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Topic: AES 2009 Audio Myths Workshop (Read 171326 times) previous topic - next topic
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AES 2009 Audio Myths Workshop

Reply #375 –
Quote from: John Eppstein on
Quote from: Ethan Winer on
Quote from: John Eppstein on
What do sine waves have to do with real world audio signals?

Everything. Unless of course you think Fourier was wrong. Hint: He wasn't.

--Ethan


No. Fourier said that any audio signal can be analyzed as a series of sine waves. But that's an analysis, a model. It isn't the thing itself.

Yes, you can reconstruct the original waves from the series of sine waves if you have enough of them - but then what you have isn't really the sine waves any more, it's a complex waves.

It's like if you have a wooden box. The wooden box can be used to hold something, say, cookies.

The wooden box can be analyzed as a group of boards. But the separate boards aren't the box, they're a bunch of boards and they won't hold your cookies.

The analysis is not the thing itself. The deconstruction is not the thing itself. The properties of the whole are different from/greater than the properties of the parts.

Fourier was not wrong. But a lot of people think he said something that was not exactly what he said.


I'm sorry but that is a load of nonsense (I am being literal here, not attacking you). The fourier transform of something (eg an audio signal) is exactly equivalent to the signal. And your analogy is completely irrelevant.

If you wish to argue that looking at the response of a system to a sine wave is not enough, there's plenty of other places to look. The most obvious being that if the processing done to the signal isn't linear then the output of the system for a single sinewave input "at each frequency" isn't enough to be able to predict its behaviour for a superposition of many of these sines (ie for any signal).

edit: a very "audiophiley" argument as to why fourier transforming stuff doesn't tell you the full story just occured to me: yes, in theory, the signal and its transform are equivalent. but in practice, a) we use FFTs, which transform over a finite window, thus missing important information, and b) we use computers, with their "well-known" numerical inaccuracies. brilliant! (a load of rubbish actually, but that is the sort of thing that is hard to argue with online, because who's going to sit down and explain this stuff in detail without sounding like an arrogant jerk? so you'll win easily like this)

AES 2009 Audio Myths Workshop

Reply #376 –
Quote from: John Eppstein on
Quote from: Ethan Winer on
Quote from: John Eppstein on
What do sine waves have to do with real world audio signals?

Everything. Unless of course you think Fourier was wrong. Hint: He wasn't.

--Ethan


No. Fourier said that any audio signal can be analyzed as a series of sine waves. But that's an analysis, a model. It isn't the thing itself.


What you don't seem to understand John is that the Fourier transform has a perfect inverse. The inverse transforms what you called an analysis back into the origional wave.

The Fourier transform looses no information no matter which direction the data goes. What you call an analysis  just transfoms the signal into an alternative form of the identical same data, 100.0000...% of it.

Quote
Yes, you can reconstruct the original waves from the series of sine waves if you have enough of them - but then what you have isn't really the sine waves any more, it's a complex waves.


Wrong again, The inverse transform reconstructs the identical origional wave. 

This basic priniciple can be used to create digital equalizers.  The input signal is transformed into a table of amplitudes and phase angles. You can adjust the ampludes and phrase angles as you wish. Adjusting the amplitudes is like a adjusting slider on a virtual graphic equalizer, orly the number of virtual sliders on the virtual graphic equalizer can be exceedingly large, so very fine adjustments are easy to make.  The table of revised amplitudes and phase angles is then transformed back into the original signal with the desired changes. Phase can be adjusted in a similar manner.  I have several of these tools, and I've been using them for years. They work very nicely, thank you!  It is a common feature of the better DAW  software.

If you perform forward and reverse transformations without any changes to the transformed data, the resulting wave looks and sounds exactly like the origional.

Therefore the coefficients of the sine and consine waves that the fourier transform creates are exact and reprsentative. Every real world wave can be transformed into an exactly representative colleciton of sine and cosine waves.

Furthermore, the Fourier transform is not a unique kind of thing, and audio data can be transformed by other means into other alternative forms. And back.

AES 2009 Audio Myths Workshop

Reply #377 –
Quote from: googlebot on
Quote from: botface on
But psychoacoustics have to come into it. EG if distortion below a certain level is inaudible a piece of gear with distortion below that threshold is transaparent as far as that parameter goes. Another piece of gear with more zeros in front of it in the spec isn't any more transparent.


