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When a single vinyl album costs more than your DAC ...

Your CD has a resolution of 16 bits.
Those are 65,536 fixed voltage steps.

Now how many steps for vinyl?
All of them (unlimited).
:facepalm:
Because of noise the effective dynamic range of LPs is around 11-bit not precise since it isn't consistent but nowhere near 16-bit.
Whilst the maximum frequency that can be extracted from a groove is not defined by the format precisely it depends on a lot of things.
Physically can the stylus trace higher frequencies? Simple shapes can't.
The max frequency one can cut to the disc, and the distortion of it is greater near the label than at the periphery - so it isn't a fixed bandwidth anyway.
Pretty well every cartridge made has distortion level of 5% and more (often much more) in the top audible octave, so even if one detects frequencies >20kHz on the output of the phono stage it could well be mainly distortion products, and, of course there is zero credible evidence anybody can hear it anyway.
Everything audible on an LP can be recorded at 16/44.1 with room to spare.
 
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I already mentioned the "technical objective evidence".
16 bits resolution are just 65535 fixed values out of a unlimited number of values.
Let me add to that 44,1kHz is just 44100 times per second out of an unlimited number in the time domain.
So the whole CD story is rather quite a bit coarse and dismembered.
Nyquist is a theorem so mathematically proven.
The key is to bandwidth limit the input signal before digitising. As long as this is done the reconstruction filter will perfectly smooth all the steps and the output of the decoder will be a perfect analogue reproduction of the input only limited by maximum frequency and about 96dB of dynamic range, which is plenty IME.
The only digital devices which have steps on the output are those without a reconstruction filter, which means they are not complying to the requirement and so the output is not a perfect analogue reproduction of the input.
Ironically the manufacturers who promulgate the bollox about digital being stepped are often those who sell DACs with non-compliant engineering so they do have steps and loads of distortion. :facepalm:
 
Nyquist is a theorem so mathematically proven.
The key is to bandwidth limit the input signal before digitising. As long as this is done the reconstruction filter will perfectly smooth all the steps and the output of the decoder will be a perfect analogue reproduction of the input only limited by maximum frequency and about 96dB of dynamic range, which is plenty IME.
The only digital devices which have steps on the output are those without a reconstruction filter, which means they are not complying to the requirement and so the output is not a perfect analogue reproduction of the input.
Ironically the manufacturers who promulgate the bollox about digital being stepped are often those who sell DACs with non-compliant engineering so they do have steps and loads of distortion. :facepalm:

It's far from perfect and introduces its own errors.
 
Frank Dernie said:
Everything audible on an LP can be recorded at 16/44.1 with room to spare.
to which you replied



And why do you doubt this? We are many, waiting for your explanations.

I doubt a lot.
But in the meantime I am absolutely sure this discussion is useless.
 
This I doubt.
What bit of this do you find hard to understand?
Have you read the Nyquist theorem?
Did you understand that the story of digital being steps is internet bollox from people who don't understand, struggle to understand, or wilfully choose not to understand for marketing reasons?
If you can't understand the maths, which is a proven theorem, announcing "This I doubt" is not a very wise thing to do.
 
It's far from perfect and introduces its own errors.
It isn't perfect but it is entirely capable of accurately recording and reproducing everything audible in music IME.
I have been making recordings for over 50 years.
The first time I made a recording where the output of the recorder was audibly indistinguishable from the microphone feed was digital (a StellaDAT) well over 20 years ago.
No analogue recorder had ever managed that. The imperfections of analogue (even excellent reel-to-reel recorders) are audible, those of 16/48 (DAT) are not. I know this from my own experience.
I was surprised but found later this is exactly what one might expect from the theory too, thankfully.
 
What bit of this do you find hard to understand?
Have you read the Nyquist theorem?
Did you understand that the story of digital being steps is internet bollox from people who don't understand, struggle to understand, or wilfully choose not to understand for marketing reasons?
If you can't understand the maths, which is a proven theorem, announcing "This I doubt" is not a very wise thing to do.
Yes I read about it.
But even math has it's errors.
For example it can't get pi exactly right.
 
It isn't perfect but it is entirely capable of accurately recording and reproducing everything audible in music IME.
I have been making recordings for over 50 years.
The first time I made a recording where the output of the recorder was audibly indistinguishable from the microphone feed was digital (a StellaDAT) well over 20 years ago.
No analogue recorder had ever managed that. The imperfections of analogue (even excellent reel-to-reel recorders) are audible, those of 16/48 (DAT) are not. I know this from my own experience.
I was surprised but found later this is exactly what one might expect from the theory too, thankfully.
Thanks for sharing.
 
