Do measurements matter?

January 20, 2017
 by Paul McGowan

No, I wasn’t thinking of starting a riot or fueling controversy with that headline.

My goal is simple enough. Let’s start looking at what we know matters and what we suspect does not.

For example, does THD matter? The answer is not a simple one. Books could be written on the subject.

But, THD is a good starting point.

Total Harmonic Distortion, THD, means there’s more of something than we started with.

THD refers to the addition of extra tones (harmonics) not originally found in the music. Those extra harmonics are called distortion.

If we put a single pure tone into an amplifier, we expect a larger—but exact—copy at the output. That’s not what we get. In fact, we get more. Added harmonics.

Here’s a picture of what I refer to.


“Fundamental Frequency” is our starting pure tone. All the others (H1 through H5) are added harmonics. Distortion. That which was not present before amplification.

Add together H1 through H5 and you get a total. (Get it? THD. Total Harmonic Distortion). The lower the THD the fewer number of added harmonics.

But before we vilify harmonics let’s remember they are also naturally occurring. In fact, naturally occurring harmonics are the tones that give musical instruments their voice. Harmonics distinguish a trumpet from a clarinet, a voice from a sinewave.

Here’s an image of naturally occurring harmonics.

Harmonics 2

Notice in this image of a guitar B-string the second harmonic is louder than the first (fundamental). That particular mix of fundamental and harmonics gives the guitar string its distinctive signature.

The challenge of an amplifier is to reduce added harmonics while preserving naturally occurring ones.

Today’s takeaway: added harmonics are unwelcome while naturally occurring harmonics give character to sound.

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23 comments on “Do measurements matter?”

  1. Paul,
    Thanks for this post. So, the way I understand tube amplifiers is that they can create euphonic distortion, say by adding 2nd-order harmonics. I have read that these euphonic distortions are why tubes can sound more life-like and in some cases, even better than the original performance. What say you?

    1. Arguments could be made either way. What you’re suggesting is that tubes or other devices that add more pleasant sounding harmonics, like the 2nd, can actually be euphonic. Can actually “improve” the original by adding warmth. While there is some merit to that, it’s not somewhere as a designer I would go.

      It’s like adding sugar to everything we eat. Sure, it gets sweeter, but after a while, you tire of the consistent taste.

  2. Do measurements matter? Yes….and no. It is not so simple. Two men are 5′-10″ and weigh 225 pounds. Does it mean they are similar? Not necessarily. One is a body builder who is all muscle, very little fat. He can lift a car with one hand. Well not quite. The other is a couch potato who sits all day at computers, TV sets, audio systems and the most exercise he ever gets is lifting his remote control. The only thing strong about him is his wrist.

    There are a lot of pitfalls you are unaware of if you are not experienced with the theory of measurements. Manufacturers focus on one where theirs is better and proclaim it a magic bullet. It isn’t. It’s like advertising that a Yugo has more trunk space than a Corvette. Even if it is true, so what? Here are some common mistakes.

    Are you measuring equipment under conditions of use? Connect an amplifier to a resistor and it looks beautiful. Connect it to certain loudspeakers or cables and it falls apart. In fact with some loads it can even shut itself down to protect itself. This is why most amplifiers, especially solid state amplifiers need protection circuits. In the early days they had a frequent tendency to blow up. Some speakers and some cables were notorious as amplifier killers. Look at Stereophile’s review of the Nagra Jazz preamp. look at what happens to performance when the amplifier input impedance is not high enough. this is bad design.

    Are your measurements accurate? Look at the FR of any speaker Stereophile tests. You will not see any indication of bass harmonic distortion. This is an especially important parameter since woofers have a tendency to “double” which means that when you drive them hard at 30 hz, the cone breaks up and actually produces 60 hz. You’d have no way to know that from Atkinson’s measurements. Teh manufacturer often leaves that specification out or doesn’t specify at what SPL it is measured. And you wonder why those expensive speakers can’t produce deep bass.

    Are the measurements meaningful. The HK A1000 had a claimed FR from 1hz to 1mhz. It actually tested to 1.5 mhz. Audiophiles, if you at your age can still hear to 20 khz, you are among the fortunate few. No you cannot hear to 40 khz and so output above 20 khz not only doesn’t contribute anything to your listening, it can spell trouble. More bad engineering.

    Are the measurements significant? Can you hear the difference between 0.1% THD and 0.001% THD? No. If you could, the cumulative effect of all of the distortions in each stage of the recording process would result in horrendous distortion. In fact they are usually insignificant, that is inaudible.

    Are the measurements complete. You don’t listen to amplifiers, speakers, phonograph cartridges, wires. You listen to sound reaching your ears. Not sound at the speaker output but sound AT your ears. Given that most people who make these measurements are electrical engineers or at least they have their training in electronics, when it comes to sound they are clueless. This is because sound is NOT an electrical phenomenon. You are listening to the entire chain from the sound reaching the microphones to the sound reaching your ears including everything in between. That includes the acoustics of your listening room. The total system is not linear. It includes among other things echoes in your room not present in the original recording while those heard in the audience are not captured on the recording or if they are, not in the same way or to the same degree. These reflections are much, even most of what you hear live an often in your own room. They have direction of arrival, time of arrival, and they undergo spectral changes with each bounce and traveling through air, especially humid air which selectively filters them.

