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AES Paper Digest: Sensitivity and Reliability of ABX Blind Testing

andreasmaaan

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#21
Are you not just going to use the best or most appropriate technology you can obtain/design/afford in each circumstance? And by 'best' I mean objectively best - which you must be able to measure/characterise/specify in order to do the science, anyway.
My basic point is that you need science to tell you what the "best" is. Let's say you're designing a loudspeaker with a particular budget, and particular performance criteria for your application (SPL, bass extension, etc.). You're choosing your woofer. You've narrowed it down to two woofers - one has lower overall nonlinear distortion than the other, but IMD is higher, and harmonics F4 and F5 are at almost the same level as harmonics F2 and F3. The other woofer has slightly higher nonlinear distortion overall, but most of this is F2, and IMD is lower overall. No need to go into every other aspect of the drivers' performance for the purposes of the hypothetical - let's assume all else is equal - but you get the idea.

Essentially, you have all these data that you've obtained from objective measurements, and you need to decide how to weight them. Do you have a better proposal as to how to do this than by turning to (in this case) distortion audibility studies?

EDIT: and I should add studies into auditory masking...
 
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Cosmik

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#22
Essentially, you have all these data that you've obtained from objective measurements, and you need to decide how to weight them. Do you have a better proposal as to how to do this than by turning to (in this case) distortion audibility studies?
Technically speaking, no. But by definition your audibility studies *won't* show that the listener may be more influenced psychologically by the colour of the box or the smell of the different diaphragm materials.

And is this a preference test, or an audibility test? Why would the latter help you if there's a suspicion that some real customers might actually prefer higher distortion in some applications (e.g. PA)? And are you going to go through every permutation of EQ and volume settings? Could be that a 0.5dB hump at 300Hz more than outweighs the audibility of distortion differences. Unless you are Apple, what are the chances you can get a meaningful result without spending *a lot* of money on these tests relative to how many speakers will be sold?

If you, yourself, can't decide after an afternoon's listening, and all other considerations are equal, then I think a coin should be tossed and the effort and expense of ritual listening tests should, instead, be directed towards the logo, the web site, the marketing, and even the packaging because all of these things may have a far more profound effect on the customer's experience than the narrowest of differences in sound that, although measurable, may be interpreted by the listener as much of a muchness regardless of how it is tuned or which woofer is used.
 

andreasmaaan

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#23
Technically speaking, no. But by definition your audibility studies *won't* show that the listener may be more influenced psychologically by the colour of the box or the smell of the different diaphragm materials.
Well the colour of the box is an independent factor, so if the listener is more influenced by it, then that can be accounted for without influence on woofer choice. The smell of the diaphragm materials - haha. Hopefully that is below the threshold of... smellability?

And is this a preference test, or an audibility test? Why would the latter help you if there's a suspicion that some real customers might actually prefer higher distortion in some applications (e.g. PA)? And are you going to go through every permutation of EQ and volume settings? Could be that a 0.5dB hump at 300Hz more than outweighs the audibility of distortion differences. Unless you are Apple, what are the chances you can get a meaningful result without spending *a lot* of money on these tests relative to how many speakers will be sold?
I'm talking about audibility studies as opposed to preference studies here. And I'm not proposing actually doing the studies yourself. The research is out there, and it shows (for example) that lower order harmonic distortion is less audible than higher order harmonic distortion.

The 0.5dB hump at 300Hz may be another factor to be weighted (but only if the speakers are passive). You won't be able to weight all the factors perfectly, but you'll do a better job relying on audibility studies than not.

If you, yourself, can't decide after an afternoon's listening, and all other considerations are equal, then I think a coin should be tossed and the effort and expense of ritual listening tests should, instead, be directed towards the logo, the web site, the marketing, and even the packaging because all of these things may have a far more profound effect on the customer's experience than the narrowest of differences in sound that, although measurable, may be interpreted by the listener as much of a muchness regardless of how it is tuned or which woofer is used.
As per the box colour, these factors are not mutually exclusive from making design choices based on audibility studies. And whether you refer to audibility studies or not, you still have to choose a woofer. I'd base the decision on a large body of controlled research, rather than an afternoon's listening - which is in itself a listening test, albeit an uncontrolled one with a sample of only one ;)

PS. I'd have thought it would be the home audiophiles who'd be more likely to prefer higher (or should I say more audible) distortion than PA listeners...
 