I haven't said that. What's your point?

Going for only 80 dB is just so close to the absolute thresholds of human hearing, that it wouldn't take much effort to produce a positive ABX result for any device incapable of delivering more than that. Since the call was for a black box to determine transparency and not a question about what's sufficient for great music listening pleasure, I just found 80 dB to be not enough. Especially when taking into consideration how much more even budget gear is able to deliver nowadays.

Sorry if I misunderstood. I thought you were saying that we should simply go for state of the art as the baseline for defining acceptable performance.

Also, I interpreted your post as an attempt to get the discussion back on to something useful and was happy to respond but since then there's been another couple of pages of unrelated discussion so maybe this isn't the place to have a discussion

AES 2009 Audio Myths Workshop

Reply #378 –
Quote from: John Eppstein on
When you take a wooden box apart into a pile of boards it's a pile of boards. When you reassemble it into a box it's a box again. But a box is not a pile of boards and a pile of boards is not a box. The whole is greater than the sum of its parts.

You can take a Bach Fugue and analyze it into a progression of chords. You can analyze those chords into a bunch of notes. Yet the fugue is something more than the notes and the pile of individual notes is not music.

Yes, you can take things apart and put them back together. That proves - that you can take things apart and put them back together.


So hang on a second. Do you really believe that knowing the effect of a linear system on each single frequency mode is not enough to tell me how it will affect a sum of them? Or are you just making the point that when I am listening to music, the feelings (or whatever) it evokes are impossible to predict from looking at its spectrum? (which is an obvious statement, the relevance of which to studying the effect of a component on a signal I, however, have difficulty seeing).

OK, to clarify things: In "Fourier was not wrong. But a lot of people think he said something that was not exactly what he said.", could you please explain a) what a lot of people think he said, b) what he actually "said" on this matter?

Actually I am guessing you won't respond again (maybe I should get into more online arguments and insult people more to deserve a reply), but I am curious nonetheless.

AES 2009 Audio Myths Workshop

Reply #379 –
Quote from: John Eppstein on
When you take a wooden box apart into a pile of boards it's a pile of boards. When you reassemble it into a box it's a box again. But a box is not a pile of boards and a pile of boards is not a box. The whole is greater than the sum of its parts.

You can take a Bach Fugue and analyze it into a progression of chords. You can analyze those chords into a bunch of notes. Yet the fugue is something more than the notes and the pile of individual notes is not music.

Yes, you can take things apart and put them back together. That proves - that you can take things apart and put them back together.


You are lacking some very basic understanding about the nature of observation. Fourier transformation is a fundamental concept of modern science. It scales to arbitrary precision and you are limited only by the precision of your measurement gear. Fourier transformation is used to describe systems magnitudes smaller and lightyears below any possible human threshold of perception.

The same applies to digital audio. Of course, bandwidth limiting for the sake of digitalization is a lossy process, but it can be scaled up to arbitrary amounts of information conservation. And in digital audio you just have a finite sequence of elements, that are put back together to reconstruct a signal at playback time. There has not been a single individual in the past, which could demonstrate under controlled and repeatable conditions, that this sum of discrete elements (e. g. at 44.1 kHz) was not sufficient to be indiscernible compared to the full signal passed over a straight wire. We have determined the resolution, that we need to be able to discern a finite set of quantizations from the original, and that's what is used today. You can rant as much as you want with your limited understanding (or even if you understood it in full), but your only way to make a point would be to show, that a given resolution (as 16 bit at 44.1 kHz) is inappropriate using real world converters. A simple way to provide such a proof would be a double blind test vs. a straight wire. Why don't you come back when you can provide that?

AES 2009 Audio Myths Workshop

Reply #380 –
Quote from: dwoz on
wrong again.  *sigh*.  A Fourier Transform in a bandwidth limited system is an approximation.


No, the Fourier Transform is mathematically exact.  Furthermore, bandwith limits are not part of the definition of the Fourier transform. The definition of the fourier transform is an intergral with infinite limits that also include as close as you can imagine coming to zero.

There is a limitataion on the Fourier transform that  can be stated many ways. Here I will state it as being that the signal has to be continuous. That means that at any point in time, the signal has only one value, but it does have that one value.  IOW, at no time is the signal undefined, nor is there any point in time where the signal has say, two values. In tjhe real world those are pretty easy restrictions to honor.

