is the difference between odd vs even harmonic distortion?
  • How does the math work?
  • Is one better than the other?

Odd vs Even Harmonic Distortion

We’ve talked recently about tube vs solid-state pre-amps, their characteristics and the harmonics they create.

The sound of harmonic distortion in your mixes can greatly affect the timbre and feel, so it’s worthwhile getting to grips with identifying them and how they will impact your workflow (as well as knowing how they behave in order to tame any trouble frequencies).

What is Harmonic Distortion?

A good way to picture what harmonic distortion looks like is first to imagine a sine wave. A sine wave will oscillate with a consistent amplitude and frequency (think of hitting a key on a synthesizer without any effects or processing on it). They are clear, constant notes which in musical terms are pretty boring to listen to.

By adding distortion to a sine wave we are actually manipulating the wave itself so that it no longer follows a strict oscillation.

This is why when you see a waveform in your DAW it looks like a ‘scribble’, because (unless you are recording a sine) the wave won’t follow a set path as it oscillates.

Image result for odd vs even harmonic distortion

When we add distortion to a sine wave (or cause it to overdrive) a clipping effect is created. The more distortion we add (or the more saturated the sound becomes) the more harmonics are produced.

Any tone you play will have a ‘fundamental frequency’. If you play an ‘A’ on a guitar, for example, the fundamental frequency will correspond with this note, however, you won’t just hear the A, you will hear lots of other frequencies around it on the spectrum.

If you insert a frequency analyzer plugin onto an instrument track this will give you a good idea as to what the fundamental frequency is.

If you’ve ever seen a vibrating guitar string under a powerful light you’ll notice it doesn’t vibrate equally, the patterns on the string will change as the string rings out.

While this doesn’t represent harmonic distortion, it does make it easier to understand that there isn’t just one frequency playing, rather there are several (as illustrated by the different vibrations and patterns in the string).

Think of harmonics as ‘other frequencies’ that surround the fundamental frequency.

Odd or Even?

So we know that harmonics are produced when distortion is applied, however, these harmonics aren’t random. Depending on the type of distortion, we can manipulate whether odd or even harmonics are produced.

Let’s say we are cranking our tube amplifier on a high gain channel, tube distortion is synonymous with warmth and clarity. This is because the tubes create EVEN harmonics which sound more pleasant to the ear. 

On the other hand, if we then turn on our solid state amp and do the same, the distortion will produce ODD harmonics which (you guessed it) are not as pleasant to listen to.

This is why you’ll often hear guitarists claim that tube amps are far superior to solid-state.

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The Math

As with a lot of aspects of audio production, odd and even harmonics can be calculated with some simple math.

Both are just multiplications of the fundamental frequency, where odd harmonics will increase in multiples of 3, 5, 7 etc then even harmonics increase in multiple of 2, 4, 6 etc.

So, if we have a tone of 440Hz playing (an A), we can calculate that the odd harmonics will be 1320Hz, then 6600Hz because we are multiplying by 3 and then 5. 

The even harmonics, in this case, would be 880Hz, then 1760Hz etc.

To go back to the example of a sine wave at 440Hz, think of these harmonics (or ‘overtones’) as frequencies that add character and define the timbre of the sound.

The addition of harmonics makes for a much more interesting sound (which is why the sound of distortion is actually pleasant to listen to).

Is One Better Than The Other?

Audio production is never straightforward, there, unfortunately, is no ‘better or worse’ when it comes to harmonic distortion!

Our ears naturally pick up on even order harmonics, we’re able to interpret them as more musical than odd order harmonics but that doesn’t mean that odd order harmonic distortion doesn’t have its place.