Has anyone been able to define well or measure differences between vinyl and digital?

@akgwhiz , some good thoughts. Dither provides added dynamic range in digital. Is there an equivalent with hearing and analog noise? Don't neurons have discrete trigger levels?

 

@teo_audio

The place it counts is in the micro expression of transients and micro transients and the differences in level and timing between them.

This sums it up well.

This is where digital and class d falls apart. Those are the points of greatest distortion, in digital and class D.

I would agree, if "digital and class d" meant "mass market digital and mass market class d". Highest-end digital and class d are much harder to differentiate from highest-end analog.

In science, things are supposed to correlate to the situation at hand. Do you understand the question? Is the measurement relevant to the question at hand? If not, go back to the start and have a go at it again. Even when done, keep questioning the results and facts don’t exist..so that all finalized things can be gone over again and altered according to new results on the complex investigation of it all. That’s science.

Exactly. That's what I was pointing out to certain ASR folks. If a theory doesn't fit facts, keep working on the theory, instead of rejecting facts out of hand.

Engineering is specifically NOT exploration, engineering is designed for building things that work and use scientific theories turned into scientific law. Law...Which is a falsehood built for the engineering trade and training within it, for linear minds which are principally dogmatic in form and function.

I see it differently. Not a falsehood, but a model simple enough to be applicable in economical way to a day-to-day engineering.

In audio, the measurement and the analysis is wrong, just plain wrong. Too many engineering minds on the job, trying to play it safe and keep things ordered & black and white.

Measurements are measurements. If they are done competently, with calibrated instruments, and only what is actually measured is claimed, I'm happy to use them.

Analysis is a different story. Analysis always presupposes a theory, or at least a paradigm. And this I consider too rigid in the current mainstream audio.

This is why the audiophile conundrum has existed for about 50 years. The ignorance of projection in the pundits that surround the engineering trade and ideals that are involved in the audio world. Interference (engineers from other areas) from outside audio (even more ignorant!!) helps keep the insanity frothing along nicely.

There are other reasons for relative ignorance of the hearing system fundamental properties among practicing engineers. One of them is that not all relevant knowledge is even discovered yet. Another is that some very relevant knowledge was discovered relatively recently, and practicing engineers weren't taught it.

To clarify, an engineer is not trained to commit to the scientific method or invention, they are trained to follow the books, as that is why they are engineers, not scientists who explore and change things as required when required.

Agree. People like me, trained as scientists, are often perceived as "irreverent" in regard to dozens of audio engineering handbooks published over several past decades. Most engineers (not all) take doubting certain things written in these handbooks as a manifestation of sheer stupidity.

Meanwhile, a whole parallel world of peer-reviewed audio science publications exists. It is instrumental to observe how drastically the theories changed over the past 50 years, prompted by more and more sophisticated experiments, and breakthrough discoveries in the field of mammalian audio system physiology. 

If you want to explore in formal sense, go back to school and get trained to see all as theories, which are subject to change from/on new data, tests and proofing, correlation, etc. Get trained as a scientist.

Not practical for most practicing engineers. The change will only occur gradually, as older generations retire and new ones are taking their place.

When this mess erupts into fully blown projections in insanity of following the dogmatic rule books of engineering, we end up with things like ASR.

I like pretty much all ASR measurements. What I don't agree with is some of the analysis they derive from the measurements. ASR crowd is very uneven: there are bone fide luminaries posting there, and also folks who keep scoring points for slighting others. Guess who ends up with more points?

The longer a problem sits unsolved, unresolved.. the more fundamental the error in the formulation of the question.

Agree. As an example, Ptolemaic System was generally believed to be true for about 14 centuries.

Thus, the audiophile conundrum is deeper than this surface level stuff that people generally think it is. It’s deep in the minds involved, regarding how they explore reality.

Indeed.

As long as dogmatic minds try to figure out what is wrong in audiophiles vs measurements, without moving to true and proper scientific method...the longer they’ll be spinning around and getting no real correlating clarity in any of it.

I'd say the truly dogmatic minds don't even try to figure out what is wrong. They just reject the facts as aberrations, just like later-centuries Ptolemaic scholars ignored observed deviations in planets movements not explainable by their preferred theory.

Let's dissect thinking behind ignoring one of such facts in audio: certain types of music, for instance classical symphonies and gamelan, tend to not sound right when published in CD format.

What is usually offered as grounds for rejecting such statement? The Sampling Theorem and one of the ways to calculate dynamic range of a digital format.

 

The Sampling Theorem (https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem) reads in its original edition:

If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

This theorem is often taken as "proof" that sampling frequency of 44.1KHz is sufficient for encoding any meaningful music signal. Because, "obviously", everything above 20 KHz can't be heard by humans, and thus is not worth encoding.

Let's look closely. What does "contains no frequencies higher than B hertz" actually mean? It means, using formulation in same Wikipedia article, that "Strictly speaking, the theorem only applies to a class of mathematical functions having a Fourier transform that is zero outside of a finite region of frequencies."

Do analog signals corresponding to practical music pieces have Fourier transform that is zero outside of a finite region of frequencies? Absolutely not! Because, as another theorem from Fourier analysis proves, only functions of infinite duration can have such Fourier transform.

Let it slowly sink in. The Sampling Theorem, strictly speaking, is not applicable to analog signals corresponding to practical music pieces. But, obviously, some form of Fourier transform is widely used in audio digital signal processing. What's going on here?

What is actually being used, in discrete form, are variations of Short-Term Fourier Transform.

A fragment of a signal, let's say with a duration of 20-25 milliseconds, is taken, then multiplied by a so-called "smoothing window". The resulting function of time is guaranteed to smoothly start as 0, and smoothly end as 0.

Then the signal is mathematically virtually replicated infinite number of times. Since it is now of infinite duration, the Fourier Transform result has limited range of frequencies.

Then the process repeats with another fragment of the signal, starting at 10-12.5 milliseconds later than the previous piece. For the purposes of digital filters, this process sometimes virtually repeats with shift of just one digital sample duration.

So, in practical applications, digital signal processing uses an approximation of Fourier Transform. Correspondingly, the Sampling Theorem only works approximately. Most of the time more than well enough. Sometimes not at all.

 

Now let's consider the issue of sufficient dynamic range. It is oft-cited that CD format has dynamic range of 96 dB. Let's see, approximately, how one could come to such conclusion. 1 bit corresponds to 6 dB SPL. So, "obviously", 16 bits correspond to 6 dB x 16 = 96 dB.

According to https://hub.yamaha.com/audio/music/what-is-dynamic-range-and-why-does-it-matter/:

As a group, classical recordings have the widest dynamic range of any genre. The same study cited above found that recorded classical music typically offers between about 20 dB and 32 dB of dynamic range. While that might seem like a lot, it’s still quite a bit smaller than that of a live symphony orchestra performance, which can be as large as 90 dB.

Technically, those are good news, aren't they? Live symphony orchestra dynamic range is 90 dB. CD dynamic range is presumably 96 dB. 90 < 96. So, CD should be able to reproduce the whole dynamic range of a symphony orchestra, right?

In practice though, we have those presumably stupid music producers and audio engineers, who fell to the Dark Side during the Loudness Wars, and who will only record classical music CDs with 20 dB to 32 dB of dynamic range.

What would happen if they attempted the 90 dB? They would need to allocate 90 / 6 = 15 bits to the dynamic range encoding. For the quietest sound, they'd only be left with 1 bit for encoding it. Wait, what?

Yes, imagine a quiet passage in a symphony, nevertheless involving a dozen of instruments, each with a complex multi-overtone spectrum. With frequency slides, amplitude rides, tremolos etc. All of this would need to be recorded with just one bit at 44,100 Hz!

