MQA creator Bob Stuart answers questions.

[Sergei]

They mention 96kHz ... 96/16 as a fomat ? Is it perhaps more likely that they are talking about 24 bits ?
Isn't that buried in noise in any practical situation ?

I think what happened is that they calibrated their formulas and graphs to LSB measure. The concrete bit depth becomes less important then.

I can find plenty of anecdotes online and offline made by 'notable individuals' as well as noobs of people hearing things... well claiming to hear things.

As to what experienced audio engineers are hearing, I have to give them that: after working for two, three, or four decades with sounds every working day, they hear a lot more nuances than an average consumer does.

A related personal anecdote. I was once in a high-grade studio, being graciously provided with an opportunity to play music of my choosing, for well over an hour, including MQA-encoded tracks.

There were two speaker systems in the mixing room: one which was theoretically in my price range - I was salivating over it for quite a while - yet hadn't actually bought it yet; the other system was way bigger and more expensive.

It was shockingly unexpected how much cleaner the more expensive system sounded to me. The other one was noticeably distorting. I was humbled. I eventually ended up buying a "little brother" of the more expensive system, made by a different company, but similarly clean-sounding.

So, IMHO the combination of talent, experience, and better gear does give the professional sound engineers a better "resolving power" for analyzing the full 24-bit range.

 

[Sergei]

Since I know the LSB is so important to you... how do you feel knowing the last few LSB's have been removed by MQA designers and are replaced by 'folded lossy HF energy' in a 'noise alike' guise ?

I feel like this is just yet another lossy format. The jury is still out on whether it is better than Vorbis in a mass-streaming context .

 

[solderdude]

I think what happened is that they calibrated their formulas and graphs to LSB measure. The concrete bit depth becomes less important then.

So there is no important difference between the actual level of an LSB in a 16 bit or 24 bit format acc. to you ?


You compare an audio engineer to an average consumer ?
Yes, that will fall in favor of the engineer for sure.
And yes I have read many porkies from sound engineers as well and also some rare ones that actually know what they are talking about.
Some of the latter are even members here.

I have heard great speakers in studios (conditioned rooms and amateur ones) as well as in hifi shops and at consumers and ended up building my own speakers (including electrostats that do not have tensioned membranes).
How's that for a story ...

 

[Cosmik]

@Sergei

Way back on page 3 of this discussion, @Sal1950 said:

You can't take a master analog tape done in 1960, transfer it to 24/192 and call it a "high resolution recording". That's a scam put forth simply in the name of $, once again being able to resell all the old catalogs of music with a promise of better SQ. There's nothing on those tapes that can't be captured at Red Book.

In reply you said:

I disagree. A studio tape can capture the frequency range of 10Hz to 20KHz without anti-aliasing filter that CD requires. Dynamic range is sufficient for most music, which rarely needs more than 30 dB. And timing of the transients is virtually perfect. This timing can't be perfect on a CD.

There followed a discussion about sample rates seemingly around an assumption that the finest timing that can be achieved with digital audio is the inverse of its sample frequency.

In the Stuart & Craven paper you just linked to they talk about the problems with analogue recording systems:

In analog systems, simple examples include level dependent noise from the particles on magnetic tape [7] (particularly noticeable at low frequencies) and Barkhausen noise in transformers, microphones, tape heads or other ferrous-cored inductive components. Such modulation noise impacts transparency and tends to impair precise reproduction of low-frequencies or of spatial cues including of reverberation or instrument location.

And isn't there a 'sampling' element to the way tape bias works, too..?

The analog tape recording process actually samples at two rates: twice the bias frequency (as every half cycle drops to the level where the signal is retained near the trailing edge of the record gap) and at the random rate of the asparity noise. Asparity noise is produced by the statistical distribution of oxide particles in the record head gap vs time. This noise is different from the simple fixed thermal noise of an amplifier, which stays at one level, regardless of the level of the signal. If you put a tone through a tape recorder and watch the output on a spectrum analyzer, you will see that as the signal level is raised the noise rises up around it in a mountain, with peaks at the odd harmonics. The truth of the matter is that tape recording is shaped noise. It is a non-linear transfer process that produces noise-like sidebands for every frequency in a complex signal. This is a major component of the tape sound.

