Harmonics and THD in Audio Systems: Are You a Subjectivist or a Rationalist?
THD of an audio system can be easily measured, but because the ultimate output of an audio system is a sound for humans to hear, human perception plays a role in determining what to do about THD.
Total harmonic distortion (THD) in an audio system (e.g., an amplifier) can be easily measured. The problem is that measurement is not as meaningful as it is for a THD measurement of a power system. To start with, an audio system operates on a range of frequencies, not just one line frequency like a power system does. That is not a big problem, though, because the THD just needs to be measured across a range of frequencies. The bigger problem is that human perception is involved. So the question arises: does the experience of hearing THD vary from person to person?
Harmonic distortion in audio systems occurs when the original audio signal (which of course is made up of sine waves) is distorted by the electronics of the system, resulting in an output audio signal that is somewhat different from the input. This distortion can easily be quantified by measuring all the extra harmonic frequencies that have been introduced by the system and calculating the total harmonic distortion from those frequencies, as discussed here.
In this article, we'll discuss the relationship between the subjective experience of THD and the technical measurements of THD as well as different views about the importance of the subjective experience when compared to the technical measurements. To start off, we should address a somewhat controversial topic—the fact that some people believe that harmonic distortion in audio systems may not actually be a bad thing.
Subjectivists and Rationalists
You would think that since harmonic distortion is a well-understood concept (it is easy to measure and it is easy to identify the sources of distortion), there would be no need for discussion except to identify the best way to minimize it. However, it turns out that harmonic distortion in audio systems can actually be a controversial topic. This is due to the subjective nature of audio; an audio system should produce the best sound, but the definition of “best” can vary from person to person.
There are two main schools of thought on this controversy:
- Subjectivists: Subjectivists think that an audio system should be allowed to shape the sound (i.e., add distortion) so that it sounds the best.
- Rationalists: Rationalists think audio systems should reproduce the original recording as authentically as possible. Not only should distortion be minimized, but so should intermodulation effects, phase delay, group delay, crosstalk, and noise.
I am not here to put this controversy to rest, and I must admit that I am not an audiophile. I certainly love listening to music, but my technical interest in audio systems is as an electrical engineer and not as an audiophile. Because my interest is technical, I tend to fall in the rationalist category. To me the rationalist’s arguments are quite compelling, with the main one being “the artist has purposefully created a particular sound—why would you want to distort that sound when you listen to it?”
There is, however, at least one strong argument for introducing distortion into an audio signal (I just hinted at it), and that is when the artist/musician wants to create a distorted sound while creating the music. The most obvious and extreme type of purposeful distortion involves overdriving an amplifier to cause clipping of the signal which turns the sinusoidal inputs into (near) square waves. Figure 1 shows what happens to the audio signal when it is purposely distorted in a couple of different ways. This distortion will obviously introduce high levels of harmonics.
Figure 1. Signal Distortion from Soft and Hard Clipping. Image courtesy of Mikhail Ryazanov [CC BY-SA 3.0]
Soft clipping attempts to keep the sinusoidal nature of the original signal, so the distortion is small. On the other hand, hard clipping removes the positive and negative peaks, resulting in a signal that looks increasingly like a square wave as the clipping becomes more severe. Both signals are distorted, but as you can imagine, since the soft clipping is more sinusoidal, its THD will be lower. As a side note, tube amps tend to create soft clipping while solid-state amps create hard clipping.
This type of distortion is popular amongst electric guitarists; the technique dates back to the late 1940s and was popularized in the 1950s by artists like Chuck Berry.
Figure 2. Chuck Berry playing some distorted licks. Image courtesy of Roland Godefroy [CC BY-SA 3.0]
The popularization of this type of distortion began in early rock and roll and is still quite prevalent in rock and heavy metal music today. Some examples of different kinds of guitar distortion can be heard here.
Another argument on the subjectivist side is the effect of tube amps (vacuum tube amplifiers), such as this one:
Figure 3. Vacuum Tube Amplifier. Image used courtesy of Keiichiro Shikano [CC BY 2.0]
Many guitar players I know swear by tube amps because they love the “warm sound” they create. These tube amps have objectively higher THD than a well-designed solid-state amplifier. The roll-off at high amplitudes instead of hard clipping and the strong second order harmonic distortion creates a subjectively pleasing sound to many listeners. So again, when the artist is using this kind of amp to create music, subjectivists and rationalists would agree that since the artist wants this distortion, it is acceptable and welcomed.
