- Harmonic distortion is when you get extra messy sounds that muddle (distort) the music when you increase loudness.
- Total harmonic distortion (THD) is a measure of how much muddiness is in music when it gets loud. Lower THD is better.
- Discover what creates harmonic distortion and how different types of distortion affect the music.
What is Harmonic Distortion?
Harmonic distortion is when new sounds distort and muddy the main frequencies in music after increasing loudness.
The fundamental music frequency is called the first harmonic, while the new frequency next to it is the second harmonic, third, and so on. Everything together is also referred as harmonic components.
To give an example:
Imagine you’re listening to a beautiful song. But when you turn up the volume, the audio quality doesn’t stay as clear and detailed as before. It becomes muddy and distorted, as if extra sounds were mixed in to make it sound messy. This is harmonic distortion.
And total harmonic distortion measures this effect. Read more about it below.
Types of harmonic distortion
There are different ways a soundwave distorts upon reproduction. When an analog signal goes through an electronic component, it changes depending on how that component processes it.
When a signal goes through a transistor, it introduces symmetrical distortion or clipping. In this case, a fundamental frequency is joined by odd-order harmonics, which humans perceive as a “cold” sound.
Symmetrical distortion creates even-order harmonics, but because their phase on positive and negative side of the signal are opposite to each other, they cancel out (as stated by the 3rd Bullard law of harmonics).
- For example, if 100Hz is the first harmonic, 300Hz is the second, 500Hz is the third, 700Hz is the fourth, and 900Hz is the fifth (see vertical lines in the graph below).
Looking at the sound waves with symmetric distortion, you’ll see both negative and positive (lower and upper part) amplitude peaks cut flat.
When a signal goes through a tube (tube amplifier with a lamp), it introduces asymmetrical distortion or saturation. In this case, a fundamental frequency is joined by even-order harmonics, which humans perceive as a “warm” sound.
- For example, if 100Hz is the first harmonic, 200Hz is the second, 400Hz is the third, 600Hz is the fourth, and 800Hz is the fifth (see vertical lines in the graph below).
Looking at the sound waves with asymmetric distortion, you’ll see positive amplitude peaks slightly wider and tilted compared to negative ones and vice versa.
Low and high-order harmonics
Another thing worth differentiating about harmonic distortion is whether you get high- or low-order harmonics.
- Low-order harmonics gradually lose loudness with each additional harmonic frequency. This type of harmonic distortion is more pleasant since, due to masking (louder fundamental frequency overpowers the others), you don’t hear harmonics as much.
- High-order harmonics all have similar loudness. Although they are still quieter than the fundamental frequency, the masking effect isn’t as effective against the harmonics that are the furthest.
For better understanding, switching between low- and high-order distorted frequency sounds like an ambulance siren.
What Causes Harmonic Distortion
Distortion occurs when an audio signal is unevenly amplified. This is also called non-linear distortion. This is unavoidable due to the imperfect world we live in.
All electronic devices add some distortion, and you also get it some more due to transducer (speaker) vibrations. So, the best we can do is to minimize it.
Harmonic distortion can be wanted or unwanted.
A clear-sounding frequency would sound dry and unnatural. Harmonics is what gives tones a full-bodied sound.
All instruments produce different harmonic distortions. That’s why they all sound different when playing a specific frequency.
Audio engineers even add harmonic distortion to audio recordings to make them sound a specific way.
On the other hand, you don’t want your headphones or amplifier to add distortion. So, a manufacturer must ensure the distortion levels are as low as possible.
6 laws of harmonics
Dan Bullard is an audio technician with decades of experience in the field. During his work, he discovered 6 laws of harmonics he named after himself. Here are short explanations:
Bullard Law 1
“Harmonic amplitudes are proportional to the area of distortion.”
The area represents the amplitude peaks of the signal wave. Depending on how loud the harmonics are, the flatter the amplitude’s peak will be.
Bullard Law 2
“The harmonics signature is the result of the angle where the sinusoid impacts the distortion as predicted by the Bullard Harmonic Solution.”
By lowering the loudness of harmonics, you get a rounder amplitude peak of the signal sound wave while retaining the same harmonic signature.
Bullard Law 3
“Even harmonics don’t appear in symmetrical distortion because they cancel each other out.”
Symmetrical distortion creates both odd and even order harmonics. However, the even harmonics on the positive side of the signal are in an opposite phase than the ones on the negative side.
Because of that, you get a “cancellation” effect where even harmonics cancel each other out (similar to how ANC or balanced cables work).
Bullard Law 4
“When a portion of a sinusoid is removed (such as in clipping), the harmonic signature mirrors the harmonics signature of the feature removed from the sinusoid.”
The more you cut (clip) away the amplitude peak, the more additional harmonics you get. The angle of clipping depends on how much of the peak you clipped off.
If the cut is made at a 90° angle, that’s a perfect non-distorted sine wave, so the number of harmonics is zero.
Bullard Law 5
“The harmonics of a distorted sine wave will always start at 0, 90, 180, or 270 degrees relative to the fundamental, no expectations.”