So I don't think analog tape is virtually perfect in anything at all.

The goalposts seem to be shifting. Are you still of the opinion that digital audio (certainly CD) is inherently worse than analogue tape in terms of timing? It seems to me that if all we have to have to do is to be better than the reality of analogue tape as you suggested earlier, then even non-high res digital audio has surely got to be there already.

 

[Blumlein 88]

That's a good insight about the 'illegal' signals. I agree. I also agree that 48/24 appears sufficient for reproducing perceptually transparently a limited number of natural music instruments and vocals - for me personally, up to about four.

Continuing on the Sampling Theorem mathematical perfection vs reality. The Theorem only works perfectly if the sampled values are captured with perfect precision, and the reconstruction is done with perfect precision as well. Stuart and Craven (https://secure.aes.org/forum/pubs/journal/?elib=20457) illustrate imperfections caused by the process of quantization, how the imperfections are affected by various types of dithering, and - rare to see in an audio publication - their impact on the accuracy in time domain.

The graphs below demonstrate how doubling the sample rate accelerates the convergence between the true value of signal and what was imperfectly captured through the quantization process. Given enough samples, the variance becomes very small: that's what the well respected gurus of the Sampling Theorem describe to us when they talk about the perfection of digital audio in their video tutorials.

However, such perfection isn't achieved right away. Qualitatively, figuring out the true shape of a signal, when the values of samples are not captured perfectly, requires averaging over time. If the signal doesn't change its shape too much during the characteristic time of averaging, the process converges. Because of that, quantization works very well for a single sinusoid with constant amplitude - a staple in the Sampling Theorem video tutorials.

If we add a second sinusoid, we now need more samples to figure out the shapes of two of them, mixed together, with the same precision as we did for one sinusoid. Qualitatively, we need twice as many samples, yet this is not exactly true, because the two sinusoids effectively start dithering each other, resulting in a quicker conversion toward true value. Still, definitely more samples are needed to achieve the same level of accuracy. Which, at a given sample rate, means more time.

As we add more and more signal components, we need to add more and more samples, in order to capture the signal in such a way that we can reconstruct if with a required level of precision. The graphs below depict averages over simulations of signals meant to approximate what is encountered in real music. You can see that the number of samples required to converge to a desired level of precision (let's say, of about 0.3 units on these graphs) is not small - on the order of thousands for the lower sampling rate. The higher the sampling rate, the quicker such convergence is achieved.

This effect, qualitatively, hints at what might be going on when a complex music - with hundreds of sinusoids exhibiting quickly varying amplitudes and frequencies, intermixed with transients - is quantized. If the sampling rate and bit depth are not high enough, the components of music may never converge close enough to to their true values during an intense music passage. Then the reconstruction - however perfect - results in an analog signal which kinda sorta resembles the fragment of original symphony, yet sounds decidedly fake.

The right question to ask at this point is - how far do we need to go with the sampling rate and bit depth for the music to sound absolutely transparent? And the right answer is "It depends": on particular music piece, on particular sound delivery system, and on particular person, including the person's neurophysiological condition at a particular moment.

Sound delivery systems are not perfect. Human hearing systems are not perfect either: even when presented with live music, we can't sometimes even approximately perceive what a particular musician is playing at a particular moment. So, there is a practical limit to the "digital perfection", beyond which the other inherent imperfections start dominating the total subjective imperfection level.


View attachment 27753

So reading thru this paper I found this statement:


However, over many years of working on this topic, we have anecdotes from more than one source that a new algorithm or piece of equipment has been judged sonically “not quite right” and that, on investigation, an undithered quantization has been found around the 22nd, 23rd or even 24th bit; and that smiles returned to the listeners’ faces when this was corrected.

 

[Sergei]

There followed a discussion about sample rates seemingly around an assumption that the finest timing that can be achieved with digital audio is the inverse of its sample frequency.

Depends on the definition of timing. Timing of (A) detecting a peak of a sinusoid with frequency below the Nyquist? Or (B) detecting vs not detecting a short pulse with duration comparable to the sampling interval?