The bandwidth and dynamic range of Redbook Digital exceeds the bandwidth and dynamic range of ANY LP
There is one huge problem though. Nowadays, most records do not use more than 6-12 dB of dynamic range.
And pretty much any record in existence isn't even close to the bandwidth limits of CD or LP format. It does not make sense to argue about the maximum media capabilities if no records use it.
In the end, the best mastering wins, and some albums are better mastered and sounds better and more dynamic in LP format. That's the reason I own both digital and analog rigs.

_4__The_Future_of_Mastering__Loudness_in_the_Age_of_Music_Streaming_-_YouTube.jpg
 
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Yes I read about it.
But even math has it's errors.
For example it can't get pi exactly right.
wtf does the accuracy of pi to do with it?
It isn't a theorem. A theorem is proven, a fact.
I see you don't want your pre-existing opinion to be challenged by facts. How very unoriginal.
 
wtf does the accuracy of pi to do with it?
It isn't a theorem. A theorem is proven, a fact.
I see you don't want your pre-existing opinion to be challenged by facts. How very unoriginal.

I know the facts, but still...
Digital is missing a lot of "information".
Like reality vs. a movie that creates the illusion of motion with just a few pictures per second.
For me it's like this.
Vinyl/tape... vs. digital.
 
I know the facts, but still...
Digital is missing a lot of "information".
Like reality vs. a movie that creates the illusion of motion with just a few pictures per second.
For me it's like this.
Vinyl/tape... vs. digital.
Trolling a bit ? Aren't you?
 
I know the facts, but still...
Digital is missing a lot of "information".
Like reality vs. a movie that creates the illusion of motion with just a few pictures per second.
For me it's like this.
Vinyl/tape... vs. digital.
It depends on the frame of reference.
If the LP is the frame of reference rather than the microphone feed all the information added by the record playing process is indeed missing.
An LP adds quite a lot of audible noise which CD doesn't.
A cartridge adds audible levels of distortion, which CD doesn't.
Cartridges add uneven frequency response which CD doesn't
Record players pick up airborne and structure born vibration and add it to the music, like a bit of extra reverb. CD players do not.

So it isn't as much that CD misses information but that the LP playing process adds information. You may like the sound it makes, I do, but it wasn't there during the recording and the microphone didn't pick it up, it was generated by the record playing process in a room, so is also variable.
I have tuned my record players to my taste.
It is certainly the case that a digital recording of an LP is indistinguishable from the LP itself IME, though the recording needs to be made (or at least in my case) whilst listening to the LP so that the airborne and structure borne pickup is on the digital recording.
 
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It depends on the frame of reference.
If the LP is the frame of reference rather than the microphone feed all the information added by the record playing process is indeed missing.
An LP adds quite a lot of audible noise which CD doesn't.
A cartridge adds audible levels of distortion, which CD doesn't.
Cartridges add uneven frequency response which CD doesn't
Record players pick up airborne and structure born vibration and add it to the music, like a bit of extra reverb.

So it isn't as much that CD misses information but that the LP playing process adds information. You may like the sound it makes, I do, but it wasn't there during the recording and the microphone didn't pick it up, it was generated by the record playing process in a room, so is also variable.
I have tuned my record players to my taste.
It is certainly the case that a digital recording of an LP is indistinguishable from the LP itself IME, though the recording needs to be made (or at least in my case) whilst listening to the LP so that the airborne and structure borne pickup is on the digital recording.

The EQ required for the cutting lathe and groove limitations, and the lathe limitations itself are additions absent in CDs.
 
The goal is to ensure a faithful restoration of what the label’s founder, Pete Hutchison, sees as a lost golden age of record-making record marketing. Even its record jackets, printed one by one on letterpress machines, show a fanatical devotion to age-old craft.

Got the typo!
 
Infinity is a philosophical and mathematical concept. It was either invented or discovered by humans, depending on whether you take the postulational (axiomatic) or platonist view of logic and mathematics. As far as I understand, infinity does not exist in reality outside of logic and mathematics. I am unaware of any natural phenomena known to be either infinitesimally small or infinitely large. It is just that we find it convenient to use mathematics that includes the infinitesimally small and infinitely large, when constructing many mathematical models of reality.

