Deep Dive

To Test or Not to Test, That is the Question (Part One)

Issue 125

How many audiophiles actually perform any form of measurement on any aspect of their system? Is there any merit in doing so? To answer the question of whether it is necessary or even advantageous to test our audio systems, we need to first understand the usefulness and the limitations of measurements. In this article, we will explore the utility of the most quoted measurement in hi fi, the total harmonic distortion.

As my training is in the medical sciences, the way I approach this question parallels my approach to ordering diagnostic tests. Doctors love tests. Patients love tests (at least, those that don’t hurt).  Everyone loves tests, (I lied. Insurance companies hate tests.) However, patients and doctors often have a different understanding of why tests need to be done. (“The loan on the Mercedes is due” is not a valid reason.) With easy access to information on the internet, the first thing many patients say to me when I see them for the first time is: “Doc, I am here to get the _______ test.”

Patients often think that the numbers printed on the test results form are the final arbiter of their health. The numbers don’t lie. However, what they often don’t understand are the concepts of false positives, false negatives, positive predictive value, negative predictive value, sensitivity, specificity etc. Every test has its idiosyncrasies; some tests are good at ruling out diagnoses, but could give you a scare since they often say you are sick when you are not (they are more accurate when the result is negative than when it is positive). On the other hand, there are tests where, if they show a positive result, you are doomed, but they can also miss a lot of cases (they are more accurate when the result is positive than when it is negative).

Some tests directly measure something that is involved in making you sick. Other tests just look at things that might suggest you are sick, but are not directly involved in the disease process. And then there are tests that are completely useless, other than to fill the coffers of the lab. (Somehow, my specialty seems to be afflicted by this more than most.) Most of these tests have not been evaluated by regulatory agencies such as the FDA, but they are nevertheless widely promoted.

A friend of mine runs a reputable clinical lab in town. He told me that certain smaller labs love to underbid for contracts to do annual employment physicals and the like. They just run a small percentage of the samples, and make up the results (always within the reference range) for the rest. These are tests that of course have little clinical significance, and if someone questions their accuracy, the labs or organizations doing the testing can simply say that a person’s health status can change within a short time or, in a worst-case scenario, that the samples got mixed up. Elizabeth Holmes of Theranos took this concept to Silicon Valley and became a billionaire (for a short while).

In a similar manner in audio, there are measurements that directly correlate to sound quality. There are measurements that indirectly give you an idea of whether something is wrong. There are also measurements that are only meant to help sell merchandise. There is an eerie symmetry between healthcare and audio.

Someone did a study on a bunch of teaching hospitals and found that the amount of spending on lab tests spikes every July. This is the time when new interns start working, and, being less confident in their own clinical skills, they tend to order more tests for reassurance. After three decades of practice, I tell patients that they don’t need to have the tests they’ve demanded, more often than actually ordering the tests. A parallel to this could also happen in the case of seasoned audiophiles who are more confident in their ability to tell what sounds good without resorting to measurements. However, even experienced clinicians rely on diagnostic tests, and experienced audiophiles could benefit from measuring certain aspects of their system too.

When someone asked Harold Leak, the founder of the eponymous British hi-fi brand, how he designed his products to sound the way they did, he said he did not know, since he never paid attention to how his products sounded. He insisted that his amplifiers must measure well, and I guess he also believed that if they measured well, they would sound good. To him, measurements were more important than subjective evaluation of the “sound quality,” an ill-defined quantity.

He designed the first amplifier ever to have a measured total harmonic distortion (THD) of less than 0.1% (At 1kHz only. The THD of the Leak TL/12.1 rises rapidly with frequency. That mattered little to Harold, as it was customary to quote only the THD at 1kHz). His priority was to find a way to keep the amplifier from oscillating while applying enough negative feedback to get to the magic THD of 0.1%. As we shall discuss later, the relationship between the level of THD and subjective sound quality is complex; the fact that the TL/12.1 has an excellent subjective sound quality is purely coincidental, or even fortuitous.

When solid state amplifiers first appeared, one of the selling points was their low distortion. It is possible to design transistor circuits with massive amounts of negative feedback, thus reducing THD as measured by conventional methods to vanishingly low levels. This gives people the erroneous impression that as amplification devices, transistors are more linear than vacuum tubes.  However, the use of such large amounts of NFB can introduce other deleterious effects on sound quality (such as transient intermodulation distortion), which goes back to my previous comment of the cure being worse than the disease. And in this case, do we even have a disease that needs curing?

Peter Walker of Quad developed a technique to cancel out the music playing in an amplifier, leaving only the distortion and noise. He surmised that as long as the distortion is not audible (at normal listening volumes) under such a condition, the amplifier is “perfect” and “can never be improved upon,” what he called a straight wire with gain. He went on to demonstrate that listeners were unable to tell whether a Quad transistor amplifier (the 405.2) was in circuit or not. His Quad II tube amplifier would have failed miserably if it were put to the same tests. However, 40-odd years later, his company chose to reissue the Quad II as the “Classic,” (the Quad II Classic reissue) whereas the 405.2 has been relegated to the footnotes of history (or maybe the junkyard of history would be a more accurate description). Go figure. David Hafler set up a similar test, which he called the Straight Wire Differential Test (SWDT). Stereophile’s J Gordon Holt did an interesting review of the Hafler XL-280, comparing the result of the SWDT with subjective evaluations1.

The late Peter Walker of Quad.