With (A), if the peak of the sinusoid happens to arrive in between the samples, it will be still reconstructed to the analog output.

With (B), if the pulse happens to fit entirely between the samples, nothing will be captured. Then there is nothing to reconstruct to the analog output.

In the Stuart & Craven paper you just linked to they talk about the problems with analogue recording systems:
...
So I don't think analog tape is virtually perfect in anything at all.

It's been a long time since I owned a reel-to-reel apparatus. It wasn't such a long time since I spoke with an engineer who wrote software for restoring classical music from old tapes. He wasn't getting too deep into the details, as it was an informal conversation, without NDA signed. Yet I got the gist.

Later I looked up the subject in research papers. There is much that can be done, and is being done, to restore the music from such tapes. The basic idea is that the algorithm uses information from entire record, or even from several records made in the same concert hall with same instruments. The instruments are recognized, their sound profiles are built, and the performance is automatically transcribed.

Then the performance is re-created, compared to the tape record, the delta analyzed for actually being a noise, and the process may repeat many times, with human in the loop at later stages. Lately, deep learning has been employed to do this rather well. So, the restored performance may not be technically 100% authentic, yet it sounds darn good, worthy of releasing in 192/24.

Are you still of the opinion that digital audio (certainly CD) is inherently worse than analogue tape in terms of timing?

Let's see. 30 ips = 0.0254 x 30 = 0.762 m/s. A γ-Fe2O3 particle looks like a needle, with average size 0.5 x 0.1 micrometer. The density of particles on a tape, compared to ideal case, was usually targeted at ~60%.

Let's assume we got an average, not such a great quality tape. All the "needles" happened to align longitudinally, and their density is 50%. So, just one particle per micrometer. Or 1,000,000 per meter. 0.762 m/s x 1,000,000 = 762,000 particles/second.

Not so shoddy! The temporal density of particles is ~17 times higher than the density of CD samples. So, inherently, yes, CD is worse in terms of timing than a 30 ips old-school studio tape. A reel-to-reel recorder of the days past wasn't likely to utilize the full temporal resolution of the tape though, so the practical advantage may not has been as large as the inherent one.

It seems to me that if all we have to have to do is to be better than the reality of analogue tape as you suggested earlier, then even non-high res digital audio has surely got to be there already.

I believe the temporal and amplitude resolutions of all analog media is under-appreciated. The average size of emulsion-polymerized vinyl "particle" is comparable to that of γ-Fe2O3, at ~0.2 micrometers. If you take an average width of a vinyl track as 60 micrometers, you can fit 60 / 0.2 = 300 of them across a track. I'm not familiar with the finer details of vinyl pressing: perhaps the particles can form even finer structure when they are melted?

The point is: the high-end analog formats kept evolving until they reached perceptual sonic transparency, as it was understood at the time. They do have inherent disadvantages compared to digital: higher levels of distortions, and higher levels of noise. However, human hearing system deals with certain types of distortions, and noise in general, quite well: often they can be heard, but not intrusively enough to distract from the enjoyment.

The 44/16 format is quite good too, until a sophisticated enough music fragment overwhelms its bit throughput. 192/24 has a bit throughput (192 x 24) / (44.1 x 16) = 6.5 times higher than the 44/16, which makes it not as easy to overwhelm. Professional audio engineers here will correct me if I'm wrong, yet it is my understanding that 192/24 master is generally considered being "just like a good tape, but without distortions and noise".

 

[SIY]

I see that your grasp of analog equals your deep knowledge of digital.

 

[amirm]

Let's assume we got an average, not such a great quality tape. All the "needles" happened to align longitudinally, and their density is 50%. So, just one particle per micrometer. Or 1,000,000 per meter. 0.762 m/s x 1,000,000 = 762,000 particles/second.

Not so shoddy! The temporal density of particles is ~17 times higher than the density of CD samples.

Yet, it is noisier and sounds worse than a CD. I can readily hear tape hiss on my Reel to Reel. Can you not?

 

[amirm]

Not so shoddy! The temporal density of particles is ~17 times higher than the density of CD samples.

A particle is not the same as a digital audio sample. But maybe you show us how it can capture the full sample value as represented by 16 bit digital sample with a single magnetic particle's orientation.