The restrictions of the Fourier Transform do not preclude the consideration of any singal that has a finite (but very, very, very large or very, very, small) bandwidth.  The Fourier transform relates to not only audio but also low frequncy signals like siesmic events, and very high frequency signals, such as TV, radar, light, X-rays, and even very high energy particle beams. 


AES 2009 Audio Myths Workshop

Reply #381 –
Quote from: googlebot on
Fourier transformation is a fundamental concept of modern science. It scales to arbitrary precision and you are limited only by the precision of your measurement gear. Fourier transformation is used to describe systems magnitudes smaller and lightyears below any possible human threshold of perception.


Perhaps we should help some people out by pointing out that there are two Fourier Transforms. This fact detracts *nothing* from the validity of anything that people from the "pro sine wave" viewpoint have been saying in this thread. But it might help some people understand how they came to have the misapprehensions that they have.

One Fourier Transform in common use is the mathematical Fourier Transform that is as its name suggests purely mathematical. Being mathermatical, it is truely exact. The applicaiton of it that we are talking about is the transformation of a time-varying signal into a collection of sine and cosine waves, or if you will, a collection of sine waves and phase angles.  From the Fourier Transform we can unambigiously say that any real world audio signal can be exactly equated to a collection of sine waves and phase angles, and vice-versa.

The other Fourier Transform that is in common use is the Fast Fourier Transfom (FFT) which is a computational method that can be applied to any digital signal. Just like its mathematical namesake, it can be used to convert a digitized signal into a set of  sine/cosine pairs, or if you will an exactly equivalent collection of sine waves and phase angles. Being numeriical, it is not exact, but its precision can be made as good as you want it to by performing it with long data words.  Its frequency resolution can be made as fine or coarse as you would like by processing data in larger or smaller chunks. The Fast Fourier Transform is the same as the FFT that we commonly use for testing and measurements, as well as spectral adjustments in DAW software.

AES 2009 Audio Myths Workshop

Reply #382 –
Quote from: madtheory on
they might have something to contribute in the area of understanding euphony.


This might be a slight misstatement - I think that what people are seeking is how to obtain euphony. Actual euphony is generally one of those things that you understand pretty quickly and intuitively when you hear it.

There *is* a teachable skill called listening for good sound quality. One widely-respected teacher of this skill can be found here: Learn how to listen for good sound quality His students have probably designed more good-sounding audio systems than just about anybody else in the world.

Disclamer: This person is both a close friend and client.

When it comes to recordings, the recipie for good sound is pretty well-known, and not much of a mystery or a secret. You simply record good music played by good musicans who are managed by good managers in a good venue with good equipment, and with reasonable smarts, education and experience your recordings will sound good.  Leave any of those out, and it will proably not be so good.  The good education part is probably the element of the bunch that can be optional. If you have to make a choice between OJT and formal education, take the OJT.

AES 2009 Audio Myths Workshop

Reply #383 –
I just went through and recycled another half-dozen posts or more. There are still some border-line posts here. We have a choice: this can be a thread full of meaningless emotional language or this can be a thread full of meaningful technical discussion. Mixing the two is counter-productive.

AES 2009 Audio Myths Workshop

Reply #384 –
Quote from: pdq on
Quote from: Arnold B. Krueger on
Here's the sequence from my noise sums spreadseet, starting at 90 dB:

1 -86.990  (3.01 dB drop)
-85.229
-83.979
    .
    .
    .
--76.990
20 -76.778 dB  (ca. 13 dB drop total, but only .322 dB drop for the iteration.

There's actually a much quicker way to calculate it. If you combine the same level of noise (uncorrelated of course) 21 times then the final noise level is square root of 21 greater. The square root of 21 is 4.58, which is 13.22 dB, so the final SNR is 90 - 13.22 = 76.78.


Thanks.

Audio calculations are IME usually quite simple but at least in my hands, frustratingly error-prone. I favor simple algorithms whose results I can look at while they operate over a goodly range of values.

This approach seems to work well in a context like this where it is important to make sense on the intuituve level.

AES 2009 Audio Myths Workshop

Reply #385 –
Fourier was of course correct  - anyone arguing against this marks themselves out as a fool.

But it would be equally foolish to claim that a system's response to one or two isolated sine waves tells us everything we need to know about that system because of Fourier.

The very things we're testing for (i.e. non-linear distortion) break the superposition principle - and IIRC ourier kind of needs superposition to work!

