Musings on THD

The total dynamic range of a THAT driver and receiver combo is over 21 bits, 20KHz bw, unweighted. They’re made for pro audio levels and systems. 128dB of DR is not reproducible in anything but a very special acoustic environment. However common mode noise down 75dB or so is.

You take your pick and apply technology that makes sense in the specific conditions.

IMO, bothering about THD below 0.01% is tilting at windmills because more than that is baked into all your recordings, and much, much more is added by your speakers. And it’s all masked by the music.
 
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Not to mention the many and various distortions involved in scraping a bit of diamond over a vinyl groove. But nonetheless it manages to sound glorious.

Low order distortions (particularly 2nd and 3rd) are harmonious with all major and minor western scales and are are benign. But high order harmonics are truly noxious; manufacturers of first rate pianos take acoustic measures to suppress high order harmonics for that reason.
 
Let me conduct a little experiment. Let's say we have an amplifier that adds 0.01% of the 2nd harmonic (H2) and 0.001% of the 3rd (H3):
1692241964387.png

The distortion is not particularly high and is all low order, harmonious and benign, perhaps even euphonic.

Now let me play a simple chord, A-C#-E:
1692242317361.png

Oops. In addition to H2 and H3, our benign test amplifier sputters a bunch of intermodulation products, musically unrelated to the chord, with levels comparable or in some cases above those of H2 and H3. These are not euphonic and would not be masked by music. Such an amplifier might be ok for simple music such as a solo vocal, but would get confused with anything moderately complex, and would mush a full orchestra.

So, while various components of the audio chain undoubtedly distort, 0.01% THD does not give your amplifier transparency, and you do get audible benefits from making one of them more linear.
 
Oops. Someone needs to google "psychoacoustic masking".

And your example never happens in real life anyway. No actual musical instrument produces a chord made up of 3 pure sine waves. Once you throw in harmonics made be real instruments (plus all the aother stuff in real sound), and you apply the principles of masking, your argument fails completely.
 
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Someone needs to pause googling and actually listen to some music through some gear 😉

Ever since I got interested in making more linear amplifiers, I hear comments along the lines "linearity makes no audible difference". Yet, if you actually try (I did), both distrtion and intermodulation products and - remember what this thread is about? - common mode noise can clearly be heard, even with imperfect speakers or headphones.

To give you one example, some years ago I designed a board for the LM3886 that has 0.0018% THD at 1kHz, 18V RMS into 8ohm. Another well known board, similar in size and layout, has 0.0052% under the same conditions, mostly because of its trace routing. The difference between these two boards can clearly be heard and is not masked even by simple musical material.

Now, some people may prefer the (slightly) distorted sound, and linearity is not just a single THD+N number (ever tried measuring it? THD depends on the measurement conditions, which no one here mentioned), but that does not invalidate the point that more linear gear sounds different. And when someone hears a difference, it's a real experience, even if Google tells you there shouldn't be any.
 
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It is extremely rare that a synth (yes, it’s a real musical instrument) patch is made up of ultra pure sine waves that are not processed by some other modifier. True of all synth technologies. Sine waves from analog synths are not pure at all, and sine waves from digital synths also have impureties, though different.

Let me emphasize this again: pure sine waves are extremely rare in a syth. A sine wave, even one with 0.5% distortion, is a very bland, unexpressive sound that doesn't occur naturally in any acoustic instrument. It barely exists in electronics, and arguable does not exist once the tone is played through speakers. Transducers, especially speakers, are massively nonlinear, and produce over 1% of THD without any problem. So, no, any test signal made with one or more sine waves is invalid.

Even more rare, that such synth patch would exist as a solo with absolutely no other sound around it. Masking is powerful, look it up. The principle is that a low level signal (fundamental or harmonic) becomes inaudible in the presence of a higher level signal within a give masking frequency curve. All lossy codecs are based on the principle of masking. Some even work well enough to be transparent.

I have never once said "linearity makes no audible difference". That's not the point at all. Linearity is not a binary characteristic, it's completely variable with the device, level, and frequency. THD numbers don't even reflect the complete reality of nonlinear distortion at all because a single number doesn't reflect level or spectrum. However, vanishingly low THD numbers that are obtained at a wide range of levels and frequencies, those below 0.005% are in fact inaudible for many reasons, and masking is the major swamping factor. We don't need to argue this, it's well researched by every codec developer.

So when you use a sine wave to judge linearity, but you're hearing it through a distortion generator producing 1% or more (a transducer), that's just not a valid test. Then, when music is the test signal, the signal is already rich in spectral density, and self-masking. It takes massive amounts of distortion to become clearly laudible to every listener, less for trained listeners.

Now, I didn't want to get into this, but clearly, it's inevitable. Testing. When testing for audibility of anything where the effect is extremely low it is vital that all biases and variables be considered carefully and brought under control. This is not trivial. The test methodology known as ABX/DBT must be followed strictly. Any direct A/B test (even if might think it's blind) is not bias controlled. When we're dealing with minute, and barely audible effects, bais swamps just about everything. So you absolutely must adhere to the protocol. Otherwise you don't have valid evidence, you have subjective opinion.
 