 

[solderdude]

Most tape recorders don't go past 25kHz... not even the 30ips ones. The problem with the latter lies in the bottom end of the frequency range.

The limits of tape is not the amount and size of the magnetic particles but the gap of the recording and playback head, the amount of bias, the type of tape, the azimuth difference between reocrding and playback head and the used low pass filter and electronics. Your analysis of the tape is completely incorrect.
You really need to learn about analog and digital recording and reproduction.

 

[Cosmik]

Depends on the definition of timing. Timing of (A) detecting a peak of a sinusoid with frequency below the Nyquist? Or (B) detecting vs not detecting a short pulse with duration comparable to the sampling interval?

With (A), if the peak of the sinusoid happens to arrive in between the samples, it will be still reconstructed to the analog output.

With (B), if the pulse happens to fit entirely between the samples, nothing will be captured. Then there is nothing to reconstruct to the analog output.


It's been a long time since I owned a reel-to-reel apparatus. It wasn't such a long time since I spoke with an engineer who wrote software for restoring classical music from old tapes. He wasn't getting too deep into the details, as it was an informal conversation, without NDA signed. Yet I got the gist.

Later I looked up the subject in research papers. There is much that can be done, and is being done, to restore the music from such tapes. The basic idea is that the algorithm uses information from entire record, or even from several records made in the same concert hall with same instruments. The instruments are recognized, their sound profiles are built, and the performance is automatically transcribed.

Then the performance is re-created, compared to the tape record, the delta analyzed for actually being a noise, and the process may repeat many times, with human in the loop at later stages. Lately, deep learning has been employed to do this rather well. So, the restored performance may not be technically 100% authentic, yet it sounds darn good, worthy of releasing in 192/24.


Let's see. 30 ips = 0.0254 x 30 = 0.762 m/s. A γ-Fe2O3 particle looks like a needle, with average size 0.5 x 0.1 micrometer. The density of particles on a tape, compared to ideal case, was usually targeted at ~60%.

Let's assume we got an average, not such a great quality tape. All the "needles" happened to align longitudinally, and their density is 50%. So, just one particle per micrometer. Or 1,000,000 per meter. 0.762 m/s x 1,000,000 = 762,000 particles/second.

Not so shoddy! The temporal density of particles is ~17 times higher than the density of CD samples. So, inherently, yes, CD is worse in terms of timing than a 30 ips old-school studio tape. A reel-to-reel recorder of the days past wasn't likely to utilize the full temporal resolution of the tape though, so the practical advantage may not has been as large as the inherent one.

I believe the temporal and amplitude resolutions of all analog media is under-appreciated. The average size of emulsion-polymerized vinyl "particle" is comparable to that of γ-Fe2O3, at ~0.2 micrometers. If you take an average width of a vinyl track as 60 micrometers, you can fit 60 / 0.2 = 300 of them across a track. I'm not familiar with the finer details of vinyl pressing: perhaps the particles can form even finer structure when they are melted?

The point is: the high-end analog formats kept evolving until they reached perceptual sonic transparency, as it was understood at the time. They do have inherent disadvantages compared to digital: higher levels of distortions, and higher levels of noise. However, human hearing system deals with certain types of distortions, and noise in general, quite well: often they can be heard, but not intrusively enough to distract from the enjoyment.

The 44/16 format is quite good too, until a sophisticated enough music fragment overwhelms its bit throughput. 192/24 has a bit throughput (192 x 24) / (44.1 x 16) = 6.5 times higher than the 44/16, which makes it not as easy to overwhelm. Professional audio engineers here will correct me if I'm wrong, yet it is my understanding that 192/24 master is generally considered being "just like a good tape, but without distortions and noise".

Part of the problem with digital audio is that it is natural to analyse it mathematically. It can be plotted in graphs and written down in formulae to any arbitrary resolution. You can always keep zooming in on it until the errors look horrendous. So you then add an extra 4 bits. But then you keep zooming in until it looks just the same. And so on.