I'm sure someone will come along and say that in the equipment they're talking about, non-linear distortion is so low that it doesn't matter. I'm sure you're right - but it's a circular argument - if you know it's that low, why are you doing measuring it in the first place tests?

The conclusion of a circular argument may be correct, but it's not a very convincing way to get there.

Cheers,
David.

AES 2009 Audio Myths Workshop

Reply #386 –
Quote from: 2Bdecided on
Fourier was of course correct  - anyone arguing against this marks themselves out as a fool.


Unfortunately, there is a lot of that going around here lately. L-(

Quote
But it would be equally foolish to claim that a system's response to one or two isolated sine waves tells us everything we need to know about that system because of Fourier.


That is, of course exactly right.

Quote
The very things we're testing for (i.e. non-linear distortion) break the superposition principle - and IIRC Fourier kind of needs superposition to work!


In the real world, every theory fails to work perfectly. Does this mean that we abandon each and every theory?

While *any* nolinearity keeps superposition from working perfectly, it seems fair to ask how much nonlinearity does it take to keep superposition from being a model that makes predictions that agree with the real world well enough for the model to remain useful.

Quote
I'm sure someone will come along and say that in the equipment they're talking about, non-linear distortion is so low that it doesn't matter.


Been there, done that. But that needs to be based on actual knowlege about how linear the equipment actually is. That should be based on more than measurements on just one or two isolated frequencies. In general, we know that nonlinear distortion tends to be highest at the extremes of the audible range.

Quote
I'm sure you're right - but it's a circular argument - if you know it's that low, why are you doing measuring it in the first place tests?


The *it* is nonlinear distortion, but nonlinear distortion is not what we are measuring at the moment. So there is no circularity.

In the real world, one makes a few nonlinear distoriton measurements. For example, one at 20 Hz, one at 1 KHz, and one at 20 KHz. Or in modern times one runs an IM sweep or a complex multitone. If this is fairly good equipment then we find that the nonlnear disortion is less than 0.02% at all 3 frequencies for for any of the tests. It might be less than 0.0005%. 

What do we say about how superposition works in a system where alll nonlinear distortion appears to be less than 0.02% or 0.0005% at all frequencies from 20-20 KHz?


 

AES 2009 Audio Myths Workshop

Reply #387 –
Quote from: Arnold B. Krueger on
What do we say about how superposition works in a system where alll nonlinear distortion appears to be less than 0.02% or 0.0005% at all frequencies from 20-20 KHz?
Assuming no weird ultrasonic stuff, we say that's just fine.

You're inching towards defining these measurements and thresholds that define transparency - but if you're going to drop one in once every 16 pages, I'm not sure I've got the patience to hang around until the end!

Is anyone going to be brave and list them properly? For each one we need: stimulus, analysis, thresholds.

Cheers,
David.

AES 2009 Audio Myths Workshop

Reply #388 –
Quote from: Arnold B. Krueger on
In the real world, one makes a few nonlinear distoriton measurements. For example, one at 20 Hz, one at 1 KHz, and one at 20 KHz. Or in modern times one runs an IM sweep or a complex multitone. If this is fairly good equipment then we find that the nonlnear disortion is less than 0.02% at all 3 frequencies for for any of the tests. It might be less than 0.0005%. 

What do we say about how superposition works in a system where alll nonlinear distortion appears to be less than 0.02% or 0.0005% at all frequencies from 20-20 KHz?

3 frequencies aren't enough for rigorous testing, although they're fine it all you're doing is writing sales literature. If you're really trying to find out what the gear is like you should run tests at octave intervals or better.

AES 2009 Audio Myths Workshop

Reply #389 –
Quote from: 2Bdecided on
Quote from: Arnold B. Krueger on
What do we say about how superposition works in a system where alll nonlinear distortion appears to be less than 0.02% or 0.0005% at all frequencies from 20-20 KHz?
Assuming no weird ultrasonic stuff, we say that's just fine.

You're inching towards defining these measurements and thresholds that define transparency - but if you're going to drop one in once every 16 pages, I'm not sure I've got the patience to hang around until the end!


I gave one of he best answers you'll get this week a few pages back. RMAA test suite, and all noise and distortion >80 dB down, response within +/- <0.1 dB. It os probably still overkill in many cases, but it is really pretty good.

