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Post research here that casts doubt on ASR objectivism

Spocko

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In an interview with Earl Geddes, @hardisj uncovered this notable insight on how masking completely renders THD nearly pointless at higher SPLs as high listening volume significantly masks distortion to where it's inaudible (I've linked this specific segment below). This is significant because home theater reference is 85 dB with peaks of 95dB. This pretty much explains why it's pointless to push AVRs and home theater applications to spend resources on reducing distortion if it's masked to inaudibility. However, the opposite is also true: listening to music at lower volumes reveals more distortion - so this likely explains why certain speakers sound better when played loud - can no longer hear the distortion LOL.

Thank you again @hardisj for this interview! We need to follow up on this discussion as it pertains to home theater audio applications where SPLs without compression are more important than distortion concerns.
 
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preload

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@ahofer Thanks for compiling this list of working hypotheses, and I more or less am working with a similar understanding personally.

I did want to offer that the current published evidence DOES support a deviation in frequency response of speaker cables when used at ordinary lengths in common situations (i.e. solid state amp, commercially available loudspeakers, and representative speaker cables). A good reference is Davis F. "Cable, loudspeaker, and amplifier interactions." JAES 1991;39:461-468.

Here's one of the figures from the paper, showing 2+ octaves of -1.25dB response.
View attachment 131819
There are other figures as well. The amount of FR deviation established by the interactions of amplifier output impedance, speaker LCR, and speaker/crossover R + L curves is not necessarily transparent. In fact, it is significant enough where I would assume that there COULD be barely noticeable differences, unless proven otherwise by a controlled, blind experiment.

Therefore, I would suggest something like:
Cables are usually audibly transparent when they feature LCR measurements close to the generic 12G cable here. However, cables can also introduce potentially audible frequency response deviations when they are longer, higher in inductance or DC resistance, are used with amplifiers with higher output impedance, and/or are supplying loudspeakers with large deviations in their impedance curves.

@ahofer
 

audio2design

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No. It happens during digital processing, with any analog signal being perfectly fine. Often, there never was an analog signal to begin with (Synth output, processed samples etc etc).

Again, if it came from a synth, then it was a math failure. At some point an illegal signal was created. This may manifest in the DAC, but the "failure" happened earlier in the process. If you are recreating a signal bigger than analog "1", then you created an erroneous signal somewhere along the line, whether in the analog domain, or digital domain.
 

MBL'er

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I thought veils would only lift in fairy tales
Meant for golden ears, but not for me
PRAT was out to get me
That's the way it seemed
Disappointment haunted all my streams

Then I saw its price, now I'm a believer
Not a trace of doubt in my mind
...
I'm bewildered that some think it's fine for companies to sell--at crazy prices--things that do not do what they say they do. I know we have some longstanding ASR contributors who say we should let adults spend their money however they want.

But would they really want to spend their money on poorly engineered and outrageously expensive devices with phony specifications? I don't think so. Most people want to make reasonably informed decisions.

Admittedly, the placebo effect is countervailing factor: If I think my expensive stuff sounds better, then, yes, it will, to me, in a sighted test. In most domains, however, we do not rely on the placebo effect to select among different alternatives. And the benefit of placebo effect goes away when you know that you're taking a sugar pill or listening to an amplifier that is a distortion generator.

I know a person with school age children who has been in and out of serious financial trouble over the last several years. Found out just last week that he is an audiophile who has six figures worth of stuff recommended by the audiophile rags. (I'm not going to be the person who breaks it to him that ASR exists.) If he had known better, I think he would have made different choices.

Pro
I'm bewildered that some think it's fine for companies to sell--at crazy prices--things that do not do what they say they do. I know we have some longstanding ASR contributors who say we should let adults spend their money however they want.

But would they really want to spend their money on poorly engineered and outrageously expensive devices with phony specifications? I don't think so. Most people want to make reasonably informed decisions.

Admittedly, the placebo effect is countervailing factor: If I think my expensive stuff sounds better, then, yes, it will, to me, in a sighted test. In most domains, however, we do not rely on the placebo effect to select among different alternatives. And the benefit of placebo effect goes away when you know that you're taking a sugar pill or listening to an amplifier that is a distortion generator.

I know a person with school age children who has been in and out of serious financial trouble over the last several years. Found out just last week that he is an audiophile who has six figures worth of stuff recommended by the audiophile rags. (I'm not going to be the person who breaks it to him that ASR exists.) If he had known better, I think he would have made different choices.