A 1977 Wireless World article1 on amplifier distortion by celebrated amplifier designer Peter Baxandall began by stating, “There is a very widely held belief that all amplifiers sound different, and that the reasons for this are so subtle and mysterious that no one has yet properly understood them. I do not agree with these views, and confidently maintain that all first-class, competently designed amplifiers, tested under completely fair and carefully-controlled conditions, including the avoidance of overloading, sound absolutely indistinguishable on normal programme material no matter how refined the listening tests, or the listeners…”

Many phenomena in science were subtle and mysterious until explanations were found, at which point they are no longer subtle nor mysterious. Psychoacoustics is a complex phenomenon, and how the brain reacts to different distortion products is still not completely understood. Jean Hiraga2 performed an experiment by asking listeners to rate amplifiers with different distortion characteristics. He concluded that it is not the absolute level of THD that matters, but the spectrum of the harmonics present in the distortion. (Harmonics are multiples of the fundamental frequency.) He found that amplifiers with orderly diminishing levels of harmonics were subjectively the best-sounding. He noticed that each harmonic has a masking effect on the harmonic above; the 2nd harmonic is masked by the fundamental, and in turn masks the 3rd harmonic and so on. If the level of a harmonic is higher than that of the harmonic below, it would no longer be masked and its effect becomes more obvious, especially if it creates dissonance (the dissonant harmonics are the 7th, 9th, 11th, 13th, 14th, 15th, 17th, 18th and 19th).

Harmonic partials on a vibrating string. Courtesy of Wikimedia Commons/Qef.

Hiraga also noted that musical instruments have very high levels of 2nd and 3rd harmonics (70% in the case of a violin), but their character is determined by the relative levels of the 4th to 20th harmonics, which are at extremely low levels. Moreover, the brain is much more sensitive to distortion at high frequencies3. In fact, at mid-bass frequencies, the distortion has to reach 20% before it is noticeable, but at high frequencies, distortion of well under 1% is noticeable. 2nd and 3rd-order harmonic distortions tend to have very little audible effect even at high levels, due to the strong masking effect of the fundamental, whereas the high-order distortions are noticeable at far lower levels. That is why a single-ended triode amplifier might have 3% 2nd harmonic distortion, and yet violins could still sound natural.

In 2006, almost 30 years after Hiraga first published his findings, Keith Howard published his research in The Absolute Sound4 as a sequel to the Hiraga experiments. By that time, single-ended triode amplifiers had made a resurgence on the hi-fi scene, and one of the explanations for their popularity was their high level of second harmonic distortion, which was believed to be euphonic.  Howard constructed a software utility that could add non-linear distortions to music through digital signal processing. He went on to add different patterns of harmonic distortions to music and assessed their effects. Howard concluded that it takes quite a large amount of distortion for the brain to take notice. He also found that none of the additional distortions was euphonic; even with the “ideal” pattern of harmonics as described by Hiraga, which at 3.33% THD would muddy the sound, but which Howard did not find objectionable. When Howard lowered the harmonics by 20dB (i.e. THD of 0.33%), the distortion was no longer noticeable.

However, the most unpleasant distortion pattern was the one with all the even-order harmonics removed (i.e. odd-order only); even though the THD has decreased to 1%, the sound was edgy and irritating. On the other hand, the pattern with all the odd-order harmonics removed, with a THD of 3.18%, sounded much less annoying, but still unnatural. In conclusion, adding second-order harmonics did not make the sound more attractive, but it did make the other added harmonics less unpleasant. Even though the early transistor amplifiers had principally odd-order harmonics, the distortion was at such a low level that it was probably not noticeable by the brain. So, what accounts for the nasty sound of some solid state amps, especially some older models?

The first 32 harmonics of a vibrating string. Courtesy of Wikimedia Commons/Hyacinth.

So far, we have only discussed THD, which is measured by playing a pure tone in an amplifier driving a resistive load. But I seldom listen to sine waves for fun, and even though my speakers don’t have crossovers, they are hardly purely resistive loads. Two amplifiers with identical harmonic distortion spectra, when playing music while driving a real-world reactive load would likely sound different, as they produce additional harmonic (e.g. crossover distortion in class A/B amplifiers) and non-harmonic (such as intermodulation distortion) distortions under dynamic conditions, as well as other as yet undefined sources of distortion. In fact, with complex musical signals, the intermodulation distortion is often two orders of magnitude higher in power (i.e. +20dB) than the harmonic distortion. Moreover, intermodulation distortion is invariably dissonant and therefore more deleterious to sound quality. Applying negative feedback (NFB) to remedy the harmonic distortion in a poorly-designed circuit could lead to additional problems. Like using bad medicine, the cure becomes the problem. However, one can avoid these problems by using NFB judiciously, as the issue is not the negative feedback per se but its improper application.

While understanding harmonic distortion would help you better appreciate the technical aspects of a Stereophile equipment review (or other review where measurements are included), few audiophiles would be interested in measuring distortion in their equipment unless they are trying to build their own or do modifications to the gear. However, there are other measurements that might be worthwhile, something we will get into in the next issue.

  1. https://www.stereophile.com/solidpoweramps/hafler_xl-280_power_amplifier/index.html
  2. https://audioxpress.com/article/Musicality-and-Distortion-A-Conversation
  3. https://www.keith-snook.info/wireless-world-magazine/Wireless-World-1977/Audible%20amplifier%20distortion%20is%20not%20a%20mystery.pdf
  4. https://www.axiomaudio.com/blog/distortion
  5. https://www.stereophile.com/reference/406howard/index.html

Header image courtesy of Wikimedia Commons/ArnoldReinhold.

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