Cosmik

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#24
I'd base the decision on a large body of controlled research, rather than an afternoon's listening - which is in itself a listening test, albeit an uncontrolled one with a sample of only one ;)
On that basis, though, why design a new speaker? Where will you find the data that allows you to make a judgement on the various factors you are going to be considering unless it duplicates an existing experiment?

There have been suggestions, for example, that speakers like the Kii Three sound 'dry' to some listeners, perhaps because they've never heard a speaker with controlled bass directivity. Where is the data that the designer could have consulted on such an issue, and even if it existed, should they have taken notice of it, or gone ahead in order to 'change people's expectations' anyway?
 

Theo

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#25
The preference subject seems to me more important when addressing the speaker question. They may be, literally, the elephant in the room:oops:. And they also are the weak link in the distortion free ideal system. So what is your choice of speakers based on? Size, shape, color, room adequacy, partner's opinion,... name it?
Oh, I forgot, :eek: sound?
 

andreasmaaan

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#26
On that basis, though, why design a new speaker? Where will you find the data that allows you to make a judgement on the various factors you are going to be considering unless it duplicates an existing experiment?
Most of the studies are not explicitly based on speakers or geared towards speaker design. Most of the choices are not (shouldn't be) based on a single experiment.

Beginning from the basics, we need to know (for example) the following, all of which are derived from listening studies:
  • What range of frequencies can humans hear? (audiometry studies)
  • In which frequency range is human hearing most sensitive? (equal loudness studies)
  • Which kinds of distortion products are most effectively masked? (masking and distortion audibility studies)
  • Which kinds of resonances are most audible? (audibility of resonance studies)
  • How much group delay is permissible? (phase audibility studies)
Just because a lot of this knowledge has become common wisdom doesn't mean that there aren't listening studies at the source of it.

And whether you're going to try some combination of design elements that results in something new, or being paid to do something that's been done in various permutations hundreds of times before, you're going to design a better speaker if you take account of the results of these listening studies.

I'm designing a 500 ml single 2" driver dual-passive radiator portable speaker at the moment. The budget is tiny and the outcome will not be special by any means. But of course, in selecting the driver, the electronics and the DSP, and in making decisions about the design, I'm referring to knowledge I have about audibility of distortion, resonances, etc. etc. On this budget I can't have a perfect driver, I can't have low bass extension, etc. But I can still optimise the extremely modest design based on what I know about which shortcomings are going to be more audible/less preferred.

Should I blow the budget on a DSP that allows me to use FIR filters to give a perfect phase response? Or should I allocate that part of the budget to better cabinet materials to reduce resonances and minimise unwanted air-flow?

Should I invest in/design a driver that has usable frequency response up to 40KHz, or focus on a driver with low distortion and clean response in the 1KHz-5KHz range?

Without reference to listening studies, the answer is unclear.

Of course, if budget is unlimited, you can have a lot, but not everything. There are always design trade-offs to be made, and these are always best served by reference to listening studies.

There have been suggestions, for example, that speakers like the Kii Three sound 'dry' to some listeners, perhaps because they've never heard a speaker with controlled bass directivity. Where is the data that the designer could have consulted on such an issue, and even if it existed, should they have taken notice of it, or gone ahead in order to 'change people's expectations' anyway?
I'd be interested to know if Kii did their own research on this. But most of the questions that listening studies answer are a lot more basic than this one.
 

Cosmik

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#27
Most of the studies are not explicitly based on speakers or geared towards speaker design. Most of the choices are not (shouldn't be) based on a single experiment.

Beginning from the basics, we need to know (for example) the following, all of which are derived from listening studies:
  • What range of frequencies can humans hear? (audiometry studies)
  • In which frequency range is human hearing most sensitive? (equal loudness studies)
  • Which kinds of distortion products are most effectively masked? (masking and distortion audibility studies)
  • Which kinds of resonances are most audible? (audibility of resonance studies)
  • How much group delay is permissible? (phase audibility studies)
Just because a lot of this knowledge has become common wisdom doesn't mean that there aren't listening studies at the source of it.

And whether you're going to try some combination of design elements that results in something new, or being paid to do something that's been done in various permutations hundreds of times before, you're going to design a better speaker if you take account of the results of these listening studies.