With analogue that isn't possible because of the high absolute levels of (modulated) noise, distortion, wow & flutter, print-through, etc. They're not analysable mathematically. And if you zoom in there is no signal at even 16-bit resolution; just massive amounts of 'sludge'. And if there is no discernible signal, there can be no errors! What's worse? Nature's own smooth, emollient sludge or those nasty, jagged, synthetic, mathematical errors that we just know are there even if we can't see them.

 

[Aprude51]

Actually, my primary objective is advancing my own understanding...

It might be worth reflecting on the relationship between this attitude and the lack of progress being made here. You‘re quick to conclude that your individual understanding has progressed beyond that of subject matter experts and established science in general.

As an aside, I find it funny that Soniclife predicted the direction of this thread 24 pages ago:

Montgomery's law. When an ASR poster has to be pointed at Montgomery's video the quality of the thread will trend towards zero.

 

[March Audio]

I don't think they are quacks ... shrude business men... perhaps.

Some of the evidence points towards the launch of MQA to being money driven.
I actually quite like the novel idea of folding ultrasonics and asking money to 'correct it for you'

Since I know the LSB is so important to you... how do you feel knowing the last few LSB's have been removed by MQA designers and are replaced by 'folded lossy HF energy' in a 'noise alike' guise ?

This. It is a simply an exercise in monetising music delivery.

 

[March Audio]

Depends on the definition of timing. Timing of (A) detecting a peak of a sinusoid with frequency below the Nyquist? Or (B) detecting vs not detecting a short pulse with duration comparable to the sampling interval?

With (A), if the peak of the sinusoid happens to arrive in between the samples, it will be still reconstructed to the analog output.

With (B), if the pulse happens to fit entirely between the samples, nothing will be captured. Then there is nothing to reconstruct to the analog output.


It's been a long time since I owned a reel-to-reel apparatus. It wasn't such a long time since I spoke with an engineer who wrote software for restoring classical music from old tapes. He wasn't getting too deep into the details, as it was an informal conversation, without NDA signed. Yet I got the gist.

Later I looked up the subject in research papers. There is much that can be done, and is being done, to restore the music from such tapes. The basic idea is that the algorithm uses information from entire record, or even from several records made in the same concert hall with same instruments. The instruments are recognized, their sound profiles are built, and the performance is automatically transcribed.

Then the performance is re-created, compared to the tape record, the delta analyzed for actually being a noise, and the process may repeat many times, with human in the loop at later stages. Lately, deep learning has been employed to do this rather well. So, the restored performance may not be technically 100% authentic, yet it sounds darn good, worthy of releasing in 192/24.


Let's see. 30 ips = 0.0254 x 30 = 0.762 m/s. A γ-Fe2O3 particle looks like a needle, with average size 0.5 x 0.1 micrometer. The density of particles on a tape, compared to ideal case, was usually targeted at ~60%.

Let's assume we got an average, not such a great quality tape. All the "needles" happened to align longitudinally, and their density is 50%. So, just one particle per micrometer. Or 1,000,000 per meter. 0.762 m/s x 1,000,000 = 762,000 particles/second.

Not so shoddy! The temporal density of particles is ~17 times higher than the density of CD samples. So, inherently, yes, CD is worse in terms of timing than a 30 ips old-school studio tape. A reel-to-reel recorder of the days past wasn't likely to utilize the full temporal resolution of the tape though, so the practical advantage may not has been as large as the inherent one.

I believe the temporal and amplitude resolutions of all analog media is under-appreciated. The average size of emulsion-polymerized vinyl "particle" is comparable to that of γ-Fe2O3, at ~0.2 micrometers. If you take an average width of a vinyl track as 60 micrometers, you can fit 60 / 0.2 = 300 of them across a track. I'm not familiar with the finer details of vinyl pressing: perhaps the particles can form even finer structure when they are melted?

The point is: the high-end analog formats kept evolving until they reached perceptual sonic transparency, as it was understood at the time. They do have inherent disadvantages compared to digital: higher levels of distortions, and higher levels of noise. However, human hearing system deals with certain types of distortions, and noise in general, quite well: often they can be heard, but not intrusively enough to distract from the enjoyment.