This is exact equivalent of DSD encoding, only its frequency is 64 times lower. Correspondingly, the highest frequency that we can hope to encode with similar fidelity as DSD will be 44,100 / 2 / 64 = 344.5 Hz. Say goodbye to the "micro expression of transients and micro transients"!

How much different is what the audio engineers are actually doing? Let's say they decided to limit the dynamic range to 30 dB. This corresponds to 30 / 6 = 5 bits. This leaves 11 bits to encode the quietest part of the symphony.

How good are 11 bits? 2 to the power of 11 is 2,048. 1/2,048 = 0.00049. An average digitization error would be half of that, which is 0.025%. Interesting, it is just below the widely accepted threshold of THD defining a hi-fi power amplifier, which is 0.03%.

This is not a coincidence. If they'd allocated less bits for the quietest parts of the signal, they would hear noise and distortions in them, similarly to how they'd be able to hear noise and distortions introduced by a low-sound-quality power amplifier.

If they's wanted to go audiophile quality for the quietest passages, they'd need to up the ante 3 bits more, to 14 bits. so that digitization noise and distortions would be approximately equal to that of a high-quality DAC, and thus would be likely unnoticeable even on a high-quality professional headphones.

So, for faithful reproduction of a symphony we would need 90 / 6 = 15 bits for encoding the dynamic range, and 14 bits for encoding the shape of the signal. 15 + 14 = 29 bits. Uh-oh, but professional ADC and DAC only encode 24 bits? How could they manage to effectively push to 29?

And here we come to understanding of why arguably overkill digital formats are desirable. The seemingly excessive amount of information per second inherent in 24/192, DSD128, and especially in 24/384 and DSD256 can be divided between encoding the dynamic range, encoding the shape of the quietest signal, and sampling the signal frequently enough to capture its evolution over shorter periods of time.

How all of the above relates to the current thread theme? By the virtue of analog recording and reproduction system, which in principle doesn't place fundamental limits, other than noise and maximum acceleration of mechanical parts, on either effective bit depth or sampling frequency.

It is commonly accepted that the best analog systems have about 70 dB of dynamic range. Which would roughly correspond to 70 / 6 = 12 bits. This gives an excuse for proponents of CD superiority over LP to claim that this must be so because obviously 16 > 12.

However, in order for the quietest signal to be still distinguishable, it only needs to be 6 db, or 1 bit, above the noise floor. This leaves an equivalent of 11 bits for dynamic range, which is more than twice of the 5 bits of the usable CD dynamic range.

Instead of the last 1 bit with which to encode the shape of the quiet signal, a high-quality analog system has many more. Actual number depends on the analog media granularity and its speed, yet the most important fact is that there is no hard stop similar to the one a digital system would have.

So, the analog system would reproduce the quiet passages in higher fidelity signal-shape wise, superimposed with noticeable noise of course. Yet the human hearing system is capable of filtering out this noise at higher levels of processing in the brain, and enjoying the quiet passage hidden underneath.

Viewed from this perspective, LP has twice as wide usable dynamic range in comparison with CD. But higher noise and distortions. For classical music especially, this could be a desirable compromise. For some other genres, for instance, extremely-narrow-dynamic-range very-simple-signal-shape electronic dance music, CD could be preferable.

I would expect a classical recording made by multiple microphones sampled at 24/384, or even at 32/384, and delivered in DSD256 after careful mixing and mastering, to be the ultimate one for the time being. As I recall, they produce such recordings in Europe.

@fair

Ref: your long tech commentary and explanation above.

This is the single best explanation I’ve (ever) heard.

Thanks for taking the time to write this here.

 

Some have stated here that digital sounds 'lifeless'.

The reason for this is obvious and immutable.  It arises because the analogue signal has been chopped up into billions of pieces.  It is chopped up in two dimensions: frequency and time.  Once it has been diced in this way, all the expensive gizmos in the world cannot put it back the way it was.  It will never sound like the original analogue experience.  Of the two dimensions, chopping time is by far the more damaging.  However good your clock the timing will be forever artificial.  it will never again sound like the real thing.

Digital sound could be compared with digital images.  It could be said that with sufficient resolution digital imaging can be of very high quality.  This may be so, but for imaging, the image is not chopped in the time dimension. 

@akgwhiz    I do not agree that a preference for vinyl is caused by noise and distortion being "desirable".  The preference arises not from negative attributes of vinyl being perceived perversely as positive, but from the negative consequences of digitisation that cannot be reversed.

@fair ,

There are far too many errors and misinterpretations in your post. It will be highly misleading to someone who is not familiar with digital audio.

Start off with sampling theory and window functions. The requirement for infinite time is only required for infinite precision. We obviously do not need infinite precision as our ears do not have infinite dynamic range, and audio does not extend to 0Hz. Purely practical, the inherent noise of the quietest rooms and the onset of pain sets hard limits on what we need. Hence we do not even need infinite time. The windowing function does its required job. Sampling theorem is absolutely applicable to music. These theories are tested day in and day out. All our communications are based on them.

Short term Fourier Transforms are analysis functions primarily. They make pretty graphs, and are used for signal analysis. The data that comes out of them is bounded by the window width, which defines the lowest frequency that can be represented, the sample rate, which sets the upper bound, and both which define how fine of frequency analysis can be done. They do what they do accurately, understanding their limitations.

This is exact equivalent of DSD encoding, only its frequency is 64 times lower. Correspondingly, the highest frequency that we can hope to encode with similar fidelity as DSD will be 44,100 / 2 / 64 = 344.5 Hz. Say goodbye to the "micro expression of transients and micro transients"!

I am going to highlight this last paragraph. This is 100% false. That is not how DSD works. The single bit in DSD is not equivalent to a single bit change in PCM. No direct comparisons can be made. Hence you conclusion cannot be made and can be assumed false.

There are two flaws in your statement of equivalence 11 bits and 0.03% distortion detection. More like 3 flaws. That distortion limit is at full scale. Assume your stereo is set for 100db peaks, which is fairly loud and you have low distortion playback. There is a particular distortion level evident at that volume. In your analysis, you are claiming to be able to hear distortion at the bit level, on sounds that are only 70db. Are you claiming to be able to hear 0.03% distortion on a 70db peak signal. Not average, peak. That is a low volume level. If you are a very quiet room, 25db, that is only 45db above the noise of your room. That is 8 bits. So there is still 3 bits of addition digital range below the noise floor. Further, CD is dithered. Dither improves the dynamic range where our hearing is most sensitive for added noise where it is not. That extends the dynamic range to where we are most sensitive to 110db. Your argument fails with that information.

 

So, for faithful reproduction of a symphony we would need 90 / 6 = 15 bits for encoding the dynamic range, and 14 bits for encoding the shape of the signal. 15 + 14 = 29 bits.

This is obviously not at all accurate. You are stacking flaws in your understanding of how digital works to come to incorrect conclusions. The digital bit depth only needs to be large enough to encompass the full dynamic range. By shifting noise, we don't even need that many bits for the dynamic range. DSD has 1 bit depth. The noise is shifted to provide large dynamic range. CD has 16 bits. The noise is shifted to increase the dynamic range.

 

However, in order for the quietest signal to be still distinguishable, it only needs to be 6 db, or 1 bit, above the noise floor. This leaves an equivalent of 11 bits for dynamic range, which is more than twice of the 5 bits of the usable CD dynamic range.

 

You are basing this conclusion on a stack of fundamental flaws. It does not represent reality. More accurate is that we can hear below the noise floor. Vinyl has a signal to noise ratio of about 70db, sometimes higher, but the dynamic range can extend 10 or 20db. CD almost beats this with a raw dynamic range over 90db. The dithering extends this to 110db far higher than vinyl.

 

Viewed from this perspective, LP has twice as wide usable dynamic range in comparison with CD. But higher noise and distortions.