@Dialectic

my remark was not about "poorly engineered and outrageously expensive devices", but on the idea that in audio money drives everything, from shopping decision to biases, to all sort of assumption, which when it comes to money many seem to be prisoner.

Personally, I do not work that way. I select a price range which I feel comfortable within, mostly on ethic grounds, and then choose prospective equipment based only on my perceived quality.

If I had to target the most expensive items I can afford, well, probably I would run into numbers I am shy to disclose which would not guarantee any sonic improvement to my current system.

In my opinion, in audio the "cheapest to deliver" approach does not efficiently work, as equipment are not "commodities" (I work in investment banking, please excuse my jargon). Tests made by Amir are of great help in taking the bad stuff out of the picture, but then nuances, tonality preferences, synergies with paired equipment and listening environment still exist.

Probably like in cars - in which I am no expert - where a Subaru can potentially have the same performance as [name your European dream sport car] but probably does not give the same driving feeling (not related to ego stuff, but to technical driving parameters like acceleration, torque, steering response, and such). All that with maximum respect to Subaru and respective owners.

At the end of the game, if one is focused on money, good for him. But it should kept in mind that not everybody "works" within that framework. Assuming that each sapiens sapiens is exclusively driven by money (or, better, by the relative lack of it) can lead some to be somewhat prisoner of such assumption.

I've read a significant proportion of comments within the above framework, also with a very stiff approach not open to any doubt.

Doubt is the foundation of improvement.

Best,

M
 

KSTR

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Again, if it came from a synth, then it was a math failure. At some point an illegal signal was created. This may manifest in the DAC, but the "failure" happened earlier in the process. If you are recreating a signal bigger than analog "1", then you created an erroneous signal somewhere along the line, whether in the analog domain, or digital domain.
This correct, of course.

The point here is that these "failures" are commonplace and often hardly can be avoided (like the "wrong" Synth digital output). Therefore the mastering should check for possible IR-overs and remove them, and that's what they do now.
 

Kvalsvoll

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Well tbh I felt post #10 covered it;

Kvalsvoll said:

Those statements do not belong to this forum or any other brand or entity, they are general statements describing basic principles that are all known and proven.

"It is known."

JSmith

Just to clarify what I meant to say, it can easily be misunderstood;

I did not mean to imply that making those statements are wrong, just that they are general and widely accepted and thus no forum or brand or company or single person can claim ownership of those statements.

The opening post #1 is very good, because we are now at a state where challenging those statements requires evidence that holds up scientifically, if they are to be taken seriously.
 
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ahofer

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it doesn't matter that they can't prove they can hear a difference. What matters is their perception of the world which is a highly subjective experience.

..except when they make claims about objective and strictly audible differences. Everyone is fully entitled to their subjective experience, but they cannot represent it as fact.
 

ctrl

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In an interview with Earl Geddes, @hardisj uncovered this notable insight on how masking completely renders THD nearly pointless at higher SPLs as high listening volume completely masks distortion to where it's inaudible (I've linked this specific segment below).
One should be careful not to misunderstand Dr. Geddes. He considers THD as a single value (e.g. 1% THD@1kHz for an amplifier) or a THD curve to be rather meaningless, because there it is no longer apparent from which proportions of distortions with which order THD is composed.

However, the distortion diagrams @amirm and @hardisj present in their speaker reviews show the individual harmonic distortions according to their order from HD2 to HD5. Therefore, these measurements are quite useful.

Although no one can definitively say at what point exactly harmonic distortion is audible to the individual, it can be assumed that anything below the masking threshold is not audible (but one should always keep in mind that individual hearing thresholds can vary greatly).

As a very rough guideline, it can be said that for the same excitation, the higher the order of the harmonic distortions, the lower their masking and thus the more likely the distortions are to be audible.
Low tones are masked "better". The higher the sound pressure level, the better the masking - for more details here.
The "worst" thing that can happen is high harmonic distortion in the 1-2kHz range, because masking is worst in this frequency range.