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"Now, some people may prefer the (slightly) distorted sound". This is along the lines of what I'm getting at. There is no one THD figure. Real distortion profiles are a 3D graph of level, frequency, and spectrum. The graph shape varies with the distortion mechanism. The rate of distortion change is highly variable from a very gradual slope to a flat brick wall. There's just no way to discuss THD audibility simply.

However, when low enough, and in the presence of other audio signals that are 50+ dB higher in level, audibility literally becomes a function of masking.
 
THD is but one, and it's the over-quoted/under specified, and yet pretty complex one. For example, "3% THD is audible" is both correct and incorrect depending on many other conditions.
Already know about that. Is that what you think lead alexcp to making his claim of audibility for the circuit of this thread (and or possibly other circuits he is involved with)? Or, do you think there can be something unexpected to hear in an ultra-low distortion and noise measuring opamp circuit? Do steady state sine wave measurements fully characterize what can be audible?
 
Can't help but notice that expectation bias works both ways. If one doesn't believe he'd hear something, he'll make sure he doesn't. In fact, most people (on either side) would not dare to challenge their beliefs and would skip the listening test altogether.

However, this thread is about a low distortion balanced line receiver. I am kindly asking everyone to take the religious (as in, concerning personal beliefs) discussion of audibility, or not, of various level of distortion to some other place.
 
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Can't help but notice that expectation bias works both ways. If one doesn't believe he'd hear something, he'll make sure he doesn't. In fact, most people (on either side) would not dare to challenge their beliefs and would skip the listening test altogether.
That's why uncontrolled, sighted testing results are invalid.
However, this thread is about a low distortion balanced line receiver. I am kindly asking everyone to take the religious (as in, concerning personal beliefs) discussion of audibility, or not, of various level of distortion to some other place.
Sorry, none of what I'm saying is personal, religious, or a particular belief. If you are doing unscientific testing, I'll always question the results, especially if the fly in the face of prior art and science. I'm sorry if that statement is inflamatory, it's meant only to be factual.
 
To elaborate....

The total range of hearing is about 140dB from threshold of hearing at 0dB SPL to threshold of pain. That means to begin to hear a harmonic distortion product at -140dB the stimulus would have to be at or above the trehsold of pain, the listening environment would have to have extremely low nose, as would the reproduction system end to end. There are obvious problems. Starting with microphones limited dynamic range, mic preamps and the release format which is probably 16/44.1 or vinyl (which is worse) because that's what we have access to. Ignoring whats between the mic preamp and the release for now, we then have the dynamic range of the room the recording was made in, with typical studios being in the NC 10 range, still above the threshold of hearing, and if the recording involves acoustic instruments, the maximum SPL at the mic being very much shy of the threshold of pain.

Then examing the extremely well researched properties of psychoacoustic masking, a principle where a louder sound at one frequency makes a quieter sound at a nearby frequency completely inaudible, presenting a masking curve that peaks at the loud tone, then slopes downward in level and away in frequency, and upon this is built every single lossy codec used today, even the ones that are transparent.

With test material played at a reasonably loud (but safe) listening level of 80dB SPL, and allowing for peaks up another 25dB above that, we have problem number 1: the dynamic range, mic to speaker, is too limited to reproduce a 140dB dynamic range, and not by just a bit. It's shot by 35-40dB of being able to do that. Or more, in practice. So you can't really reproduce those low level harmonics to being with, with them ending up 35dB below the threshold of human hearing. Then over the top of that you have to consider psychoacoustic masking.

But there's another huge problem: that of expectation bias. It has been proven countless times that when offered two identical choices, but informed that one is different, a test subject will "detect" that difference with shocking accuracy! But it doesn't actually exist. It has also been proven that when offered two choices with miniscule differences, but where the choices identity is known, biases appear that completely influence the test result. Yet, when the choices are kept blind, and the tester is asked to compare choice A and B, then compare to a third choice, X, that is in reality A or B, but unknown, the testers ability to discern differences drops significantly, and when differences are small, it drops to the noise floor of random choice. Thus, where human perception or human physiological response is the intended metric, it is critical that biases of all types be brought under control.

Once controlled testing has been established, then it becomes possible to determine if a difference is really audible to one or more test subjects given sufficient trials (which would be around 30, with X randomized).

I suspect that in the claim of the ability to hear distortion at -140dB is probably based on uncontrolled, sighted and biased testing being done.

The above is what I mean by a subjective observation with uncontrolled bias not matching what the rest of audio science woud dictate. The logical assumption would be to find the biases, control them, and see if the results conform with the scientific expectation. But that's not what's often done. Rather, the "I know what I hear" bias is triggered along with the "we can't measure everything we hear" bais (both are completely wrong), and scientific testing is abandon, and myth is born or propagated.

Finally, while THD may be interesting, it is a difficult metric to assign the aspect of audibility. Partly because, being caused by nonlinearities, it changes with level constantly, and often changes with frequency as well. Different mechanisms produce different harmonic distributions too. And the human hearing system itself produces level and frequency variant THD. Yet, because it's easy to measure, THD gets a lot of attention. However, there are other types of distortions that are even more audible, like any of those that produce products that are not harmonically related, or fold down to frequencies below the stumuls. High frequency multi-tone testing reveals things about certain systems that THD doesn't. But you rarely read anything about anybody doing that. The tools are still free. But by the time we get to "I can hear THD at -140dB", it's progressively less likely they will ever be used.