This is also based on a stack of flawed assumptions. It is incorrect

 

@clearthinker ,

The MOFI debacle I think is the best counter to your argument about digitizing of an analog signal. That they could do this for over a decade, while creating some of the best rated vinyl for sound puts a hole into the argument that useful information is forever lost. Can you explain your concern with chopping time? What do you think is lost when this happens knowing we can only hear a limited range of frequencies?

Movies and video chop images in the time domain.

The answer to your point is the forever related issues of clock error and dither.  When CDs started in 1984, these errors were gross and most agree many CDs were unlistenable.  Retrospective engineering of clocks and DACs has improved performance considerably but my fundamental theorem will always remain.  The issue isn't related to the fact we can only hear a limited range of frequencies.  Whatever the medium, they all record and reproduce a limited range of frequencies.  The issue affects what some have acronymed 'pace, rhythm and timing - PRAT. 

Shameless 

@clearthinker , I don't think there is anything to support you current view. I am not sure issues in playback when CDs came out was due to jitter, the brickwall filters, or just poor quality playback equipment. I have not delved into it extensively and I am more interested in the here and now. When I can look at a jitter test on a Schitt Modi+ for $129 and even on Toslink the jitter components are -130db, and better on other inputs, jitter is not something to concern ourselves. I have read even old studio equipment had good clocks for the ADC even if the DACs did not for the stuff we bought.  Dither can be added analog or digital. It extends the dynamic range. It works. What is your concern about it?

CD reproduces to 20KHz.  It have been many decades since my ears heard 20KHz. What do you think we are losing by not having higher frequencies. 24/96 would solve that issue.  Someone posted above that with vinyl as you move to the inner grooves, there is not much above 10KHz and it is all distorted.

I am still back with @asctim. All the points he lists are real. I am more inclined to believe that things that are real and identifiable, including mastering, are why we often like vinyl, as opposed to interpretations of digital audio that are either incorrect or have no evidence to support. Is that the simple explanation? I think so.

@thespeakerdude     My issue is certainly not with HF performance.  Like yours, my ears now go nowhere near 20kHz now anyway.  My first post referenced those comments that digital sound is 'lifeless' compared with vinyl.  I also find this with a lot of CDs but certainly not all.  The absolute worst one I heard was actually by Chesky (a symphony, can't remember which, I haven't looked at it for 25 years) that I found unlistenable, notwithstanding it was supposed to be better.

So what is the cause of this perceived lifelessness?  Certainly uprated digital generally sounds much better, no argument.  I have a few SACDs.  Pretty well all are better than the best CDs; and some of are excellent and sound to me better than the vinyl equivalents.  In my view this doesn't deny my proposition; breaking the performance down into smaller pieces reduces the translation error - this is proved by elementary calculus.

Just read this lighter version towards the maths and physics of these two formats:

Scientific American 2017 article 

 

There seems to be competing explanations of the recording file format characteristics. This is a maths and physics question and should be able to be resolved.

Then there are subjective experiences and these are equally conflicting. There are areas of agreement such as higher or airier mid-range of vinyl and the less noisy cd format and some agreement of SACD as better than cd.

Ideas like some music styles may better suit certain formats better, classical with vinyl for example depend on technology justification that isn’t yet fully accepted.

On the other hand, the civility in this conversation despite differences has been glorious and I hope that we can continue this way.

 

 

@thespeakerdude

... These theories are tested day in and day out ...

... They do what they do accurately, understanding their limitations ...

I agree with these two statements of yours. What I was referring to are approaches where limitations of the classic theory were disregarded. Let me try to explain from a different angle what I meant, using a concrete example.

Imagine an audio signal which is a sinusoid of frequency 12 KHz, with amplitude described as piecewise function of two segments linear on dB scale. First segment goes from 0 to 100 dB SPL during first half cycle of the the sinusoid. Second segment goes from 100 db SPL to below quantization noise during the next four cycles of the sinusoid.

Try to sample it with 16/44.1. Then try to reconstruct the signal from the samples. Then shift capture time of the first sample by 1/8 of the sinusoid period. Repeat the exercise.

What you’ll find is that, first, reconstruction will be pretty rough, and second, that it will be wildly changing with even small shifts of the first sample capture time.

From Fourier Analysis viewpoint, this is an example of a signal with spectrum extending significantly beyond 20 KHz, which makes sampling at 44.1 KHz untenable, and result of reverse transform unpredictable.

Yet from human hearing system standpoint, such a signal is perfectly valid, and will result in physiological reactions inside several inner hair cells. Most likely, if it manages to evoke a sensation of pitch in a particular individual, perceived pitch frequency will be close to the intended 12 KHz.

An analog system doesn’t care about the sampling frequency, and at what precise moment of time the first sample happens to be taken, and would capture this signal fully, with some distortions of course, yet nevertheless it will capture the shape definitively. And it will be reconstructed definitively as well.

Imagine further, that some short time later, another signal comes in, which is exact reversal of the first one.

Depending on the time difference of the signals start, the sampled values of the second signal may range from exact opposites of the first set of sampled values to something seemingly unrelated.

Once again, human hearing system, with its half-wave rectification capability, will react to the second signal in a similar way it reacted to the first. And once again, the analog system, not restrained by sampling and time shift considerations, will capture the second signal fully.

If, on the other hand, we significantly increase the piece-wise linear segments duration: let’s say first segment goes up for 100 cycles, and the second one goes down for 1,000 cycles, then the 16/44.1 sampling with consequent reconstruction will produce much more agreeable result.

So, I gave an example of a signal which is meaningful and definitive both from the hearing systems and analog recording standpoints, yet non-definitive from the digital sampling standpoint.

Also, an example of a signal with the same general shape, yet with different duration of its characteristic segments. Which happens to be both meaningful and definitive from all three standpoints.

Which illustrates the limitations of digital sampling and classic Fourier-analysis-based DSP: they work well enough in most practically encountered cases, yet not always.

In contrast, analog may be worse in most cases in terms of distortions and noise, yet it works consistently in all practically encountered cases, which may be important for recording and reproduction of certain genres of music.

Increasing the sampling rate effectively rescales the problem: certain signal fragments and components which couldn’t be perceptually transparently captured at a lower sampling rate are now captured well enough at the increased sampling rate.

At the limit, sampling at increasing rate becomes perceptually equivalent to analog recording, sans the distortions and noise. At which point does it happen? It depends greatly on the characteristics of music, and on critical listening abilities of the person who tries to enjoy that music.

Correspondingly, the highest frequency that we can hope to encode with similar fidelity as DSD will be 44,100 / 2 / 64 = 344.5 Hz. Say goodbye to the "micro expression of transients and micro transients"!

I am going to highlight this last paragraph. This is 100% false. That is not how DSD works. The single bit in DSD is not equivalent to a single bit change in PCM. No direct comparisons can be made. Hence you conclusion cannot be made and can be assumed false.

Let me clarify. I wrote "encoded" meaning that we could use the remaining still available stream of one-bit values to encode in the same way that DSD does. Of course bits are used differently by PCM and DSD - pulse vs delta etc.

That was to illustrate the point that the amount of information per second remaining available, in the case if we’d decided to use 15 bits for encoding of dynamic range, is indeed equivalent to a very low-fi format.

There are two flaws in your statement of equivalence 11 bits and 0.03% distortion detection. More like 3 flaws. That distortion limit is at full scale.

To understand what I meant, look at the physical bits of the quietest in this context PCM-encoded signal. All the upper bits, which I called "used for encoding dynamic range", will be zero.

It is not that these specific bits of PCM stream would be always used for encoding dynamic range. What counts is the number of bits that we have to keep unused while encoding the quietest segment of music.

Secondly, please take into account that human hearing system is capable of adjusting its sensitivity, and symphony composers tend to use this factor fully.