The 44/16 format is quite good too, until a sophisticated enough music fragment overwhelms its bit throughput. 192/24 has a bit throughput (192 x 24) / (44.1 x 16) = 6.5 times higher than the 44/16, which makes it not as easy to overwhelm. Professional audio engineers here will correct me if I'm wrong, yet it is my understanding that 192/24 master is generally considered being "just like a good tape, but without distortions and noise".

You still haven't grasped the basics of bandwidth limited recording.

This doesn't just apply to digital audio, it applies to analogue. If a transient is of higher frequency than the bandwidth of the system it won't be recorded, be it an analogue or digital system.

Tape also suffers from inherent speed instability which significantly affects the timing of transients /signals that are in band.

This is really basic stuff and you are arguing beyond your understanding. In fact it's clear you have a fundamental lack of understanding of the subject.

The "bullshit baffles brains" approach you are using in this thread is entirely ineffective. You need to address your dogma before this can turn into a constructive conversation.

 

[RayDunzl]

What's worse? Nature's own smooth, emollient sludge or those nasty, jagged, synthetic, mathematical errors that we just know are there even if we can't see them.

I had the task of ripping, for an acquaintance, an LP, last night, for the first time.

Here's the first 10 seconds. No additional tools have been applied, and the magnification is about x10:

Legend:

1 - stylus approaches the disk - purely electronic noise
2 - stylus rides the flat waiting for the groove to come around
3 - stylus meets groove
4 - initial silent groove
5 - violinists begin scratching their rosinous horsehair across the metal wound synthetic sheepgut.




-dBfs display:

The groove silence energises about the first 16 of the 24 bits available...

 

[Blumlein 88]

Depends on the definition of timing. Timing of (A) detecting a peak of a sinusoid with frequency below the Nyquist? Or (B) detecting vs not detecting a short pulse with duration comparable to the sampling interval?

With (A), if the peak of the sinusoid happens to arrive in between the samples, it will be still reconstructed to the analog output.

With (B), if the pulse happens to fit entirely between the samples, nothing will be captured. Then there is nothing to reconstruct to the analog output.


It's been a long time since I owned a reel-to-reel apparatus. It wasn't such a long time since I spoke with an engineer who wrote software for restoring classical music from old tapes. He wasn't getting too deep into the details, as it was an informal conversation, without NDA signed. Yet I got the gist.

Later I looked up the subject in research papers. There is much that can be done, and is being done, to restore the music from such tapes. The basic idea is that the algorithm uses information from entire record, or even from several records made in the same concert hall with same instruments. The instruments are recognized, their sound profiles are built, and the performance is automatically transcribed.

Then the performance is re-created, compared to the tape record, the delta analyzed for actually being a noise, and the process may repeat many times, with human in the loop at later stages. Lately, deep learning has been employed to do this rather well. So, the restored performance may not be technically 100% authentic, yet it sounds darn good, worthy of releasing in 192/24.


Let's see. 30 ips = 0.0254 x 30 = 0.762 m/s. A γ-Fe2O3 particle looks like a needle, with average size 0.5 x 0.1 micrometer. The density of particles on a tape, compared to ideal case, was usually targeted at ~60%.

Let's assume we got an average, not such a great quality tape. All the "needles" happened to align longitudinally, and their density is 50%. So, just one particle per micrometer. Or 1,000,000 per meter. 0.762 m/s x 1,000,000 = 762,000 particles/second.

Not so shoddy! The temporal density of particles is ~17 times higher than the density of CD samples. So, inherently, yes, CD is worse in terms of timing than a 30 ips old-school studio tape. A reel-to-reel recorder of the days past wasn't likely to utilize the full temporal resolution of the tape though, so the practical advantage may not has been as large as the inherent one.

I believe the temporal and amplitude resolutions of all analog media is under-appreciated. The average size of emulsion-polymerized vinyl "particle" is comparable to that of γ-Fe2O3, at ~0.2 micrometers. If you take an average width of a vinyl track as 60 micrometers, you can fit 60 / 0.2 = 300 of them across a track. I'm not familiar with the finer details of vinyl pressing: perhaps the particles can form even finer structure when they are melted?

The point is: the high-end analog formats kept evolving until they reached perceptual sonic transparency, as it was understood at the time. They do have inherent disadvantages compared to digital: higher levels of distortions, and higher levels of noise. However, human hearing system deals with certain types of distortions, and noise in general, quite well: often they can be heard, but not intrusively enough to distract from the enjoyment.