Here's your challenge: Find some piece of regular audio gear, find that it passes the RMAA test suite and fails an ABX test. No tricks, no made up pathological signals, do use regular commercial recordings, no hypothetical situations, no broken equipment, no bad gain staging and no equipment abuse. Something that would actually happen in a regular audio production or playback situation.

AES 2009 Audio Myths Workshop

Reply #390 –
Quote from: Arnold B. Krueger on
and all noise and distortion >80 dB down,


Quote from: Arnold B. Krueger on
Something that would actually happen in a regular audio production or playback situation.


A 12 track production of a slow, contemporary classical piece. Each microphone is connected via a cheap DAC with an uncorrelated noise floor of -81 dB. The resulting mix would have a -45 dB noise floor, clearly audible during each silent moment, and I would be ashamed to deliver something like that to a client.

That's, of course, only the case if you don't use the "passing of a RMAA test" as a submarine argument. If you were meaning by "passing" only excellent scores, for example, that would imply any noise being down much further than 80 dB.

That's why I have repeatedly underlined: don't go too cheap, when defining transparency requirements for studio gear. It is not necessary, if you want to make a point against fetish level requirements. Nowadays you get complete converter cards with a SNR of 107 dB for $50 and less.

AES 2009 Audio Myths Workshop

Reply #391 –
Can't edit anymore, but I think it should be -48 dB resulting noise floor (with no difference in meaning).

AES 2009 Audio Myths Workshop

Reply #392 –
Googlebot, you've made a math error. Every doubling of inputs increases the noise floor 3 dB. The noise floor in your scenario would be around -70 dB. Also realize that ambient noise in the room will probably be -60 dB and that's correlated noise (6 dB per doubling) giving you a net -40 dB acoustic noise floor.

AES 2009 Audio Myths Workshop

Reply #393 –
I calculated input number ((((((((((1+2)+3)+4)+5)+6)+7)+8)+9)+10)+11)+12 and thought that would mean you add 11 times 3 dB. How would it be done right?

Edit: Ok, got it myself. ((((((((((1+2)+3)+4)+5)+6)+7)+8)+9)+10)+11)+12 doesn't sum equal amounts of noise in all but the first step. If one cascades the summing it is even easier to see, why it was flawed. So you are right.

Quote from: Notat on
Also realize that ambient noise in the room will probably be -60 dB and that's correlated noise (6 dB per doubling) giving you a net -40 dB acoustic noise floor.


That should only be true for concurrent recording, shouldn't it?

AES 2009 Audio Myths Workshop

Reply #394 –
Quote from: Arnold B. Krueger on
Here's your challenge: Find some piece of regular audio gear, find that it passes the RMAA test suite and fails an ABX test. No tricks, no made up pathological signals, do use regular commercial recordings, no hypothetical situations, no broken equipment, no bad gain staging and no equipment abuse. Something that would actually happen in a regular audio production or playback situation.
Surely RMAA would identify broken equipment anyway?

What about commercial recordings of pathological signals?

If not, why not?

It's a relevant point: HA exists because Dibrom was so disappointed with mp3's treatment of his favourite music - signals that many people wouldn't count as "music", and which codec developers had never tried.


Let's face it - we don't need RMAA following your post - with enough restrictions, and enough opportunities to cry "foul, that's not normal use", almost any piece of half-decent equipment can't be ABXed.


However, it's a fair start. But I still haven't found a list of the stimuli used in the RMAA test - am I going to have to run the thing, listen to the signals, and write them down?

Cheers,
David.

AES 2009 Audio Myths Workshop

Reply #395 –
Quote from: googlebot on
Quote from: Arnold B. Krueger on
and all noise and distortion >80 dB down,


Quote from: Arnold B. Krueger on
Something that would actually happen in a regular audio production or playback situation.


A 12 track production of a slow, contemporary classical piece. Each microphone is connected via a cheap DAC with an uncorrelated noise floor of -81 dB. The resulting mix would have a -45 dB noise floor, clearly audible during each silent moment, and I would be ashamed to deliver something like that to a client.


That's interesting because if each input to a real world 12 channel mixer that was being use to record a live performance had even 80 dB SNR, it would be an unusually wonderful day. 

The mixer electronics itself may have 90-100  dB SNR, but once you hook up the mics, their noise  (usually equivalent to 10-20 dB SPL)  and the room noise they pick up (usually 25-35 dB SPL)  usually pushes the noise floor up quite a bit. 