The symphonies typically have quiet segments, when a neighboring spectator shuffling her purse may be pretty distracting, and they also have short bursts of apotheosis, with SPL falling just short of hearing system pain threshold.

In the context of a quiet segment, the perceived distortion level threshold is scaled down. That’s why I do indeed consider it as if it was a full-scale signal.

There are other factors of course: e.g. the equivalent loudness curve shifts.Yet if we only consider the most stable part of the curve, at mid-frequencies, the rule-of-thumb calculations generally work, plus-minus a bit.

Assume your stereo is set for 100db peaks, which is fairly loud and you have low distortion playback. There is a particular distortion level evident at that volume. In your analysis, you are claiming to be able to hear distortion at the bit level, on sounds that are only 70db. Are you claiming to be able to hear 0.03% distortion on a 70db peak signal.

That would depend on nature of the music fragment, right? And on my hearing ability. In general, I didn’t claim anything of the sort. Only that, as an order of magnitude estimation, an amp with 0.3% THD is usually considered low quality, an amp with 0.003% THD very high quality. The middle on logarithmic scale: 0.03%, was considered in enough accounts I found credible as a threshold of quality.

Further, CD is dithered. Dither improves the dynamic range where our hearing is most sensitive for added noise where it is not. That extends the dynamic range to where we are most sensitive to 110db. Your argument fails with that information.

Dithering is helpful in most practical cases. Yet, if you look at the mathematical derivations of the common dithering schemes, you’ll see that the characteristic duration of signal stability is a factor in calculations.

Similarly to the examples I gave earlier in this reply. If a signal is composed of slowly changing sinusoids, dithering helps a lot.

It a signal consists mostly of harmonic components quickly changing their amplitudes, non-harmonic transients, and frequently appearing/disappearing components, dithering is not as effective.

>>> So, for faithful reproduction of a symphony we would need

>>> 90 / 6 = 15 bits for encoding the dynamic range, and 14 bits for

>>> encoding the shape of the signal. 15 + 14 = 29 bits.

This is obviously not at all accurate. You are stacking flaws in your understanding of how digital works to come to incorrect conclusions.

I believe at that point I provided enough explanations. Your reactions are quite typical of engineers who consider the classic DSP based on Fourier Analysis the only true paradigm.

From my perspective, it is only absolutely true for abstract mathematical constructs.

It is nothing but useful approximation of real world. One ought to be very careful with the corner cases, where the abstractions stray too far away from the phenomena they are supposed to model.

The digital bit depth only needs to be large enough to encompass the full dynamic range.

As I highlighted, the approach you are advocating doesn’t address the need of having some bits left available for encoding the shape of signal faithfully enough to be perceived as distortions-free.

The theory I use explains well enough why the so-called Loudness Wars can be considered a rational, professionally responsible, reaction to deficiencies of the most widely used at the time audio recording format - CD.

This theory explains why some listeners still prefer listening to LP for some genres of music, despite the fact that, according to the classic theory, CD is vastly superior. Once again, this is a rational and responsible reaction.

The theory explains with good enough for me personally precision why most professional sound mixing and mastering studios didn’t advance beyond the 24/192 PCM format.

It also explains why some modern symphony recording engineers moved to 24/384 and DSD256 formats. And other otherwise unexplainable for me phenomena.

By shifting noise, we don’t even need that many bits for the dynamic range. DSD has 1 bit depth. The noise is shifted to provide large dynamic range. CD has 16 bits. The noise is shifted to increase the dynamic range.

DSD is a delta format. Formally, general DSD has unlimited bit depth, and thus dynamic range. It is only constrained in specific versions of the format to correspond to a set bit depth at an PCM-equivalent sampling rate.

The noise considerations started to amuse me lately. Practical examples were a trio of class-D power amplifies, highly regarded by ASR. I bought them over the years, evaluated, and quickly got rid of, due to intolerable for me distortions.

Yet SINAD of these amplifiers was excellent. Which made me look closely at SINAD measurement procedures. Long story short, SINAD is predicated on taking Fourier transform over a very long window, of a signal comprising of a set of sinusoids with equal and unchanging amplitudes.

Where all three failed miserably for me was reproduction of low-signal-level transients, something SINAD doesn’t capture all that well. Yet the theory I use explained their behavior rather precisely. It also predicted what power amplifiers would be more acceptable to me.

>>> However, in order for the quietest signal to be still

>>> distinguishable, it only needs to be 6 db, or 1 bit, above the noise

>>> floor. This leaves an equivalent of 11 bits for dynamic range,

>>> which is more than twice of the 5 bits of the usable CD dynamic

>>> range.

You are basing this conclusion on a stack of fundamental flaws. It does not represent reality. More accurate is that we can hear below the noise floor.

It depends on the nature of noise and nature of signal, doesn’t it? For white noise and a short sinusoidal burst, I’d agree with you. I’m more interested in a typical music signal, with spectrum close to pink noise, masked by pink noise. In that case, having it 6 dB over the noise floor results in more reliable perception.

>>> Viewed from this perspective, LP has twice as wide usable dynamic

>>> range in comparison with CD. But higher noise and distortions.

This is also based on a stack of flawed assumptions. It is incorrect.

Not on assumptions. On theories. Fitting experimental facts. The theory I use is more sophisticated than the classic one, taking into account analog characteristics of human hearing system.

On its simplest level, instead of considering just dynamic range, it also considers the shape of what the dynamic range is applied to. Once this is done, preference for LP in certain situations ceases to be a mystery.

Cochlea is not a Fourier transforming machine. In some regards it is more crude, yet in others it is far more advanced. As an example, it starts noticeably reacting only after observing two cycles of a pure sinusoid, virtually irrespective of frequency.

For higher frequencies, at 44.1 KHz sampling rate, this may correspond to only a few samples. The shape of a quickly changing signal can’t be faithfully captured by such small number of samples.

Once we get into signals comprised of quickly appearing and disappearing components, the simple intuition good enough for the previous example no longer works, and math becomes much heavier, yet fundamentals remain: the higher the sampling rate (assuming equal quantization accuracy), the deeper the bit depth (assuming equal timing accuracy), the better it gets.

And yes, I’m aware of the oversampling nature of practical ADC and DAC. Of the fact that internally they are sampling/reconstructing signal at significantly higher rates, and then encode adjustments not only into the slower-sampled values within the signal time range, but also outside it.

Still, Information Theory is a bitch. If there isn’t enough bits to encode the changes in the signal that would be noticed by cochlea, some meaningful information would be lost. I did some experiments on fragments of music that I recorded and mixed myself. The distortions of 16/44 compared to 24/192, albeit subtle, mostly manifested themselves as uneven rhythm of smaller-volume transients.

With all this esoterica being discussed, how does one account for the phenomena of the fact that most lps these days use digital files, and vinylista think they sound great, as long as they don’t know the truth?

@fair ,

 

I believe at that point I provided enough explanations. Your reactions are quite typical of engineers who consider the classic DSP based on Fourier Analysis the only true paradigm.

 

From where I am sitting you have not provided one explanation because every single explanation or example you have used is wrong, stacking misunderstanding on top of misunderstanding. Fourier analysis is not a paradigm, it is a mathematical translation from time to frequency, it just is. The accuracy, as I previously wrote, is based on suitable bandwidth limitations, and appropriate windowing functions, much which occur naturally in audio, but are still supplemented by the appropriate analog filters, over sampling, and digital processing. People are not just guessing at the implementation and not considering what the underlying waveforms can and do look like. Let me break just one section down to illustrate your logic flaws and misunderstandings. It carries through to the rest of what you have wrote:

Imagine an audio signal which is a sinusoid of frequency 12 KHz, with amplitude described as piecewise function of two segments linear on dB scale. First segment goes from 0 to 100 dB SPL during first half cycle of the the sinusoid. Second segment goes from 100 db SPL to below quantization noise during the next four cycles of the sinusoid.