The worst masker of harmonic distortion is a single tone. Completely "pure" single tones are very rare when listening to music, but quite often almost pure tones occur, such as a piano keystroke.
This can then look like this, for example, that at C6 (~1kHz) there is an almost pure tone (overtones are of course always somewhat present) - more details here.
1621959163297.png
A very good loudspeaker would now have so little harmonic distortion around 1kHz that it would always be below the perception threshold, i.e. completely masked by the 1kHz masker tone (the piano key stroke at 1kHz).

The masking diagram for a pure tone at 1kHz looks like this:
1621959585832.png

Source: Zwicker, Fastl - Psychoacoustics

So a 1kHz tone masker with 80dB SPL masks HD2 (a parasitic tone at 2kHz) up to about 43dB (or -37dB, see gray lines), but HD5 (a parasitic tone at 5kHz) only up to about 20dB (-60dB, see blue lines).
Similarly, the values for a 1kHz masker tone at 90dB SPL can be determined - HD2 53dB (-37dB) and HD5 43dB (-47dB).
1621960462649.png
Similarly, one can determine the perception thresholds for HD3.

This would result in the following theoretical perception thresholds for harmonic distortion at 80-90dB SPL for the frequency range around 1kHz:
HD2 (80/90dB): around -37dB
HD3 (80/90dB): -48dB / -41dB
HD5 (80/90dB): -60dB / -47dB

(Please do not interpret the dB values mentioned as absolute, +-1dB does not matter much, it is more about the qualitative conclusion)

So, to be absolutely sure that it is impossible to perceive harmonic distortion, a loudspeaker should be, preferably significantly, below these values.
Unfortunately, this is not the case in the example shown below. Both HD3 and HD5 are close to the range of theoretical perceptibility at 86dB (which, as mentioned, can vary from individual to individual) - so this could be better.
1621961270324.png


Even though it is not possible to clearly determine when harmonic distortions cause audible problems, it is fairly safe to say below which perception threshold no problems are very likely to be expected.
 
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ahofer

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I appreciate your response and it is well received. However, I think that science can't currently explain everything that is going on in terms of our perception of reality.

What I am trying to get at is what we perceive through a controlled, proper double blind test, or whatever kind of test meets your criteria, is different than what we perceive when all of our faculties and biases are being employed in ordinary listening... since people do not enjoy their music in such a controlled way it is not of that much value other then to inform the basis for ones beliefs and shape their bias. Most members of this forum, audiophiles, and music lovers in general, are not in a position to authenticate, validate, or personally attest to these results through their own experience. They lack both the tools and technical expertise. They believe based on the work of others. This is, of course, all fine and there is nothing wrong with these beliefs. They are not better or worse than any other harmless beliefs.

What difference does it make whether what we perceive is the result of a device itself or our bias? For objectivists, I can say, sure, I can see how you might lean toward this point of view purely due to economics and the exorbitant prices of audio gear; however, for those whom money is of no concern, this point of view seems to be narrow and limited in its scope and experience and may even diminish ones ceiling for enjoyment of the hobby.

The topic does interest me which is why I am making an effort to challenge my understanding and hopefully learn something by interacting with it.

One may be unable to pick out a cable or device while being limited to only their hearing, but that doesn't mean that their perception of what they hear and their aural experience isn't heightened when they are able to employ all their faculties such as in normal listening. There may be more going on that we don't yet understand and we have no way to measure or test for it. You can't tell someone their experience is incorrect because they are unable to prove it using only one sense when we know that our perception of reality is determined by much more than hearing alone. It may very well be a combination of things, not just hearing, that allows people to perceive what they hear differently than others... imagination, bias, personal experience, etc... whatever the case may be, if it heightens your enjoyment and allows you to experience something that others deny the existence of... then, well, who is the real winner in this situation? The denier or the believer?

I think its the lack of humility and the audacity to claim scientific certainty that I find most off putting.

If we are designing the electrical functioning of the equipment, we need to understand what elements of signal processing will make a difference. If we are designing something so that it influences the listener through some other means than the electrical signal, then by all means your questions are valid, but understand you are answering a completely different sort of questions with different measurement tools (and a lot of research there as well).
 
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ahofer

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The opening post #1 is very good, because we are now at a state where challenging those statements requires evidence that holds up scientifically, if they are to be taken seriously.

Thanks, getting there. Still need to work on thresholds for measurement variance and confidence levels for refuting them.
 