Every finite-sized signal acquisition, conversion, storage, and processing system, be it analog or digital, introduces error into the signal through sampling error, conversion error, processing error and if applicable digitization (quantization) error. The errors include systematic errors which can be reduced by clever redesign choices, and random errors (noise) inherent in the functioning of the components. The size, complexity, effort or money (actual cost, not snake-oil inflation) to reduce random noise seems to be a high-power or exponential function of the decrease in random noise, tending to infinity as the noise approaches irreducible quantum uncertainty levels. Of course, with either digital or analog systems, we do not need to spend money to reduce errors further below the threshold of human audibility.

In audio recording and reproduction, the digital approach that is dominant now includes some errors not present in a purely analog system. These are quantization (ADC), digital processing and DAC errors. Errors accrued during digital processing in recording studios amount to perhaps three bits of amplitude or dynamic range. Fairly high accuracy / low error ADC at high sample rates from microphone (amplified) electrical output to bits at reasonable cost is used by recording studios. Modern delta-sigma DACs produce highly accurate analog output at low cost, with low error in the electrical voltage as compared with the mathematical signal implied by the reconstruction filters.

In a purely analog approach involving vinyl records (or analog magnetic traces on tape for that matter), errors include some not present in a digital approach. These include errors in conversion of the microphone's (amplified) electrical output to the geometry of the grooves in the master mold, errors in the pressing of the vinyl, deterioration of the pressed vinyl with age and use, and errors in conversion of the groove geometry to an electrical signal by a turntable, needle and phono cartridge. Certainly, the geometry of the master or pressed vinyl grooves is analog, and therefore "infinitely" divisible (for all practical purposes we can ignore quantum discreteness and randomness at the molecular and lower levels; noise of the geometric imperfections and dynamics of assemblages of billions of molecules is encountered before that). However, it contains a significant level of error as compared with the (analog) electrical output of the microphone. This is due to the noise of the electro-mechanical cutting and pressing processes. No matter how much you spend on the finest steadiest turntable, needle and cartridge with the least noise, you cannot overcome the error/noise already present in the pressed vinyl. The noise in vinyl storage has been estimated from measurements, and it exceeds that in 16/44.1 digital systems by at least three bits. This is also accepted by most posters in this thread. Add to this the various inconveniences and high cost of vinyl records. None of this need prevent anyone from enjoying playback of vinyl records. Certainly, the analog system, including cutting the master and pressing the distributed vinyl as well as playback, can be made more accurate than 16/44.1 digital processing by reducing the noise in the analog conversion processes mentioned previously. However, this would involve systems of much greater complexity, precision and exorbitant cost. And in turn we can switch to higher bit-rate digital sampling/ADC (also "infinitely divisible"), storage and DAC, which is already available at a far lower cost than would be the equivalent analog system. The bottom line is that the cost/accuracy trade-off for the electrical-to-binary-to-electrical conversions is far better than for the electrical-to-vinyl-to-electrical conversions, even though the latter conversion stays in the analog ("infinitely divisible") domain all the way.

The same thing has proved true in the video world when considering optical-to-binary-to-optical versus optical-to-exposed-film-to-optical conversions. You could use the best film stock available to make your photo or movie. If your vision was miraculously capable of discerning infinitesimally small details, you could peer all you wanted at the analog image thrown by your film projector on the white screen and compare it with the original (analog) scene observed directly with the naked eye, and there would be tiny details in the original scene that would not be present in the projected image, and vice-versa. Even though they are both analog, with no digital representation intervening between them. In the digital system, the TV acts as the DAC and amp.
 
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There is one huge problem though. Nowadays, most records do not use more than 6-12 dB of dynamic range.
And pretty much any record in existence isn't even close to the bandwidth limits of CD or LP format. It does not make sense to argue about the maximum media capabilities if no records use it.
In the end, the best mastering wins, and some albums are better mastered and sounds better and more dynamic in LP format. That's the reason I own both digital and analog rigs.

View attachment 61966
Not an accurate representation: Loads of pre-digital recordings are dynamically squashed ON PURPOSE, like almost all pop/rock records, and Classical LPs have loads of gain riding. An LP that actually attempted the full dynamic range [there's a direct to disc Boston Pops LP I once owned that was recorded like that] would have the quietest passages bump up against the noise floor of the vinyl and/or turntable. The average level would seem weak unless one raised the volume to the point where the peaks would audibly overload. There's plenty of classical CDs that have 60db of dynamic range [like the BIS CDs] , with the noise floor well out of the way of audibility, but the same problems with too much dynamic range for most domestic environments. "Born to be Wild" and "Quarter to Three" are squashed to a dynamic range of less than 12 db. Pop recordings of the sixties and seventies [and fifties and forties] were dynamically squashed for the same reasons that modern recordings are squashed.
 
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