Try to sample it with 16/44.1. Then try to reconstruct the signal from the samples. Then shift capture time of the first sample by 1/8 of the sinusoid period. Repeat the exercise.

What you’ll find is that, first, reconstruction will be pretty rough, and second, that it will be wildly changing with even small shifts of the first sample capture time.

You start with a flawed premise, proceed to a flawed understanding of digitization, and finish with an incorrect understanding of reconstruction.

Flawed premise: 12 KHz sine wave do not suddenly appear, starting at 0. As I previously wrote, we are dealing with a bandwidth limited and defined system. You cannot go from 0, silence, directly into what looks exactly like a sine wave. That transition exceeds the 20KHz (or whatever we are using). Also, the digitizer, filters, etc. will have been running and settled to required accuracy by the time this tone burst arrives. Whatever you send it, will have been limited in frequency, by design, by the analog filters preceding the digitizer.

Flawed understanding of Digitization: As written above, the digitizer was already running when the tone burst arrives. Whether the sample clock is shifted globally the equivalent of 1/8 of a 12KHz tone, or not, will have no impact on the digitization of the information in the band limited analog signal.

Flawed understanding of reconstruction: When I reconstruct the analog signal, using the captured data, whether I use the original clock, or the shifted one, the resulting waveform that results will be exactly the same. In relationship to the data file, all the analog information will be shifted by about 10 useconds. That will happen equally on all channels. The waveforms will look exactly the same either case. One set of data files will have an extra 10 useconds of silence at the front of them (or at the end).

 

As I highlighted, the approach you are advocating doesn’t address the need of having some bits left available for encoding the shape of signal faithfully enough to be perceived as distortions-free.

 

I am sure you believe this, but you used flawed logic, a flawed understanding of the waveform, and a flawed understanding of digitization, reconstruction, and the associated math.

I went back and looked looked at the research. In lab controlled situations, humans can detect, a very specific signal up to 25db below the noise floor, A-weighted. That is not listening to music, that is an experiment designed to give a human the best possible chance. For vinyl, that means in a controlled experiment, maybe you could hear a tone at -95db referencing 0db as max. With CD, the same would be true at -110db (or more) due to the 100% use of dithering.

 

It a signal consists mostly of harmonic components quickly changing their amplitudes, non-harmonic transients, and frequently appearing/disappearing components, dithering is not as effective.

I cannot respond to this as it is wrong, and I am not certain where exactly you have gone wrong. As I wrote above, you have made errors of logic and understanding in all the areas critical to digital audio. As I wrote previously, dithering can be applied in analog prior to digitization.

 

The noise considerations started to amuse me lately. Practical examples were a trio of class-D power amplifies, highly regarded by ASR. I bought them over the years, evaluated, and quickly got rid of, due to intolerable for me distortions.

To be sure we are on the same page. Class-D amplifiers are analog amplifiers. They are not digital. I will correct you. Perception of distortion. You are making an assumption of something that is there, without proof it is there.

 

Not on assumptions. On theories. Fitting experimental facts. The theory I use is more sophisticated than the classic one, taking into account analog characteristics of human hearing system.

Which theory is it that you are using? I noted many flaws in your understanding of critical elements of digital audio, and assertions that are also incorrect. I have already falsified your theory.

 

Perhaps not important to this discussion, but 16/44.1 is a delivery format. From what my colleagues tell me, is has not been used as a digitization format in decades, and depending on your point of demarcation, it has not been used as a digitization format since the 1980’s, as all the hardware internally samples at a higher rate and bit depth.

@fair do you think that the people working on this technology never do comparisons of input and output waveforms with real music?

 

@fair 

For the record, I am not an engineer by training.

@fair ,

One last point,

For higher frequencies, at 44.1 KHz sampling rate, this may correspond to only a few samples. The shape of a quickly changing signal can’t be faithfully captured by such small number of samples.

This demonstrates, succinctly, a lack of understanding of the topic we are discussing. Perhaps the problem is you only see a few samples. What you should see is a few samples, taken at very precise time intervals. The information is not only the sample value, but the exact relative time of each sample. Both are critical.

There are so many errors in @fair's word salad that it makes my head spin. Kudos to @thespeakerdude for having the patience to sort them out.

One thing to consider about digital audio is that the math that makes it work is the same math that explains the squiggles on an LP: the Fourier Transform. That's not just a theory, but a theorem; it can be proven with math. In that sense, it's perfect, and I'm saying that as an analog guy.

If there is any interest, this is probably the best single article I have discovered that explains digital audio. It is not light reading nor heavy reading. Dan, who put it together obviously put a lot of time into it. It is almost 20 years old so comments about processing power are no longer relevant, but everything else is. I have come across many articles on digital audio written by less technical people. They get the basics right, but they often make mistakes and they never go into the depth that this article provides. You may need to read it 2 or 3 times to understand well enough, but if you do, it will dispel a lot of misconceptions about digital audio.

https://lavryengineering.com/pdfs/lavry-sampling-theory.pdf

 

If you have any questions about the article I will try to answer them.

This video provides an excellent explanation and actual demonstration of how digital audio works, and how it doesn't.

Thanks for the extensive explanations of digital audio and references @thespeakerdude

Can we now summarize (are we there yet?) and identify general principles that help shape the differences between these two formats. I’m not interested in which one is better, as judgments are too system and context as well as music and preferences dependent.

Rather, can we draw conclusions about their differences that are more or less general or specific conclusions (about dynamics, freq range, noise and noise floor, PRAT, mid or high freq airiness and so on or our hearing preferences, sensitivities and limits) that shed light on common experiences?

 

I just watched Paul at PS Audio say how what MOFI was doing recording using DSD was in his view the right way to record and preserve masters in digital and then transfer onto vinyl for playback. Is vinyl playback giving anything different to digital playback from the same master copy?

[MOFI Marketing representations aside. I don’t want to touch the Marcoms involved here in this discussion.]

 

we are wired to appreciate sound based on our memories of the sound we grew up on.

It may be what resembles it, perfects it or what the total opposite is but in either case, it's still our baseline. Most of the characteristics is in our head: what it evokes, what we think it is vs. what it does sound like.

To me vinyl is raw, unfiltered, imperfect, "authentic" which translates to dynamic, lively, bold  and  forward. The key is that I like that sound. 

Digital (unless tweaked) goes for the opposite: neutral and processed. For a lot of productions, I prefer that, e.g. when the recording was a mess, tiring after a few seconds, I need the digital fix.

 

Hello.

All this discussing seems for me to be based on terrifficness.

You got a couple of ears, usually.

That is the source to measure with. And if your ears prefer digital, thats ok. Same with analog.

So, in my opinion, humble or not, your ears are your guidance.

My ears are my only reference.

I also wonder when people are going to start lisening to the performance of the music, whether analog or digital.

Regards,

Zappasan

You're going to have a hard time deriving objective generalizations about these two formats in relation to each other, the whole thread is subjective based and will continue down that path. No single person can hear every single permutation of digital or analog setups, without this knowledge they are only hearing the difference in individual setups. Certainly, those with experience of having listened to many analog and digital setups can arrive at more objective conclusions, still doesn't account for all variables.

 

I'm with Zappasan, enjoy the music. While this discussion may be fine exercise in logic, I'm happy to let it all go and  simply enjoy the music from my vinyl and streaming setups. No longer any need to analyze the differences.

grislybutter

we are wired to appreciate sound based on our memories of the sound we grew up on ...

What makes you think that?

Have you ever asked yourself if you could get another over analytical answer than you can possibly receive on this forum? I would say absolutely not!
 