Wes

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[QUOTE="danadam, post: 793490, member: 262"
As long as there is no proof of hearing differences for same-measuring devices, it is neither presumptuous nor arrogant. It is practical. Once there is a proof, no one will claim that more measurements are not needed.[/QUOTE]


The post you quoted was about whether one could be confident. I agree that the practical (buying) is not at issue.

However, that is far from saying that DAC units, amps, or pre-amps cannot be improved upon in terms of SQ or euphonics.

A full search of the factor space involved has not been conducted; moreover, there are serious reasons to suspect that not all effects can be subsumed into SINAD, THD or other simplistic figures of merit, much less the use of engineering judgement as a gap-filler for actual listening tests.

So, IMO there are two levels of analysis. The easy one is what to spend $$ on; the hard one is a scientific research issue.
 

Wes

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I don't claim to understand really any of this, especially in terms of measurements and what that relates to in terms of audio reproduction. I've spent all my time collecting pieces of gear based on the impressions of others that fall within my budget. I've never bought anything based on how it measures and have only recently discovered this forum. I suspect for many people who enjoy audio they are coming from a similar background.

I guess I consider myself somewhere in between objectivist/subjectivist... probably leaning more toward objectivist simply because I cannot afford any true hi fi gear. Most everything I own is from the 80s and 90s aside from the two DACs I have purchased. I did recently purchase a new, modern preamp that supposedly measures well and I found it personally to be subpar compared to my 1980s preamp. All I can go on is my personal experience. I notice big changes between speakers -- less but still noticeable are the changes between preamps and digital sources -- amps, as I state above, I mostly notice in terms of woofer control and listening fatigue. Since I have never owned any new audiophile hi fi gear I can't comment on how it sounds but my experience makes me believe it likely sounds very good... I can only assume that the hi end gear I own from the 80s and 90s, which I believe sounds very good, would likely be improved upon through advancements in the past 30-40 years.

So far my experience, limited as it may be, tells me that just because something measures well doesn't guarantee it will sound better to my ears.


you cannot afford a Topping DAC?
 

Blumlein 88

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In an interview with Earl Geddes, @hardisj uncovered this notable insight on how masking completely renders THD nearly pointless at higher SPLs as high listening volume significantly masks distortion to where it's inaudible (I've linked this specific segment below). This is significant because home theater reference is 85 dB with peaks of 95dB. This pretty much explains why it's pointless to push AVRs and home theater applications to spend resources on reducing distortion if it's masked to inaudibility. However, the opposite is also true: listening to music at lower volumes reveals more distortion - so this likely explains why certain speakers sound better when played loud - can no longer hear the distortion LOL.

Thank you again @hardisj for this interview! We need to follow up on this discussion as it pertains to home theater audio applications where SPLs without compression are more important than distortion concerns.
I think your ear just overloads at higher volumes creating its own distortion. I've worked where a building had several large methane powered engines driving large Roots blowers. SPL was 100-110 db depending upon where you were. Pretty much an undecipherable cacophony of noise. Put on some hearing protection which knocked levels down 20-25 db, and a world of difference. Suddenly you could hear much detail. The ticking of the valves if some of them were out of adjustment, a wrist pin going bad in one engine, a clutch whose bearings were starting to grumble a little. We adjusted mixture by exhaust gas temps, but with lower noise levels you could tell by ear if an engine were trimmed up good or not. Instead of an indescribable roar you had many things one could hear separately from everything else.
 

Xulonn

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I guess I consider myself somewhere in between objectivist/subjectivist... probably leaning more toward objectivist simply because I cannot afford any true hi fi gear.

Au contraire. The only way to find "true hi-fi gear" is via trusted measurements. There is a lot of new and used, good-measuring, and reasonably-priced hi-fi gear available around the world. Measurements can weed out much of the distorted and overpriced gear, still leaving a very large selection of equipment that both measures and sounds excellent - and satisfies many different tastes in appearance.

-----------------------------
This discussion brought me an image of a closet full of strawmen - many of them identical to each other - that allowed a new one to be brought out as soon as the last one was burned up by reason and logic.

Chinese Strawmen.jpg
 

BinkieHuckerback

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It's not the source of the audio that matters, it's the end point...your hearing...?
 

Spocko

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One should be careful not to misunderstand Dr. Geddes. He considers THD as a single value (e.g. 1% THD@1kHz for an amplifier) or a THD curve to be rather meaningless, because there it is no longer apparent from which proportions of distortions with which order THD is composed.