In practice, no matter at what angle you clip the amplitude’s peak to cause harmonics distortion, the latter will always be in either 0°, 90°, 180°, or 270° phase relative to the fundamental.
Bullard Law 6
“The harmonic signature will be identical for distortions that happen at the reciprocal angle in the wave.”
What is Total Harmonic Distortion (THD)?
THD, or total harmonic distortion, is the total amount of harmonic distortion in the output signal. It tells how much music harmonically distorts when you listen to it with a given device.
Note that all electrical device suffers from harmonic distortion, not just audio-related ones.
THD is typically represented with percentages or a dB value.
- Percentages tell the amount of distortion next to a fundamental frequency, like “THD: <1%”.
- dB or damping factor (expressed in negative value) tells how quieter harmonic distortion is next to a fundamental frequency, which is 0dB. Like THD: -60dB (the same as THD: 0.1%).
Here’s the table showing the correlation between THD percentages and damping factors:
|dB or damping factor
Calculation of THD
Every signal has some voltage distortion, no matter how perfect you think it is. The basic equation for a harmonically distorted signal is:
- Harmonically distorted signal = fundamental frequency + harmonic frequencies + DC or direct-current
To calculate THD, you need 2 values: the RMS value of all harmonics combined and the RMS value of fundamental frequency.
The equation changes depending on what values are provided, and THD needs to be greater or equal to 0:
Importance of THD in audio equipment
The importance of measuring THD in audio equipment is to reveal how faithfully it can reproduce the original signal.
As mentioned above, harmonic distortion is wanted as it gives instruments and vocals unique characteristics.
However, when you record an instrument or vocal, you want to capture only its natural harmonics. Therefore, harmonic distortion in audio equipment is unwanted, as you don’t want it to add new harmonics.
Fortunately, our ears aren’t as sensitive as measuring equipment. So, as long as the THD value is less than 1%, your ears don’t notice the difference.
What are acceptable THD levels
Acceptable THD levels are 0.1% or below (although even 1% is passable), depending on the type of distortion. Asymmetrical distortion is more pleasing than symmetrical, so you notice it quicker.
A Youtuber, Julian Krause, made a great video where he gradually increases the distortion of 3 different audio samples:
Check the video to understand how different levels of total harmonic distortion sound when listening to music.
If you listen carefully, you can notice that harmonic distortion present in higher frequencies (treble) gets noticeable at lower THD levels than in lower frequencies.
Remember that your system’s amp and headphones add a little distortion, too.
Harmonic Distortion vs. Total Harmonic Distortion
Harmonic distortion are extra frequencies produced during the reproduction of a specific (fundamental) frequency. In contrast, total harmonic distortion is a sum of harmonic distortion in a signal expressed in % or dB.
Every electronic piece of equipment (and instruments and vocals) produces a little bit of harmonic distortion. Even equipment that isn’t specific for audio.
You can measure total harmonic distortion in all electronic devices. To do so, you need a spectrum analyzer.
How to measure harmonic distortion
To measure harmonic distortion, you play a specific tone (fundamental frequency) at a particular voltage and measure the output with a frequency spectrum analyzer.
You get a high peak (fundamental frequency) and a bunch of smaller peaks (harmonics or distortion).
How to measure THD
To make a THD calculation by hand, you must square the RMS voltage values of all harmonics and sum them together under a square root. The result needs to be later divided by the voltage of the fundamental frequency.
Why THD isn’t an Indicator of Sound Quality
THD isn’t an indicator of sound quality (anymore) due to advancements in technology and human ears.
Using the latest tech and design, modern audio equipment produces THD values so low only professional measuring tools can detect them, let alone human ears.
Nonetheless, some headphones still present THD measurements in their specifications because it’s a standard practice to perform a THD measurement for electronic devices.
That doesn’t prevent manufacturers from convincing you their device with extremely low THD: <0.01% sounds better than the other with THD: <0.1%.
Basically, just like insane bit depth and sampling rate values of DACs mean nothing in reality. Tiny THD differences also mean nothing for listening to music.
That said, headphones like Skullcandy Crusher ANC 2 are one of rare ones with a high THD value of <3%, which is audible to a trained ear.
Frequently Asked Questions (FAQ)
What does total harmonic distortion tell you?
Total harmonic distortion, or THD, tells you how much distortion a device creates in the original input signal (music) on output. Or, more accurately, how loud harmonic distortion is.
What is a good THD rating?
A good THD rating is 0.1% or below (or THD: -60dB), although you shouldn’t hear any audible difference even at 1% (or -42dB).
Is 0.5% total harmonic distortion good?
0.5% of THD is acceptable. You may hear some difference when listening to a specific frequency tone, but a THD of 0.5% isn’t noticeable for music listening.
Hopefully, you now better understand what harmonic distortion is and what those THD values in specifications mean.
The most important takeaway should be knowing what are acceptable total harmonic distortion values and which ones you should ignore while buying new audio equipment. At some point, going lower simply doesn’t make a difference.
Learn more about other audio equipment like amps and DACs, so you’ll better understand what each component in your audio system does.