Which sounds better to YOU! Why do we seem to think we need some long overly technical explanation of why one form of audio sounds better than another. Its your system. Its your room and Environment. Its your ears. 
 

Just listen to what sounds best to YOU! Relax and enjoy your hobby. Listen to the music my friend🥳

@teo_audio

To clarify, an engineer is not trained to commit to the scientific method or invention, they are trained to follow the books, as that is why they are engineers, not scientists who explore and change things as required when required.

I respectfully disagree. Engineering is the practical application of science to solve problems. I went to university to study engineering and made my career of it. I was never trained to “follow the books.” My entire university experience can be summed up as “learn how to think and problem solve, don’t waste precious memory on things you can reference in a book.” My entire engineering career can be summarized as “I am a truth seeker, not a case maker. The data will guide my decisions. We cannot always have all the data we want, but we will endeavor to use reliable data and we will be flexible and adapt as needed.” I am very inquisitive and inventive. My work and personal interests straddle the line between science and engineering. My work 100% follows the scientific method.

@cleeds 

What makes you think that?

overanalyzing everything.

 

 

First of all I would suggest a blind listening, switching from CD to Vinyl. Humans are full or bias, what you hear may be because it is what you want to hear.  For example when listeners listened to music with various speaker cables, they always said the music played thru thicker speaker cables sounded better than thru lamp cord.  However, that was only when they saw that it was thicker cable.  When lamp cord was disguised as a thick cable they thought the disguised lamp cord sounded better than the normal lamp cord.  Also blind tests showed that most people could not tell the difference between music played over You Tube compared to the same music played from a CD. To me I can always hear the difference between vinyl and digital because digital has none of the dust pops or crackle in quiet sections of the music.

On the bench CD and digital blows away vinyl.  Vinyl wins in the romantic, tactile, visual departments.

@prosdds , there is value in a blind test, but there is no point doing that test for vinyl and CD. The noise, even the faintest clicks/pops, will quickly identify the vinyl. Even if it did not, you would need 1 of each mastered exactly the same. Does that exist? Is there a test record that matches a test CD?  After that you need a perfectly set up turntable. Nice to test to aspire too, practically impossible.

@asctim , @grislybutter , I think they are on the right track. @asctim has provided concrete differences between CD and vinyl. @grislybutter talks about learned responses or learned likes. If you tie your self worth to your likes and purchases, then you may be inclined to argue that those likes and purchases are inherently better, not just for you, but for everyone. Maybe it is just the mastering, but I am inclined to believe it is the flaws in the vinyl that often give it that special magic. Not always, not even 50% of the time for me, but when it works, it works really well. For me, it does not need to be superior technically for me to like it.

 

For discussion accuracy, vinyl, tape, and analog are not the same thing. Vinyl and tape are storage mediums that are predominantly analog in nature. What would perfect analog sound like? Digital!! :-)

 

@mahler123

With all this esoterica being discussed, how does one account for the phenomena of the fact that most lps these days use digital files, and vinylista think they sound great, as long as they don’t know the truth?

Thinking in terms of LP vs Digital dichotomy doesn't explain it. More nuance is needed. At the very least, the Digital formats needs to be split onto Below The Transparency Threshold and Over the Transparency Threshold.

The Transparency Threshold depends on nature of music and hearing abilities of listener. It is different between typical pop music and untrained listeners vs classical symphonies and professional musicians or sound engineers.

Since this is an audiophile forum, I prefer to talk about the High Transparency Threshold. Here I deliberately use terminology different from official, e.g. High Definition Audio, to keep it free from marketing attachments.

In my previous posts, I gave hints as to why I believe CD format is significantly below the High Transparency Threshold, whereas 192/24 PCM and DSD128 are slightly above it. Going into even more detailed technical discussions here does not appear fruitful.

So, as I understand it, if an LP is pressed from a digital format that is over the High Transparency Threshold, it ought to sound no different compared to one pressed from an analog studio master of the same recording.

Finally, after all this science, we get to enjoy the music. Imagine that. 

Fascinating discussion. I've not read every reply thoroughly, but I want to add a thought. I have made digital recordings of the best vinyl records I own. Playback of these recordings is indistinguishable from live vinyl playback (blind-tested).

The reverse is not true. I don't have an easy way to know if a particular vinyl pressing of an album was cut the same master as the CD release. However, I am confident that most listeners could easily distinguish between the two during playback.

As a practical matter, recording and mastering quality for a given album trump delivery format. If the best-preserved recording of a performance exists only on vinyl (e.g., tapes are degraded or lost), then vinyl will be the best format for that album. The same applies if all digital masters suffer from dynamic range compression because the mastering intent was earbuds listeners.

Another practical point: I have listened to a few systems that were highly optimized for vinyl playback. Every component in the analog playback chain was selected for maximum synergy to deliver an even, engaging response. For example, if the speakers were overly forward, a phono cartridge was chosen with a more relaxed presentation. The owners usually did not apply the same care when they added digital playback capability to these systems. As a result, vinyl playback genuinely sounded better, but that need not have been the case.

Ultimately, it does not matter which format is objectively superior. Vinyl will generally sound better on a system that is turned better for vinyl playback. The best available master for a particular album will generally sound best, regardless of delivery format (ignoring flawed pressings, damaged media, and low-bit-rate MP3 :-).

@mahler123 

even if the source was digitized, the vinyl will be analog. It will be different but still analog. 

Analog is not always or sometimes better. It's always different. I have 2 or 3 copies of my favorite LPs and CDs, Each LP sounds very different. CDs not so much. Vinyl to me is the shortest distance between the source and the speaker - processing-wise

Vinyl to me is the shortest distance between the source and the speaker - processing-wise

Perhaps, but consider the processing involved to go from the artist-approved 2-track studio master to RIAA pre-equalization, cutting the lacquer, electroplating, creating the father and mother, and creating stampers to pressing a record. More processing is involved in playing the record back, including a stylus tracking the grove, the cantilever driving a generator, RIAA EQ, and adding between 40 and 70 dB of gain to bring levels up to what an amplifier requires to drive speakers.

Honestly, it's astonishing to me that such processing (call it the vinyl production and playback transfer function) can produce sound that even remotely matches the source. :-)

 

We are getting somewhere.

@thespeakerdude

From where I am sitting you have not provided one explanation because every single explanation or example you have used is wrong, stacking misunderstanding on top of misunderstanding.

This is precisely how it should feel, from the point of view of someone remaining in an old paradigm. New paradigm overturns some of the old paradigm's assumptions and conclusions, which is obviously "wrong" in the context of the old paradigm.

Fourier analysis is not a paradigm, it is a mathematical translation from time to frequency, it just is.

Mathematically, Fourier Analysis is a theory based on integral transforms with harmonic kernels. "Integral" means that there is an integral involved, calculated from low boundary of integration to high boundary of integration.

Direct Fourier Transform takes bounds from time domain. Reverse Fourier transform takes bounds from frequency domain. Time domain and frequency domain can be, as classes of specific cases, continuous or discrete.

This theory is beautiful in its simplicity. For instance, formulas for direct and reverse transforms, in their traditional formulation, only differ in one sign in one place. The simplicity affords efficient implementation of the transforms in computer code.

The accuracy, as I previously wrote, is based on suitable bandwidth limitations, and appropriate windowing functions, much which occur naturally in audio, but are still supplemented by the appropriate analog filters, over sampling, and digital processing.

And here we move away from the theory and arrive to a paradigm. The "suitable bandwidth limitations" remove information contained in original analog air pressure variations over time at the point of recording.

Central belief of the paradigm states that removal of frequency components beyond 20Hz and 20 KHz is perceptually benign, for all types of music, and all listeners. Technically, this is the crux of our disagreements. I do not subscribe to this belief.