I'm designing a 500 ml single 2" driver dual-passive radiator portable speaker at the moment. The budget is tiny and the outcome will not be special by any means. But of course, in selecting the driver, the electronics and the DSP, and in making decisions about the design, I'm referring to knowledge I have about audibility of distortion, resonances, etc. etc. On this budget I can't have a perfect driver, I can't have low bass extension, etc. But I can still optimise the extremely modest design based on what I know about which shortcomings are going to be more audible/less preferred.

Should I blow the budget on a DSP that allows me to use FIR filters to give a perfect phase response? Or should I allocate that part of the budget to better cabinet materials to reduce resonances and minimise unwanted air-flow?

Should I invest in/design a driver that has usable frequency response up to 40KHz, or focus on a driver with low distortion and clean response in the 1KHz-5KHz range?

Without reference to listening studies, the answer is unclear.

Of course, if budget is unlimited, you can have a lot, but not everything. There are always design trade-offs to be made, and these are always best served by reference to listening studies.



I'd be interested to know if Kii did their own research on this. But most of the questions that listening studies answer are a lot more basic than this one.
If all the data is available and usable in the way you suggest then you don't need a designer: give each factor the appropriate weighting (looked up from the appropriate studies), feed in your fixed values (based on the comprehensive data sheet for the woofer you've bought), limits of size, weight, acceptable shapes etc., and give a computer the task of simply iterating to the optimum score. Within minutes, your answer is delivered to you.

But I think there is a flaw in this utopian idea: if *any* of that process requires 'the designer' to use his judgement e.g. in setting 'the appropriate weighting', then this procedure is no different whatsoever from someone listening to his creation for an afternoon and judging it on that basis.

The automated method would be applicable to more than audio of course. In cooking, the optimal recipe for any combination of available ingredients could be calculated based on elementary taste test studies that established people's preferences for salts, fats, sugar, acids etc. As with the speaker problem, it would be possible to perform a multidimensional interpolation to an optimal recipe automatically, even if the previous studies had never explicitly used a particular combination of specific ingredients. E.g. if substituting a lower cost variety of potato, the various analyses of its chemical composition could be used to update the figures, indicating that the average customer, eating his dinner at the average time of day in an average eating environment, having had an average breakfast and average lunch during the day, and having consumed an average amount of coffee in the afternoon, would need an extra 0.2g of salt and 0.05g of acetic acid for the optimal gastronomic experience based on those particular low budget ingredients.

I'm sceptical! :) The aim of audio (IMO) is a couple of clean communications channels. If that is not possible (as it never is), there will be some limitations imposed by physics and economics. These limitations will result in highly complex behaviour, and the listener will prefer different permutations of that behaviour at different volume levels, and in different moods, etc. If there is meaningful data available to make the automatic interpolated optimisation, then great, but I am almost certain that there isn't, and never will be. To think that the low budget speaker is *really* optimal is a delusion: ultimately it will be dictated by physics, economics and the designer's own listening to it to establish that it sounds broadly acceptable within quite a wide 'dead zone', where juggling with the various permutations just results in a similar quality of overall sound.
 

andreasmaaan

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#28
If all the data is available and usable in the way you suggest then you don't need a designer: give each factor the appropriate weighting (looked up from the appropriate studies), feed in your fixed values (based on the comprehensive data sheet for the woofer you've bought), limits of size, weight, acceptable shapes etc., and give a computer the task of simply iterating to the optimum score. Within minutes, your answer is delivered to you.
In theory, absolutely. In practice, where is the AI that does this right now? I see it likely existing in the future of course.

But I think there is a flaw in this utopian idea: if *any* of that process requires 'the designer' to use his judgement e.g. in setting 'the appropriate weighting', then this procedure is no different whatsoever from someone listening to his creation for an afternoon and judging it on that basis.
Strongly disagree. The designer's ears may not be represent of the average/intended listener, the room and setup will certainly skew the outcome, etc. etc.