The 44/16 format is quite good too, until a sophisticated enough music fragment overwhelms its bit throughput. 192/24 has a bit throughput (192 x 24) / (44.1 x 16) = 6.5 times higher than the 44/16, which makes it not as easy to overwhelm. Professional audio engineers here will correct me if I'm wrong, yet it is my understanding that 192/24 master is generally considered being "just like a good tape, but without distortions and noise".

Try listening to some piano recordings with long sustained notes on RTR or LP. Do the same on CD. Then get back to me on this analog timing business.

 

[Sergei]

Most tape recorders don't go past 25kHz... not even the 30ips ones. The problem with the latter lies in the bottom end of the frequency range.

The limits of tape is not the amount and size of the magnetic particles but the gap of the recording and playback head, the azimuth and the used low pass filter and electronics. Your analysis of the tape is completely incorrect.
You really need to learn about analog and digital recording and reproduction.

I learned about it back in the 1980s: https://en.wikipedia.org/wiki/Tape_bias. Contrary to popular opinion, the gap of recording head is not the limiting factor, the gradient of magnetic field at the trailing edge of the recording head is. Yes, nearly-perfect azimuth is important, and setting it on a machine without a servo-adjuster could be an unpleasant chore.

The gap at playback head, yes, is a limiting factor. We replaced worn out playback heads much more often than the recording heads. I recall the laser-cut gaps being on the order of several micrometers on high-end machines back then, and https://ccrma.stanford.edu/courses/192a/Lecture7-Magnetic_recording.pdf confirms that.

I'm taking about serious machines from the 1970s. Like Ampex ATR-100. See page 32 of https://www.americanradiohistory.com/Archive-DB-Magazine/70s/DB-1976-12.pdf, and page 36 of https://www.americanradiohistory.com/Archive-DB-Magazine/70s/DB-1977-02.pdf. Note the bias frequency: 432 KHz. Note servo motors power: 1/4 HP. Note the discussion about phase coherency and testing with square waves.

ATR-100 SNR spec is not entirely clear: I've seen 68, 72, and 80 dB at 30 ips (depending on tape material and weighting?). Was this that much worse than the PCM decks of that era, such as 13-bit Sony PCM-1: http://www.thevintageknob.org/sony-PCM-1.html? In its marketing materials, Sony only dared to compare the PCM-1 with a 15 ips reel-to-reel.

Moving on to 1980s, consider Studer A820: http://www.theaudioarchive.com/TAA_Tape_Studer_A820.htm. SNR up to 77 dB (A-weighted). For a while, those monsters were still competitive with the direct PCM recorders. Yes, as I mentioned in the previous post, distortions and noise were always their weak spots. Yet were they as bad as those of the consumer-grade tape recorders? Clearly not.

What gets me is people not getting that analog SNR is not the same as digital SNR. In the analog case, as long as the noise floor at -77 .. -68 dB is masked by music, the music itself doesn't really have the amplitude resolution of just 13 or 14 bits as so many people think. It is analog: you can digitize it with 24 bits and this will be meaningful.

Similarly with timing. Yes, electronics band-limits the signal, typically to 22 KHz on high-end machines. Yet again, being an analog system, it doesn't need the 10-20 ms for the dithered PCM samples to catch up with the true signal value with a precision of ~0.2 LSB, after a signal's component "jumps": what's recorded on the tape just "jumps" too, straight to a very close approximation of the true value.

Of course, if you just plug the output of a reel-to-reel deck into DAC and push play and record buttons, you are going to record the hiss on silent intervals. Gate it out, digitally if you must. The real-life music's dynamic range rarely exceeds 45 dB anyway. IMHO, 192/24 PCM carefully captured from a high-end analog tape master can be better sounding than a CD.

 

[solderdude]

What gets me is people not getting that analog SNR is not the same as digital SNR. In the analog case, as long as the noise floor at -77 .. -68 dB is masked by music,

The solution for you is really simple. Playback your digital recordings (the ones that have a higher S/N ratio from the studio recording) and mix some analog noise of around -70dB which 'masks' the things you seem to worry about.