People are not just guessing at the implementation and not considering what the underlying waveforms can and do look like. Let me break just one section down to illustrate your logic flaws and misunderstandings. It carries through to the rest of what you have wrote:

You start with a flawed premise, proceed to a flawed understanding of digitization, and finish with an incorrect understanding of reconstruction.

I value your opinion. Couldn't asked for a better illustration of what I had to endure in my prior discussions at ASR.

However, my professors, from leading European universities, and their teaching assistants, had other opinions, giving me straight As on all courses related to Fourier Analysis and DSP.

The theory I'm using today contains the classic Fourier Analysis, and classic DSP based on it, as subsets. I absolutely do use them in domains of their applicability, when I believe they are going to provide accuracy sufficient for a task at hand.

Yet there is more, which came mostly from research conducted by others over past three decades. Unfortunately, too much of it is still widely dispersed in numerous peer-reviewed papers, rather than concentrated in a few engineering handbooks.

Flawed premise: 12 KHz sine wave do not suddenly appear, starting at 0. As I previously wrote, we are dealing with a bandwidth limited and defined system. You cannot go from 0, silence, directly into what looks exactly like a sine wave. That transition exceeds the 20KHz (or whatever we are using). Also, the digitizer, filters, etc. will have been running and settled to required accuracy by the time this tone burst arrives. Whatever you send it, will have been limited in frequency, by design, by the analog filters preceding the digitizer.

When one writes enough code processing real-life music recorded with high enough fidelity, one absolutely starts believing that such music components do exist: going from zero to almost pain threshold in a matter of microseconds, and then rapidly decaying.

One of the best examples of music genres rich in such components that I know of is Indonesian Gamelan. It is a curious genre: worshiped by its devotees in native land, and almost completely ignored by listeners outside the region.

Even the best gamelan CD recordings of famous Indonesian ensembles sound to me like incoherent early practices. Live, classical gamelan compositions, played with passion by experienced musicians, sound heavenly to me.

Flawed understanding of Digitization: As written above, the digitizer was already running when the tone burst arrives. Whether the sample clock is shifted globally the equivalent of 1/8 of a 12KHz tone, or not, will have no impact on the digitization of the information in the band limited analog signal.

This depends greatly on the nature of the band-limiting filter used. For analog filters this statement is generally true, with understanding that perfect brick wall filters don't exist, so there are still some smaller artifacts to be expected because of that. For digital filters applied to stream of oversampled values in some ADC devices, not so much. 

Flawed understanding of reconstruction: When I reconstruct the analog signal, using the captured data, whether I use the original clock, or the shifted one, the resulting waveform that results will be exactly the same. In relationship to the data file, all the analog information will be shifted by about 10 useconds. That will happen equally on all channels. The waveforms will look exactly the same either case. One set of data files will have an extra 10 useconds of silence at the front of them (or at the end).

See my comment above. Depends on the nature of bandwidth-limiting filter.

I am sure you believe this, but you used flawed logic, a flawed understanding of the waveform, and a flawed understanding of digitization, reconstruction, and the associated math.

I don't believe so. I used more sophisticated understanding of those. Knowing, both from learning the theory and from practical experience, that absolute predicted perfection isn't practically achievable, and that one needs to very carefully look at what artifacts are produced by this or that digitization method, and whether the artifacts may be heard under certain conditions by certain listeners.

I went back and looked looked at the research. In lab controlled situations, humans can detect, a very specific signal up to 25db below the noise floor, A-weighted. That is not listening to music, that is an experiment designed to give a human the best possible chance. For vinyl, that means in a controlled experiment, maybe you could hear a tone at -95db referencing 0db as max. With CD, the same would be true at -110db (or more) due to the 100% use of dithering.

Research on masking of signal by noise is kind of 101 of psychoacoustics. What we already established is that I'm more interested in how practically encountered noise is masking practically encountered quiet music passages. I do realize that masking thresholds for specially constructed signals and noise patterns may be different. 

To be sure we are on the same page. Class-D amplifiers are analog amplifiers. They are not digital. I will correct you. Perception of distortion. You are making an assumption of something that is there, without proof it is there.

Yes an no. Implemented with analog circuitry, yes. But, at some point inside a class-D amp analog signal is transformed into a sequence of discrete +V and -V segments, starting and ending at analog time boundaries.

So, it is kind of a hybrid. Analog in time domain throughout, discrete at an intermediate stage in amplitude domain. Not what most people would call classically digital, yet not quite purely analog either.

Which theory is it that you are using? I noted many flaws in your understanding of critical elements of digital audio, and assertions that are also incorrect. I have already falsified your theory.

I see it differently. The old paradigm is falsified by phenomena for which it gives invalid predictions. For instance, according to the old paradigm, LPs shall be long gone, the way of cassette tape recorders and VCR video tapes. Yet LPs persisted, and the classic paradigm produces no convincing explanation as to why.

New paradigm not only explains why LPs persisted for so long, but also specifically predicts what they'll be replaced with. To repeat once again, to the best of my understanding, eventually they'll be replaced by digital recordings with information density equal to, or higher than, those of PCM 192/24 and DSD128 formats.

Perhaps not important to this discussion, but 16/44.1 is a delivery format. From what my colleagues tell me, is has not been used as a digitization format in decades, and depending on your point of demarcation, it has not been used as a digitization format since the 1980’s, as all the hardware internally samples at a higher rate and bit depth.

Yet another phenomenon not explained by the old paradigm.

According to the old paradigm, 16/44.1 format shall be sufficient for capturing and delivering any type of music, yet in practice all those "pesky producers and sound engineers", for some mysterious reasons, want to use digital formats providing higher information density.

The new paradigm not only qualitatively explains this phenomenon, but also accurately describes the numerical parameters of the formats that were found sufficient by trial and error by many highly qualified practitioners.

The new paradigm also explains why gear providing even higher information densities, easily available these days (e.g. I own several nice 32/768 ADC/DACs), isn't as widely used at its highest settings in practical music production.

 

 

@thespeakerdude

If there is any interest, this is probably the best single article I have discovered that explains digital audio. It is not light reading nor heavy reading. Dan, who put it together obviously put a lot of time into it. It is almost 20 years old so comments about processing power are no longer relevant, but everything else is. I have come across many articles on digital audio written by less technical people. They get the basics right, but they often make mistakes and they never go into the depth that this article provides. You may need to read it 2 or 3 times to understand well enough, but if you do, it will dispel a lot of misconceptions about digital audio.

https://lavryengineering.com/pdfs/lavry-sampling-theory.pdf

If you have any questions about the article I will try to answer them.

Thank you for referring this document. Oldie but goodie. Excellent for illustrating the older paradigm vs newer paradigm.

Let’s look at the graph there marked with "Let us begin by examining a band limited square wave". That’s what I meant by saying that quickly changing signals start looking ragged when band limited. The document goes into a detailed explanation of why this is happening. For a briefer explanation, one can peruse a Wikipedia article about Gibbs Phenomenon.

Note that what we see on a square wave is an extreme example. The underlying mechanism of the Gibbs Phenomenon is in action on any harmonic signal with changing magnitude - just to a lesser degree, depending on ratio between characteristic time of the harmonic components magnitude change and sampling interval.

The concentrated difference between the older and the newer paradigm is this:

Subscribers to the old paradigm believe that the wiggles we see on charts like that don’t ever affect perception of sound quality, as long as the signal to be band-limited is "music", and the upper boundary is set at 22 KHz.

The new paradigm tells us that it depends. That certain wiggles may affect perceived sound quality of certain music signals band-limited under the conditions above, for certain listeners.

By the way, 0.1% THD corresponds to a width of one pixel on a typical laptop display, if a graph like that is enlarged to fill the whole screen.

Basically, we can hear a difference that we can barely see on a graph.

If one sees any visual difference of a band-limited music signal compared to the original one, this should arise strong suspicion that such difference may be heard.