The automated method would be applicable to more than audio of course. In cooking, the optimal recipe for any combination of available ingredients could be calculated based on elementary taste test studies that established people's preferences for salts, fats, sugar, acids etc. As with the speaker problem, it would be possible to perform a multidimensional interpolation to an optimal recipe automatically, even if the previous studies had never explicitly used a particular combination of specific ingredients. E.g. if substituting a lower cost variety of potato, the various analyses of its chemical composition could be used to update the figures, indicating that the average customer, eating his dinner at the average time of day in an average eating environment, having had an average breakfast and average lunch during the day, and having consumed an average amount of coffee in the afternoon, would need an extra 0.2g of salt and 0.05g of acetic acid for the optimal gastronomic experience based on those particular low budget ingredients.
We're probably just a few years away, if not already when it comes to McDonalds and the like ;)

I'm sceptical! :) The aim of audio (IMO) is a couple of clean communications channels. If that is not possible (as it never is), there will be some limitations imposed by physics and economics. These limitations will result in highly complex behaviour, and the listener will prefer different permutations of that behaviour at different volume levels, and in different moods, etc. If there is meaningful data available to make the automatic interpolated optimisation, then great, but I am almost certain that there isn't, and never will be. To think that the low budget speaker is *really* optimal is a delusion: ultimately it will be dictated by physics, economics and the designer's own listening to it to establish that it sounds broadly acceptable within quite a wide 'dead zone', where juggling with the various permutations just results in a similar quality of overall sound.
Refer to your first paragraph. Whether a particular human or computer can do a better job at a particular point in technological history is interesting to think about, but doesn't change the fact that reference to the results of research into how humans hear will always result in a better speaker, or a narrower "grey zone" to borrow your terminology.
 

Cosmik

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#29
Strongly disagree. The designer's ears may not be represent of the average/intended listener, the room and setup will certainly skew the outcome, etc. etc.
Yes, but how is it any different if the designer uses his judgement to say that he thinks that high order distortion level deserves a 0.37 weighting in the formula, and cabinet resonances a 0.25 weighting? In order to come to those weightings (that you say AI cannot provide), he must be doing it based on his personal experience. Not scientific studies - if the studies could give him those figures he would use them, but they don't, so he can't, so he uses his experience instead. Not science.

I say it again: if the designer uses his judgement at any point in the design process, this is no different from him listening to a speaker and basing his decisions on it. Or guessing. Or observing other people in uncontrolled circumstances, etc. He is just deferring/disguising/obscuring subjective experiences by representing them as cold, hard figures.
 

andreasmaaan

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#30
Yes, but how is it any different if the designer uses his judgement to say that he thinks that high order distortion level deserves a 0.37 weighting in the formula, and cabinet resonances a 0.258 weighting?
I said that I'm not aware of any AI currently available that provides this weighting, although there are definitely various formulas based on evidence obtained from listening studies that could be easily plugged into an AI to do it. Some of these are described here. So yes, AI theoretically can provide such a weighting, and could theoretically do so better - or at least faster - than a human.

In order to come to those weightings (that you say AI cannot provide), he must be doing it based on his personal experience. Not scientific studies - if the studies could give him those figures he would use them, but they don't, so he can't, so he uses his experience instead. Not science.
It would be a lot of work, but a person (or a machine) could sit down with all the data obtained from listening studies and build a very detailed algorithm to do exactly this. In practice, this would be a hugely resource-intensive process of course, and would have to include sub-algorithms for determining the value/validity of the results of each study. But it can be approximated by carefully performing or reading research and making informed judgements as to weighting.

I say it again: if the designer uses his judgement at any point in the design process, this is no different from him listening to a speaker and basing his decisions on it. Or guessing. Or observing other people in uncontrolled circumstances, etc. It is just deferring/disguising/obscuring subjective experiences by representing them as cold, hard figures.
It's fundamentally different. The studies control for all kinds of variables that listening to a specific speaker in a specific room with one specific pair of ears does not. That is, in a nutshell, what it comes down to :)
 

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#31
It's fundamentally different. The studies control for all kinds of variables that listening to a specific speaker in a specific room with one specific pair of ears does not. That is, in a nutshell, what it comes down to :)
We'll have to disagree on that one.