Most recordings I heard all had their own noise HIGH above the noise floor of the DAC itself which is nicely captured in digital as well.

You're a 'numbers and research' afficionado... that's fine.
You worry too much.

 

[amirm]

Moving on to 1980s, consider Studer A820: http://www.theaudioarchive.com/TAA_Tape_Studer_A820.htm. SNR up to 77 dB (A-weighted). For a while, those monsters were still competitive with the direct PCM recorders. Yes, as I mentioned in the previous post, distortions and noise were always their weak spots. Yet were they as bad as those of the consumer-grade tape recorders? Clearly not.

How did we go from 16 bit audio is not good enough to thinking tape specs were good enough? Seems like you are arguing now that even 16 bit is too good!

 

[Cosmik]

I learned about it back in the 1980s: https://en.wikipedia.org/wiki/Tape_bias. Contrary to popular opinion, the gap of recording head is not the limiting factor, the gradient of magnetic field at the trailing edge of the recording head is. Yes, nearly-perfect azimuth is important, and setting it on a machine without a servo-adjuster could be an unpleasant chore.

The gap at playback head, yes, is a limiting factor. We replaced worn out playback heads much more often than the recording heads. I recall the laser-cut gaps being on the order of several micrometers on high-end machines back then, and https://ccrma.stanford.edu/courses/192a/Lecture7-Magnetic_recording.pdf confirms that.

I'm taking about serious machines from the 1970s. Like Ampex ATR-100. See page 32 of https://www.americanradiohistory.com/Archive-DB-Magazine/70s/DB-1976-12.pdf, and page 36 of https://www.americanradiohistory.com/Archive-DB-Magazine/70s/DB-1977-02.pdf. Note the bias frequency: 432 KHz. Note servo motors power: 1/4 HP. Note the discussion about phase coherency and testing with square waves.

ATR-100 SNR spec is not entirely clear: I've seen 68, 72, and 80 dB at 30 ips (depending on tape material and weighting?). Was this that much worse than the PCM decks of that era, such as 13-bit Sony PCM-1: http://www.thevintageknob.org/sony-PCM-1.html? In its marketing materials, Sony only dared to compare the PCM-1 with a 15 ips reel-to-reel.

Moving on to 1980s, consider Studer A820: http://www.theaudioarchive.com/TAA_Tape_Studer_A820.htm. SNR up to 77 dB (A-weighted). For a while, those monsters were still competitive with the direct PCM recorders. Yes, as I mentioned in the previous post, distortions and noise were always their weak spots. Yet were they as bad as those of the consumer-grade tape recorders? Clearly not.

What gets me is people not getting that analog SNR is not the same as digital SNR. In the analog case, as long as the noise floor at -77 .. -68 dB is masked by music, the music itself doesn't really have the amplitude resolution of just 13 or 14 bits as so many people think. It is analog: you can digitize it with 24 bits and this will be meaningful.

Similarly with timing. Yes, electronics band-limits the signal, typically to 22 KHz on high-end machines. Yet again, being an analog system, it doesn't need the 10-20 ms for the dithered PCM samples to catch up with the true signal value with a precision of ~0.2 LSB, after a signal's component "jumps": what's recorded on the tape just "jumps" too, straight to a very close approximation of the true value.

Of course, if you just plug the output of a reel-to-reel deck into DAC and push play and record buttons, you are going to record the hiss on silent intervals. Gate it out, digitally if you must. The real-life music's dynamic range rarely exceeds 45 dB anyway. IMHO, 192/24 PCM carefully captured from a high-end analog tape master can be better sounding than a CD.

What about that quote I linked to earlier? Is it correct in what it is saying?

If you put a tone through a tape recorder and watch the output on a spectrum analyzer, you will see that as the signal level is raised the noise rises up around it in a mountain, with peaks at the odd harmonics. The truth of the matter is that tape recording is shaped noise. It is a non-linear transfer process that produces noise-like sidebands for every frequency in a complex signal. This is a major component of the tape sound.

Sounds like modulated noise, the very worst thing imaginable in a digital system - apparently. What effect does this have on timing?