However, my professors, from leading European universities, and their teaching assistants, had other opinions, giving me straight As on all courses related to Fourier Analysis and DSP.

Call me skeptical. No that is not right. I flat out don’t believe you are telling the truth.

 

Yet there is more, which came mostly from research conducted by others over past three decades. Unfortunately, too much of it is still widely dispersed in numerous peer-reviewed papers, rather than concentrated in a few engineering handbooks.

Well isn’t that convenient. Hate ta break it to ya but I learned all the theory in an applied math course. Because little of this has to do with engineering. It’s applied math.

 

This depends greatly on the nature of the band-limiting filter used.

That is totally irrelevant to what you replied to.

 

Implemented with analog circuitry, yes. But, at some point inside a class-D amp analog signal is transformed into a sequence of discrete +V and -V segments, starting and ending at analog time boundaries.

Wrong. Very wrong.

 

 

for some mysterious reasons, want to use digital formats providing higher information density.

For processing not delivery just like I said

 

(e.g. I own several nice 32/768 ADC/DACs),

No such thing as a 32 bit ADC or DAC. Purely a data standard ... And a marketing ploy. Maybe you will find some rounding errors in those bottom 8-9 bits.

 

By the way, 0.1% THD corresponds to a width of one pixel on a typical laptop display, if a graph like that is enlarged to fill the whole screen.

I am only storing that last paragraph for posterity.

 

Shhhh don’t tell anyone, but vinyl is terrible at <20hz and pretty awful in practice >20khz .... But I can’t hear it so I don’t care

If anyone cares my patience is officially at an end :-)

 

Nyquist is not a paradigm or a guess about how things work. It is not about engineering. It is a well understood, well researched, to this point not disproven mathematical theory. Nothing in the last 30 years has changed that. How it is applied is also well understood including translating real world limitations to accuracy. Those are not engineering principles, they are math principles.

This has been one of the deepest technical discussions I’ve read on Audiogon. Thanks to Fair and TheSpeakerDude for sharing their viewpoints here.

I watched the video posted earlier to explain digital and that helped me to understand some of these recent expositions.

@Fair can you summarize on this issue?

@johnread57 ,

 

I did not present an opinion. I presented verifiable, researched, well understood, mathematical facts. Facts not disputed by those with the deepest understanding of the underlying math, and those able to adapt the math to practical implementation.

 

Below is an opinion. It misinterprets personal opinion, narrow market popularity, and different to "something". That something is only described in easily falsified claims, falsified with math, not an appeal to narrow market popularity.

Perhaps @Fair, can enlighten with at least 2 or 3 of these research papers he claims are hard to find? A new paradigm with 3 decades of research that legitimately calls into question all current signal processing and hearing knowledge should have many available sources to reference.

 

I see it differently. The old paradigm is falsified by phenomena for which it gives invalid predictions. For instance, according to the old paradigm, LPs shall be long gone, the way of cassette tape recorders and VCR video tapes. Yet LPs persisted, and the classic paradigm produces no convincing explanation as to why.

@dsnyder0cnn

 

you are correct, I thought of that afterwards.

I should have said "from the finished product"

I can also add, the whole vinyl pressing process doesn't fix, alter, improve, up or down sample the grooves

 

@johnread57

@thespeakerdude

I did not present an opinion. I presented verifiable, researched, well understood, mathematical facts. Facts not disputed by those with the deepest understanding of the underlying math, and those able to adapt the math to practical implementation.

 

Below is an opinion. It misinterprets personal opinion, narrow market popularity, and different to "something". That something is only described in easily falsified claims, falsified with math, not an appeal to narrow market popularity.

Perhaps @Fair, can enlighten with at least 2 or 3 of these research papers he claims are hard to find? A new paradigm with 3 decades of research that legitimately calls into question all current signal processing and hearing knowledge should have many available sources to reference.

>>> I see it differently. The old paradigm is falsified by phenomena

>>> for which it gives invalid predictions.

>>> For instance, according to the old paradigm,

>>> LPs shall be long gone, the way of cassette tape recorders

>>> and VCR video tapes. Yet LPs persisted,

>>> and the classic paradigm produces no convincing explanation

>>> as to why.

Very well. This 2016 review  A Meta-Analysis of High Resolution Audio Perceptual Evaluation contains references to

"18 published experiments for which sufficient data could be obtained ... providing a meta-analysis involving over 400 participants in over 12,500 trials"

Conclusion is:

"Results showed a small but statistically significant ability of test subjects to discriminate high resolution content, and this effect increased dramatically when test subjects received extensive training."

 

Pair of charts below illustrates my statement about the growing LPs popularity and vanishing CDs purchases. In a wider context: digital streaming appears to be decimating CD sales, yet LPs have not been affected by that (or maybe even helped?).

CD sales in the US

LP sales in the US

@johnread57

@Fair can you summarize on this issue?

Will do, referring to questions in the original post.

It’s obvious right? They sound different, and I’m sure they measure differently.

Yes and yes.

Well we know the dynamic range of cd’s is larger than vinyl.

This is debatable.

But do we have an agreed description or agreed measurements of the differences between vinyl and digital?

No. Because there are multiple - at least two - paradigms, defining certain important characteristics like dynamic range differently.

I know this is a hot topic so I am asking not for trouble but for well reasoned and detailed replies, if possible. And courtesy among us. Please.

Tried my best to abide.

I’ve always wondered why vinyl sounds more open, airy and transparent in the mid range. And of cd’s and most digital sounds quieter and yet lifeless than compared with vinyl. YMMV of course, I am looking for the reasons, and appreciation of one another’s experience.

In the first paradigm, CD is superior in sound quality to LP. Digitizing CDs and delivering their content via online streaming should have killed off LPs.

In the second paradigm theoretical framework, LP occupies a middle ground between CD and such perceptually transparent digital formats as PCM 192/24 and DSD128.

Correspondingly, the second paradigm maintains that CDs, physical or digitized, are not capable of superseding LPs. But perceptually transparent digital formats likely will.

I’ve always wondered why vinyl sounds more open, airy and transparent in the mid range. And of cd’s and most digital sounds quieter and yet lifeless than compared with vinyl.

Most studios record fully digital nowadays. When streamed lossless via Tidal or Qubuz you get this source straight to your DAC. Assuming it’s a capable DAC you get the best representation possible.

To make a vinyl, there are countless extra steps:

- audio compression and RIAA to limit the low frequency groove amplitude.

- mechanical process of cutting the master disk

- chemical / mechanical process of pressing a disk

- wear and tear of the (master) disk

- added wow and flutter of the turntable

- mechanical / electrical process of pick up element

- Reverse RIAA correction and pre amplification of pick up voltage

And now all of a sudden it sounds more open, airy, and transparent?

 

I know especially if it’s a MOFI…

Yet it sounds different often, not always but often enough for me and many others to notice it.

 

That said I was just trying to understand why…

Yes, given all the added steps it will sound different. And to some it may even sound nicer. Tastes differ.

Let's talk about this subject just from a musical standpoint.  In classical music, when a composer writes a score, he or she notates dynamics (forte, pianissimo, etc) to denote how loud or soft a passage is to be played.  These dynamic markings are as much a part of the musical score as the melody or harmony.  By definition, vinyl is a compressed format and cannot completely express loud or soft the way digital can.  This is not an issue in most rock music, because there are not the dynamic markers in rock charts.  In jazz, very few artists put dynamics into their performances.  Art Blakey was one who made his ensemble play with a large dynamic range (I was lucky enough to see his band live before he passed away).  This is not an attempt to plug or criticize either vinyl or digital, but to what audio should strive for from a purely musical perspective.  I hope anyone reading this gets a chance to sit front row to hear a great symphony orchestra, so you can really hear the dynamics I'm talking about.