We have gone down a path from where I assumed you were going to do your own small-scale listening tests, but you say that it is not necessary:
  • the historical laboratory tests already exist that mean you can multi-dimensionally interpolate to a preference rating for any combination of hardware, distortion factors, intended 'programme material', placement, deomgraphic profile of listeners, etc. compared to any other - even if that combination has never existed before
  • you can objectively characterise your hardware to the level of what it will do with any signal at any volume level, thereby allowing you to plug the information into the assumption above
  • No human judgement will touch the process; no weightings based on guesswork will be assigned, no formula will be tweaked in light of a stray comment that "it seems a bit bass-light for its size...", or "my Bose sounds richer...". No extra data will be added or substituted after the first iteration, because the first iteration will be objectively optimal.
I just don't believe it. At some point in the process (probably in the first five seconds), the designer is going to tweak something arbitrarily, even if it's just which data he judges he should include in his computations. And at that point, the pure objectivity claim falls apart - and it becomes like every other thing that keeps real life interesting and unpredictable. Thank goodness! :)
 

andreasmaaan

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#32
@Cosmik what I’m arguing seems not to be coming across clearly somehow.

the historical laboratory tests already exist that mean you can multi-dimensionally interpolate to a preference rating for any combination of hardware, distortion factors, intended 'programme material', placement, deomgraphic profile of listeners, etc. compared to any other - even if that combination has never existed before
No. What I’m saying is that decisions based on the existing research are going to be better than decisions that are oblivious to it. That’s all.

Depending on the application and/or the design, additional research may be desirable. Nothing in this world is ever perfect.

you can objectively characterise your hardware to the level of what it will do with any signal at any volume level, thereby allowing you to plug the information into the assumption above
No. But you can get better results than if you remain wilfully oblivious to the research.

No human judgement will touch the process; no weightings based on guesswork will be assigned, no formula will be tweaked in light of a stray comment that "it seems a bit bass-light for its size...", or "my Bose sounds richer...".
Correct.

No extra data will be added or substituted after the first iteration, because the first iteration will be objectively optimal.
The model will never be perfect so there will always be new data and new iterations as new studies are performed and new phenomena are investigated. But yes, the model is already better than e.g. how my uncle Bob reckons his system sounds in his living room.

I just don't believe it. At some point in the process (probably in the first five seconds), the designer is going to tweak something arbitrarily, even if it's just which data he judges he should include in his computations. And at that point, the pure objectivity claim falls apart - and it becomes like every other thing that keeps real life interesting and unpredictable. Thank goodness! :)
I’m talking about the best way to do it, not the way humans are most likely to do it. The creativity and excitement comes in as we find new ways to achieve optimal performance, not as we tweak our model of “optimal” performance based on how a particular thing sounds in a particular place to a particular person after their nth particular beer (although this might be a perfectly legitimate way to DIY one’s own system).

Further, I’m saying that even what might seem like abstract ideals in audio reproduction are in fact grounded in listening studies.

To illustrate this: an average-performing speaker with 40Hz-20KHz response is better than a 0.001% distortion constant-directivity point source with a frequency response of 20KHz-20MHz. We know this because we’ve tested listeners and we know they won’t be able to hear much if any of the latter.
 
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andrew

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#33
This is abbreviated synopsis of the paper, Ten Years of ABX Testing, by David Clark: http://www.aes.org/e-lib/browse.cfm?elib=5549
Summary
All in all, the position of audio science on this matter is clear: fast AB switching is far more revealing than any long term tests. No evidence has ever been presented to show otherwise or to demonstrate anything based on psychoacoustics why that would be so.
Just saw this interesting thread. The result isn’t s surprise but if a change isn’t identifiable through long term listening at home then what value is it even if the ABX testing identifies a difference?
 

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#34
Just saw this interesting thread. The result isn’t s surprise but if a change isn’t identifiable through long term listening at home then what value is it even if the ABX testing identifies a difference?
The value is to show that the differences are small and inconsequential.
Rapid AB switching is exquisitely sensitive to small differences, especially level differences, hence the need for close level matching, but because of this sensitivity, it will show up things which will often pass unnoticed with long-term listening, at home.

Generally, the opposite is the case, that differences immediately claimed to be obvious at home, sighted and not level matched disappear when tested with more rigour.

S.
 

Cosmik

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#35
@CosmikWhat I’m saying is that decisions based on the existing research are going to be better than decisions that are oblivious to it.
I don't think there is any guarantee of that, unless the research is close to replicating your design dilemma.

The reason is, that if you take some sparse data points there is no reason to think that you can interpolate to a new point somewhere between them and assume that you can read off a meaningful score. As neural network training people know well, you can end up with a far worse result from such an approach because you don't know what the multidimensional surface is doing in between the sampled points. In digital audio terms, the sampling is not obeying any sort of bandwidth-limiting constraint on the input, so you can't reconstruct the surface in between the data points.

