Harmonics and Harmonic Distortion

Last week I wrote about Bias, and how if an amplifier or an audio component isn’t biased correctly it might not work or it might cause a lot of harmonic distortion.

This week: what the heck is harmonic distortion, and what the heck is a harmonic?

What’s a Harmonic?

So, first of all, what is a harmonic.

If you take a note, like a C, and play it on a guitar or a piano, because of the physics involved, not only do you hear the note C, you also hear, very quietly, other notes that are mathematically related to the C you’re playing. Like, you might hear a C an octave higher, and then another octave above that, and you might hear an E and G mixed in there as well. It’s actually quite a bit more complex than that, but the point is that if you play a note on virtually any instrument, you get more than the single note that defines the perceived pitch. That other stuff are the harmonics.

The harmonics of a note are caused by the physics of vibrations, and by the construction of an instrument, or of a persons’ face if we’re talking about the harmonics of a sung note. And, in fact, the harmonics of an instrument are a huge factor in why an instrument sounds the way it does. A guitar with steel strings has a different set of harmonics than a guitar with nylon strings. The two types of guitars have a lot in common in terms of harmonics — you can tell they’re both guitars — but the steel string is typically brighter and more metallic, and that’s because of its harmonics.

The harmonics have a mathematical relationship to that C you played (we can call that the fundamental), and the particular pattern of harmonics is what makes an instrument recognizable as an instrument. And some patterns of harmonics sound better to our ears than other patters of harmonics.

In fact, harmonics do tend to be high frequency information, and we will see why that is important in a bit.

What’s Harmonic Distortion?

Harmonic distortion is when harmonics are added to a sound, a signal, that aren’t there in the original signal.

Back to playing a C. If we played a C on a very simple instrument, like a flute, you would get a very pure sounding C — it wouldn’t have a lot of extra harmonics happening, unlike a guitar, for instance. The complex body and physics of a guitar actually add harmonics to the C. It’s a bizarre way to think of it, but you can consider a guitar a generator of harmonic distortion. So is a piano, a trombone, a human voice, etc. These all are sort of "harmonic distortion generators". But we want that particular harmonic distortion - it’s how those instruments sound.

Electronic components (amplifiers, etc.) also add harmonics to a signal. Usually a well-designed circuit adds a very, very tiny amount of harmonics, and we really can’t hear it because it's such a small amount. That is also harmonic distortion. A badly designed circuit can add enough harmonic distortion that one can really hear it. There are amounts of harmonic distortion that can be very noticeable, and certain patterns of harmonics are more noticeable, and some patterns sound good, and some sound like shit.

Harmonic Distortion = Sonic Finger Print

All the elements in an audio recording signal chain add some amount of harmonic distortion. Microphones, speakers, preamps, compressors, power amps, guitar amps, effects pedals — all of these things add harmonic distortion. Some are designed to add as little as possible, and others are designed to add huge amounts. Microphones sound different from each other, in part, due to the harmonic distortion they add, as do speakers, mic preamps, etc.

As mentioned earlier, some patterns of harmonics our ears like better than others. Tubes, whether in compressors or guitar amps, tend to have harmonic distortion that our ears like. Tubes are often described as sounding “warm.” That’s the mathematical relationship of the harmonic distortion (the harmonics added) of a tube circuit.

Solid state equipment also has distinctive harmonics patterns that it adds to a signal. That’s part of the reason Neve sounds like a Neve, and a Mackie sounds like a Mackie.

THD

THD stands for Total Harmonic Distortion, and it’s a measurement of the amount of harmonics a piece of equipment adds to a signal passing through it. The manufacturer of the equipment will usually specify this as a percentage at certain frequencies, something like, “Less than 0.5% percent THD from 20 Hz to 20 kHz at full rated power.” Some manufacturers specify it in much looser terms: “Less that 1% THD.” Generally, the better the gear, the lower the % of harmonic distortion, and the more specific the manufacturer will be about it.

What’s a lot of harmonic distortion, and what’s a little? Depends. 0.5% is pretty good for a tube component, but pretty awful for a solid state component. A really high end solid state device can have incredibly low harmonic distortions - like 0.002%.

Tube mics are typically in the 1% THD neck of the woods. 1176 Limiters have around 0.5%. A Neve 5211 is down around 0.0015%. Obviously, guitar amps designed for distortion have much higher amounts of THD. And also obviously, is that the more you turn stuff up (increase the power), the more you increase harmonic distortion.

But, THD is really only a small part of the harmonic distortion story. There’s also the “sound” of the harmonics added, the math of their pattern, that make a huge difference.

Even vs. Odd Harmonics

Quickly, let's look at the way a string vibrates.

A vibrating string is very complex. Back to our C, if you fret and pluck a C on a guitar, you'll get a nice loud fundamental, vibrating at 261.63hz. Let's round that to 262 to make the math easier.

So, we have a string vibrating at 262hz, but it's also vibrating at twice that - 524hz. But it isn't vibrating with as much power, so this 1st harmonic is much quieter than the fundamental.

There's also a harmonic vibrating four times as fast as the fundamental — 1048hz.

When these vibrations all happen on one string, the result is a much more complex waveform than any fundamental or harmonic by itself.

There are also other math things happening there. There's an E, which is the third, and which is around 1.25 times the fundamental.

These harmonic relationships that sound good to our ears tend to be even number multiples, often called even order harmonics. Our ears tend to not like odd number multiples - 3, 5, 7, etc. These particular odd harmonics sound kinda ugly to our ears — the 7x is especially dislikable, and they tend to square the wave off...

In general, our ears think even harmonics sound better than odd. In general, tube equipment generates a lot of even harmonics. Does that explain to a large extent why everyone likes the sounds of tube amps?

Many Things Explained

Understanding some of the math of harmonics also explains why distortion seems to make something sound brighter: because what you're adding is harmonics ABOVE the fundamental, and those harmonics stack up and increase the apparent high frequency tonality of a sound. It also explains why too much harmonic distortion can sound harsh and painful — it's causing a lot of high frequency activity, and our ears don't like that very much.

Now, some of you might be thinking, "Even on a really good day people can only hear up to 20kHz. If I have something at 8kHz, then it's harmonics are at 16kHz and 32kHz and other frequencies, all high, and most of them beyond the range of hearing. How can this possibly affect what we hear?"

The answer is that we can sense frequencies we can't clearly hear, and very high, over 20kHz frequencies can affect the equipment we are using, especially digital stuff, and we can hear that effect.

Some stuff you just have to take on faith, you stumpy bastard.

Next week, we'll talk about why cranking things up causes an increase in harmonic distortion, and we'll start talking about some recording techniques that take advantage of the physics involved.