However, the distortion diagrams @amirm and @hardisj present in their speaker reviews show the individual harmonic distortions according to their order from HD2 to HD5. Therefore, these measurements are quite useful.

Although no one can definitively say at what point exactly harmonic distortion is audible to the individual, it can be assumed that anything below the masking threshold is not audible (but one should always keep in mind that individual hearing thresholds can vary greatly).

As a very rough guideline, it can be said that for the same excitation, the higher the order of the harmonic distortions, the lower their masking and thus the more likely the distortions are to be audible.
Low tones are masked "better". The higher the sound pressure level, the better the masking - for more details here.
The "worst" thing that can happen is high harmonic distortion in the 1-2kHz range, because masking is worst in this frequency range.

The worst masker of harmonic distortion is a single tone. Completely "pure" single tones are very rare when listening to music, but quite often almost pure tones occur, such as a piano keystroke.
This can then look like this, for example, that at C6 (~1kHz) there is an almost pure tone (overtones are of course always somewhat present) - more details here.
View attachment 131923
A very good loudspeaker would now have so little harmonic distortion around 1kHz that it would always be below the perception threshold, i.e. completely masked by the 1kHz masker tone (the piano key stroke at 1kHz).

The masking diagram for a pure tone at 1kHz looks like this:
View attachment 131925
Source: Zwicker, Fastl - Psychoacoustics

So a 1kHz tone masker with 80dB SPL masks HD2 (a parasitic tone at 2kHz) up to about 43dB (or -37dB, see gray lines), but HD5 (a parasitic tone at 5kHz) only up to about 20dB (-60dB, see blue lines).
Similarly, the values for a 1kHz masker tone at 90dB SPL can be determined - HD2 53dB (-37dB) and HD5 43dB (-47dB).
View attachment 131928
Similarly, one can determine the perception thresholds for HD3.

This would result in the following theoretical perception thresholds for harmonic distortion at 80-90dB SPL for the frequency range around 1kHz:
HD2 (80/90dB): around -37dB
HD3 (80/90dB): -48dB / -41dB
HD5 (80/90dB): -60dB / -47dB

(Please do not interpret the dB values mentioned as absolute, +-1dB does not matter much, it is more about the qualitative conclusion)

So, to be absolutely sure that it is impossible to perceive harmonic distortion, a loudspeaker should be, preferably significantly, below these values.
Unfortunately, this is not the case in the example shown below. Both HD3 and HD5 are close to the range of theoretical perceptibility at 86dB (which, as mentioned, can vary from individual to individual) - so this could be better.
View attachment 131930

Even though it is not possible to clearly determine when harmonic distortions cause audible problems, it is fairly safe to say below which perception threshold no problems are very likely to be expected.
Thanks for this, so for real content (mainstream music and movies), what should we conclude in terms of the masking effect on electronic distortion from amplifiers and AVRs? It appears that electronics continue to invest and spend greatly on lowering distortion but at what point should they just stop and find something else to improve (like more signal headroom to offset attenuation required by DSP)
 

Blumlein 88

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Thanks for this, so for real content (mainstream music and movies), what should we conclude in terms of the masking effect on electronic distortion from amplifiers and AVRs? It appears that electronics continue to invest and spend greatly on lowering distortion but at what point should they just stop and find something else to improve (like more signal headroom to offset attenuation required by DSP)
Always going to be hard to say. Certainly -120 db is enough. Probably for nearly all situations -60 db would be enough if you achieve that at the phones or speakers. So having everything feeding the transducers at -80 db and better is probably enough. You can't count on AVRs to reach -80 db. Probably for music rarely would even -40 db be a problem.
 

abdo123

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One should be careful not to misunderstand Dr. Geddes. He considers THD as a single value (e.g. 1% THD@1kHz for an amplifier) or a THD curve to be rather meaningless, because there it is no longer apparent from which proportions of distortions with which order THD is composed.

However, the distortion diagrams @amirm and @hardisj present in their speaker reviews show the individual harmonic distortions according to their order from HD2 to HD5. Therefore, these measurements are quite useful.

Although no one can definitively say at what point exactly harmonic distortion is audible to the individual, it can be assumed that anything below the masking threshold is not audible (but one should always keep in mind that individual hearing thresholds can vary greatly).