Where the controversy lies is when tube amps are used for playback of recordings. Rationalists argue that the tube amps distort the recording from what the artist desired, while subjectivists argue that the distortion creates an even richer sound.
I’d like to make one final note about when harmonic distortion is desired in audio signals. Once again, this distortion comes about when the audio is being created. If you play a middle C (which has a frequency of about 261.63 Hz) on a piano, it sounds different from a middle C on a trumpet. The reason is that the way the different instruments create the note leads to different harmonics (in musical terms, these are often called overtones, but they are not exactly the same thing: see here for more details).
I certainly haven’t resolved the subjectivist vs. rationalist argument here, but I have pointed out a few cases where harmonic distortion is acceptable and even desired. From this point on, I want to consider systems that are involved in the playback of audio. While there is still debate between subjectivists and rationalists over these types of systems, from a purely technical point of view, minimizing harmonic distortion is a worthy effort.
Let’s go back to the statement I made earlier in support of the rationalist argument: “the artist has purposefully created a particular sound—why would you want to distort that sound when you listen to it?” For the sake of this article, let’s assume that everyone agrees that THD should be kept very low. How low should it be? And are there any other factors involved? Since audio amplifiers amplify signals for humans to hear, the psychoacoustics of human hearing should be considered. There is no point in designing a system that drops THD well below the threshold of human hearing. Humans typically cannot detect THD less than 1%, but a single THD measurement doesn’t tell the whole story.
Our sensitivity is frequency dependent, and we are also more sensitive to higher-order distortions. With training and with certain types of distortion, some distortion effects as low as 0.3% can be heard.1 When designing an audio amplifier, if cost is no object, it would make sense to design a system with THD below the threshold of human hearing across all frequency ranges. Of course, cost is often a concern, so a good cost/benefit trade-off would be to focus on designing out things that create THD where humans are most sensitive.
This article has discussed some of the issues behind evaluating the THD of an audio amplifier and has explained why the THD measurements of an audio system cannot tell the whole story. Whether you are a subjectivist or a rationalist, human perception has a significant impact on the way a THD measurement should be used. In the next article, I will describe the sources of harmonic distortion in a classic three-stage, solid-state audio amplifier and then explain how to minimize harmonic distortion in these systems.
 D. Self, Audio power amplifier design handbook, 4th ed. Newnes, 2006.
Hi David and thank you for an interesting article. Fully agree with most of what you said. However, I’d like to point out that most published distortion figures, including THD, are usually measured into a purely resistive load. In reality, the amplifier is typically driving a complex inductive load with a huge mechanical resonant component.
In my experience, amplifier measurements into resistive load do not even begin to describe the behaviour of the device into real-world loads. Resistive load measurements are somewhat useful for basic troubleshooting, but their correlation with subjectively perceived reproduction quality is rather poor.
It seems to me that the problem with a lot of these discussions is that they concentrate on harmonic distortion without considering intermodulation distortion. Any non-linearity produces both - the mathematics insist that it can’t do otherwise.
Harmonic distortion is measured by feeding a pure sine wave of a given frequency into the input of a system and measuring the harmonics of that frequency that come out of the other end. But if you feed in 2 frequencies into a non-linear system then you will not only get harmonics of each frequency but also the sum and difference of those frequencies, and also sums and differences of all the harmonics. This is intermodulation distortion and is produced in the same measure as harmonic distortion, and in proportion to the degree of non-linearity.
If you have a single instrument playing such as a rock guitar then you only have one frequency (and its harmonics) at a time and so you will only hear harmonic distortion. This changes the timbre of the sound in a way that some performers and audiences may find pleasing (though personally I might beg to differ). The same may be partially true if the sound is dominated by a lead singer.
The problems start when you have a full concert orchestra, maybe with a choir as well, or even just a solo piano. We now have many frequencies sounding together, with any non-linearity creating intermodulation distortion . The number of new frequencies created now goes up roughly as the square of the number of frequencies you started with! The result is a muddy sound with a loss of clarity and an inability to hear individual parts, which surely cannot be pleasing to anyone seeking more than background noise. Classical music can suffer particularly badly as it relies heavily on harmony for its effect, in addition to melody and rhythm.
So in any discussion of THD let’s give equal consideration to intermodulation distortion.