    Does the sound field that reaches your ears from your recording in your listening room have any resemblance to what you would have heard in the audience live? No, not even remotely close. A system that could genuinely measure that would easily prove it. What you get instead has been described by one perceptive and honest audiophile as “canned music.” Is there anything you can do about it? Short of inventing a way to record and reproduce these missing elements or reconstructing them, no, it is beyond what you can do or buy. So if you are expecting low bass and your speaker can’t really reproduce it no matter what Atkinson’s measurements or the manufacturer’s claims say, you won’t hear it. If you are expecting the audible sound of live music from recordings, forget it. That is well beyond the current state of the art. Tweaking existing ideas to perfection (whatever that means) even where cost is no object won’t work. Enjoy your recordings and equipment for what it is but don’t imagine that it is something it isn’t. You are sure to be disappointed and keep hunting for something better like a cat chasing its tail but never catching it. It is always beyond reach.

  3. Hi Paul,
    Very helpful example of THD with with the B-String on a guitar – so do amplifiers distort by creating new harmonics of the original harmonic or do they increase/decrease the amplitude of the existing harmonics? Also does the concept of THD only apply to amplifiers or does it also apply to speakers / headphones? Thanks

    1. Thanks. Amplifiers can do both. In general, when they distort, it is to add back unwanted harmonics. Most leave naturally occurring harmonics intact. Speakers and headphones are even bigger generators of THD than amplifiers and by a magnitude.

  4. Trying to become “an educated stereo consumer” prompted me to buy one of those equipment review magazines and I could not figure out how it could be that a super expensive amp had poorer values than something cheap. I figured it was all part of the magic.
    “Better than the original performance”? I get that all the time.

  5. I guess we define ourselves as listeners by how we view the “better than the original” idea.

    If one is on the “lowest added information must be truest to the original” side of things (essentially an intellectual position, independent of the ability to “prove” it via measurement) – distortion – or even “coloration”, whether constructive or destructive, is anathema.

    On the other extreme we have “This SOUNDS GOOD. To ME. What else is there? Measurements are comparatively meaningless”. Measurement falls short of giving a full and accurate picture of what we end up hearing. The reproduction that does the best job of removing the analytic thought processes from the experience, where we forget about the technical and get lost in the musical – as with a positive experience of real music – is best. (Don’t forget – real, live music isn’t always fun, good, technically perfect or comfortable)

    If you subscribe to the notion that no reproduction of music is truly like real music, where’s the harm in making something more pleasing to the ear? Isn’t that the point? Or is the point to endlessly suffer the shortcomings of the technology?

  6. Paul, prior to this post I thought I understood the basics of harmonics. Now however you’ve left me confused.

    My understanding was that any sound (musical or otherwise) is defined by two components, the fundamental tone and the harmonic tones, the latter being multiples of the first. For example a sound with a fundamental of 60 Hz will have harmonic tones at 120 Hz (2x), 180 Hz (3x), 240 Hz (4x) and so on. Those tones will diminish in level to the point of inaudibility, although not in a straight slope, as your guitar note graph displays.

    You suggest, “THD refers to the addition of extra tones (harmonics) not originally found in the music.” But your first illustration shows the representative tones following an unamplified fundamental. My understanding was that distortion would cause in increase or decrease to any of those natural harmonics. That would mean a change in intensity for the naturally occurring harmonic tones, not an “extra” tone. So if the 494 Hz tone of a guitar is not produced at the level shown in your second graph then it will change the reproduced sound and represent distortion to the original event.

    Also I believe there is a mistake in your second figure. It identifies the fundamental tone as 247 Hz, but then calls that the 1st harmonic in the bar graph. I thought 494 Hz would be the 1st harmonic. Is that what you intended?

    1. The way I figure the big picture is that every time I listen it is a unique experience unto itself. Whether at a bar, a concert hall or this or that venue it is it’s own unique signature sound including crowd noise and acoustics and personal comfort. I absolutely love my stereos because they cater to me and my idea of great sound and they deliver on their promise.

    2. There is a mistake on the 2nd drawing in its labeling. You’re right. Such is the result of a lazy man’s reprinting of internet graphs.

      THD is always measured with a pure tone – one without any harmonics. A pure sinewave from a generator. This pure sine wave goes through the amp or speaker and out comes more than you started with. Harmonics. Add those harmonics up and that’s their total.

      The idea that an amp or speaker also doesn’t properly reproduce existing overtones (harmonics) is another subject altogether.

      1. Thanks Paul but I’m still confused.

        Are you saying a test tone can be generated which contains only the fundamental pitch, no harmonics? But when that tone is produced through an amp and speaker the harmonics are present, and so have been added?

        If so then I misunderstood the basics of sound. As mentioned, I thought every sound had the two components of fundamental pitch and harmonic overtones?

        1. A sine tone generator produces a single tone. Nearly everything you play it through will produce some harmonics along with it.

          As Paul mentioned above, the basic difference between different instruments playing a single note are the harmonics created that are unique to that instrument.

        2. Correct. Our test equipment produces a pure tone without any ovetones at all. We use this to gauge what’s been added by an amplifier or speaker. All amps and speakers add something unnatural to the sound. The measurements just tell us to what degree.

          But don’t despair. You’re not wrong. Every sound you might hear in real life has overtones. The note without is an artificial construct engineers developed to test. You don’t normally hear that unless through a synthesizer. Every musical instrument makes these tones.

  7. This is from a website from another manufacturer (for example purposes):

    THD:< 0.002% @ 1 kHz
    < 0.015% (20 Hz – 20 kHz)

    Why state numbers for a certain frequency, then restate it for the entire band? You see this all of the time.

    1. Distortion varies a LOT (100:1) with frequency and level. To understand distortion on musical signals, a good start is a family of log curves at different frequencies over power outputs from under a MilliWatt to over full rated output.

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