I do 2 channel live recordings all the time with no mixer at all, and the recordings generally have about 70 dB SNR, +/- 5 dB.  So do just about everybody else's.  So, that would be the SNR for each chanel at the summing junction of a hypothetical mixer.

When I do multi-micing of live performances, each channel follows a similar pattern.

What the above analysis of yours did not consider is that each channel fader in the mixer would normally be set for some significant amount of attenuation which attenuates both the signal and the noise. 

This has to be true because the clipipng point for each input channel on a mixer is usually about the same as the clipping point for the entire mix.  The only way you can sum 12 things and have the same maximum level as any of them is to attenuate all of them.


AES 2009 Audio Myths Workshop

Reply #396 –
Quote from: 2Bdecided on
Quote from: Arnold B. Krueger on
Here's your challenge: Find some piece of regular audio gear, find that it passes the RMAA test suite and fails an ABX test. No tricks, no made up pathological signals, do use regular commercial recordings, no hypothetical situations, no broken equipment, no bad gain staging and no equipment abuse. Something that would actually happen in a regular audio production or playback situation.
Surely RMAA would identify broken equipment anyway?

What about commercial recordings of pathological signals?

If not, why not?


Depends what you mean.

The origional Telarc 1812 was an example in that day of a commerical recording of a pathological signal that was created by more-or-less natural means. I would consider it to be a reasonable recording to use to do listening tests of equipment, and in fact I've done just that.

I think that the sort of pathological reocordings that I've seen used to break MP3 coders are also legitimate to use to test general kinds of audio gear.

Quote
It's a relevant point: HA exists because Dibrom was so disappointed with mp3's treatment of his favourite music - signals that many people wouldn't count as "music", and which codec developers had never tried.


I'm good with that sort of thing.


Quote
Let's face it - we don't need RMAA following your post - with enough restrictions, and enough opportunities to cry "foul, that's not normal use", almost any piece of half-decent equipment can't be ABXed.


I think you're taking what I said way outside of its intended meaning.

Quote
However, it's a fair start. But I still haven't found a list of the stimuli used in the RMAA test - am I going to have to run the thing, listen to the signals, and write them down?


That's pretty much what I've had to do. Except the signals were too complex for me to identify by ear, so I used various standard audio analysis tools.

You could write the author - I believe he's a good guy.

I find it amusing that so many people complain so hard about doing things that I have done as a matter of course!

AES 2009 Audio Myths Workshop

Reply #397 –
Noise growth.

Each DOUBLING of inputs added AT THE SAME LEVEL adds 3dB to the noise level, for decorrelated (i.e. thermal, or the like) noise.

2 inputs -3dB to SNR
4 inputs -6
8 intputs -9
16 inputs -12

This is true if both INPUTS and NOISE are decorrelated.

However, if we have the same signal in all the mikes, now the signals add in amplitude vs. noise in power.  Then, you get exactly the opposite growth, instead of -3dB you get +3dB, and so on.

This case is true, for example, in things like array mikes. It's not usually a factor in mixing applications.
-----
J. D. (jj) Johnston

AES 2009 Audio Myths Workshop

Reply #398 –
Quote from: Arnold B. Krueger on
I find it amusing that so many people complain so hard about doing things that I have done as a matter of course!
I'm allowed to complain!

Anyway, this thread started (many pages ago  ) with a discussion about these characteristics that define an audio system. It moved onto measurements, but no one has a list.

Surely it knocks people's confidence in the whole thing when various people imply there are measurements which pretty much guarantee transparency, but in 16 pages no one can actually come up with a list?!

Cheers,
David.

AES 2009 Audio Myths Workshop

Reply #399 –
Quote from: 2Bdecided on
Quote from: Arnold B. Krueger on
I find it amusing that so many people complain so hard about doing things that I have done as a matter of course!
I'm allowed to complain!

Anyway, this thread started (many pages ago  ) with a discussion about these characteristics that define an audio system. It moved onto measurements, but no one has a list.

Surely it knocks people's confidence in the whole thing when various people imply there are measurements which pretty much guarantee transparency, but in 16 pages no one can actually come up with a list?!



You've had a list as long as you've had RMAA to run!

I also referenced you to an archived copy of my PCAVTech web site, which had that list in every test report I posted.