As a very rough guideline, it can be said that for the same excitation, the higher the order of the harmonic distortions, the lower their masking and thus the more likely the distortions are to be audible.
Low tones are masked "better". The higher the sound pressure level, the better the masking - for more details here.
The "worst" thing that can happen is high harmonic distortion in the 1-2kHz range, because masking is worst in this frequency range.

The worst masker of harmonic distortion is a single tone. Completely "pure" single tones are very rare when listening to music, but quite often almost pure tones occur, such as a piano keystroke.
This can then look like this, for example, that at C6 (~1kHz) there is an almost pure tone (overtones are of course always somewhat present) - more details here.
View attachment 131923
A very good loudspeaker would now have so little harmonic distortion around 1kHz that it would always be below the perception threshold, i.e. completely masked by the 1kHz masker tone (the piano key stroke at 1kHz).

The masking diagram for a pure tone at 1kHz looks like this:
View attachment 131925
Source: Zwicker, Fastl - Psychoacoustics

So a 1kHz tone masker with 80dB SPL masks HD2 (a parasitic tone at 2kHz) up to about 43dB (or -37dB, see gray lines), but HD5 (a parasitic tone at 5kHz) only up to about 20dB (-60dB, see blue lines).
Similarly, the values for a 1kHz masker tone at 90dB SPL can be determined - HD2 53dB (-37dB) and HD5 43dB (-47dB).
View attachment 131928
Similarly, one can determine the perception thresholds for HD3.

This would result in the following theoretical perception thresholds for harmonic distortion at 80-90dB SPL for the frequency range around 1kHz:
HD2 (80/90dB): around -37dB
HD3 (80/90dB): -48dB / -41dB
HD5 (80/90dB): -60dB / -47dB

(Please do not interpret the dB values mentioned as absolute, +-1dB does not matter much, it is more about the qualitative conclusion)

So, to be absolutely sure that it is impossible to perceive harmonic distortion, a loudspeaker should be, preferably significantly, below these values.
Unfortunately, this is not the case in the example shown below. Both HD3 and HD5 are close to the range of theoretical perceptibility at 86dB (which, as mentioned, can vary from individual to individual) - so this could be better.
View attachment 131930

Even though it is not possible to clearly determine when harmonic distortions cause audible problems, it is fairly safe to say below which perception threshold no problems are very likely to be expected.

it would be interesting if you would kindly make a similar analysis on Intermodular distortion, which is usually at a much higher level and is not alleviated with masking effects.
 
D

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How many people actually have an unlimited amount of money to spend on audio equipment? I think it is safe to say that would be less than 0.00000001% of audio enthusiasts. Everyone else, even if they have six figures to spend, wants to get maximum value for their money.

There's also the matter of where to apportion the budget. Understanding what matters and what doesn't is vital in that respect.

We are in a hobby where there are products that demonstrably have no effect but can cost a lot of money. You are arguing that for some people the placebo alone makes that spend worthwhile but the problem with that is that placebo effect will not apply to all equally, since it has no basis in reality. Even if it does apply to some it will only apply sometimes, it will not be consistent.

On the other hand spending the money on, say. better engineered speakers, will make a real difference, one that is consistent over time and across all people.

This is not the same thing as 'saving money'. It's about obtaining optimum results for any given budget.

Would anyone, if questioned, say that they don't want to achieve optimum results? In any aspect of life?
Part of my point is that we don't fully understand how placebo works, and there are plenty of studies regarding sham surgery where there are lasting effects even after it has been revealed. We simply do not fully understand how the mind works and how it shapes what we perceive as reality. I simply think its unfair to judge people with absolute certainty as "audiophools" when we don't have all the answers.
 
D

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My biggest issue with subjective perception is NOT what some person thinks about an over-priced piece of gear in their own home. My biggest issue are REVIEWERS who use subjective criteria to explain why that over-priced gear is the greatest available gear.

So the guy who enjoys some questionable quality amplifier and enjoys it in his own home because he just had two glasses of wine and a beautiful date on his arm, doesn't bother me. But if that guy is a reviewer, and is about to post his audiophile article about that amp after doing a line of coke, well, lets just say I'd like that disclosed so I can replicate his subjective review in my own home.

..except when they make claims about objective and strictly audible differences. Everyone is fully entitled to their subjective experience, but they cannot represent it as fact.
I agree that subjective impressions shouldn't be listed as fact.
 
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