Maybe listeners' response to distortion follows some sort of 'law'; and maybe their response to bass cutoff frequency and slopes follows another sort of 'law'. But if you are hoping that these two pieces of research can be combined to tell you whether to build a speaker that goes lower but has higher distortion or vice versa you will be out of luck. Even if someone has addressed that exact dilemma with some actual experiments you might find they used string quartets and jazz for their tests, but some of your customers are metal-heads. Or maybe the research was carried out at low listening levels and your customers prefer loud, or vice versa. I can't see that it will ever be solved from research alone, and even if it is, you will never know whether it was or not...

For sure, the basic benchmarks of hi-fi are derived from listening tests of some sort, but I don't see them as much more difficult than, say, arriving at the basic requirements for the width of a door or temperature range of a room thermostat. You could say that they are the results of careful scientific research, but you could be pretty sure that most people would iterate to about the right values if they gave it a little thought and did a few experiments on themselves - and they would probably even observe that a youngster wandering by could hear the high pitched whistles that they couldn't :).
 

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#36
Just saw this interesting thread. The result isn’t s surprise but if a change isn’t identifiable through long term listening at home then what value is it even if the ABX testing identifies a difference?
It is an engineering aid to improve the system until no difference is heard.
 

andreasmaaan

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#37
Maybe listeners' response to distortion follows some sort of 'law'; and maybe their response to bass cutoff frequency and slopes follows another sort of 'law'. But if you are hoping that these two pieces of research can be combined to tell you whether to build a speaker that goes lower but has higher distortion or vice versa you will be out of luck. Even if someone has addressed that exact dilemma with some actual experiments you might find they used string quartets and jazz for their tests, but some of your customers are metal-heads. Or maybe the research was carried out at low listening levels and your customers prefer loud, or vice versa. I can't see that it will ever be solved from research alone, and even if it is, you will never know whether it was or not...
I'm maybe not being clear enough that I think a lot of weight needs to be placed on research that doesn't involve music signals (or that references experiments using music signals against those using pure tones and noise). Three very important pieces of research I can think of for example are:
  • Fletcher and Munson on perceived loudness
  • Olive and Toole on the modification of timbre by resonances
  • Fastl and Zwicker on masking
But there are many more. The subject of the research is not how people perceive music reproduction, but how humans hear.

For sure, the basic benchmarks of hi-fi are derived from listening tests of some sort, but I don't see them as much more difficult than, say, arriving at the basic requirements for the width of a door or temperature range of a room thermostat.
I agree in general, there's nothing magical about listening studies. They are just experiments designed to test a natural system (human hearing) in the context of solving engineering problems, suggesting approaches, or making engineering decisions. There's nothing fundamentally different about measuring something like how air humidity affects perception of temperature and how he presence of a masking signal affects the perception of a maskee signal.

You could say that they are the results of careful scientific research, but you could be pretty sure that most people would iterate to about the right values if they gave it a little thought and did a few experiments on themselves - and they would probably even observe that a youngster wandering by could hear the high pitched whistles that they couldn't :).
Most of the key listening studies involved creativity, knowledge and skill, access to resources (e.g. anechoic chambers and other acoustic environments), and a large number of subjects. I know you're half joking here :) But noticing that a youngster can hear high-pitched things that you can't might give you a clue that there's something worth investigating, but it won't give any meaningful information upon which to base decisions.
 

andreasmaaan

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#38
By the way @Cosmik, I think it's worth adding that all of those three studies I gave as examples gave results that were not particularly intuitive or that went against the common wisdom at the time (and which in many cases persists).

For example, the research into equal loudness and thresholds of audibility gave (if my history is correct) an early glimpse into just how non-linear human hearing is.

The research into modification of perceived timbre by the presence of resonances upended the persistent belief that high-Q resonances were more audible than low-Q resonances.

The research into masking not only showed how surprisingly effective it was, but also revealed that it was extremely dependent on signal level, and moreover that there were some (fairly) predictable relationships between variables like frequency, level, and masking spectrum. It also revealed some surprising counter-intuitive aspects like post-masking, which I doubt would have been picked up by the the man walking past the whistling child while a bus drove by (and which BTW no doubt help those who use pre-ringing FIR filters sleep at night ;) ).
 
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