[...] You double the dynamic range with each bit [...]

You misunderstand DSD.  DSD, like PCM can go from one rail to the other as fast as the reconstruction filter allows.
[...]
In DSD you'd go from a series of 0's to a series of 1's in one sample [...]

I've recently revived an interest in music/equipment, but am only slowly putting the pieces together regarding the PCM/DSD discussions.

My main query is regarding the value of a sampled bit. There are plenty of references that state things like '24 bits has a higher dynamic range than 16 bits'.

Why does a bit sample always have to have the same amplitude value?

Why can't you expand (say) 90dB into 24 bits instead of 16 bits, and get higher resolution?

With DSD, is a 0/1 bit switch the same amplitude as one of the 65535 16 bit bits?

DSD is quoted as having a better impulse response than PCM.

Surely though (at least in theory) PCM can go from 0-65535 in one sample, whereas DSD would take 65535 samples to do the same?

So DSD would have to be at 65535 times the sample rate to get the same response?

Obviously in practice you wouldn't get these extreme values, but what is the reality of the speed of a transient? DSD would only be good with transients of low amplitude.

Or have I got everything completely bass-ackwards?

Ouch, my entire post was somehow lost. I don't feel like typing this all over again... :-(

If you use more bits for the signal, you have more resolution to express smaller, quieter signals. A potentially larger difference between the loudest and quietest signal means a larger dynamic range. But increasing the resolution of an existing signal obviously does not magically increase the resolution of its contents. It's just being stretched across the new space.

Decibel is a relative scale that doubles values every time you add 6. That number comes from the logarithmic math, so it's not a random number someone chose. So if you have an ampitude of x, then adding 6 dB means your amplitude is now 2x. Conversely, increasing the bit-depth by 1 means you make room for small signals that have half the amplitude of the previous smallest signal, and lo and behold, half the amplitude is an extra 6dB range.

My knowledge of the actual mathematics of dB is shallow at best, so I can't go much deeper than that.

> Why does a bit sample always have to have the same amplitude value?
It doesn't. It's all relative to 1, also called fullscale, also called 100% volume. The only absolute sense of amplitude is in the real world with pressure levels in air and voltages in the wire. When we say 16 bits has X dB dynamic range, it means the difference between the largest and smallest storeable signal is X dB. If you want to put that in an amplifier and blast it or play it quietly, sure, that doesn't change the relative amplitudes of what's coming out of your speakers.

No, DSD is really simple: a stream of ones and zeros.  A one means to head for the positive voltage rail as fast as possible and a zero means head for the negative rail as fast as possible.  The speed of movement is restricted by a low pass filter.  - That's it.  All you need to play DSD is a low pass filter on the stream of bits.

For example 0101010101 for ever represents a 0 output (as does 1100110011001100...)  The stream 0001000100010001... represents a value 1/2 of the way from a zero output to the maximum negative output...  Tho these patterns flop around, by the time they go thru the low pass filter that noise is filtered out.

Calculating those bits is very weird, but one method that's very inefficient but really does work is to search thru all streams of bits looking for the one that (after being low pass filtered) gets you closest to the signal you want.  Usually a sigma delta modulator is used: one way of thinking of a SDM is to compare the low pass filtered stream of bits generated so far to the input signal and produce a one if the stream is too low and a zero if the stream is too high - then repeat forever.

Quote from: shakeshuck on 2017-04-23 10:21:17

I've recently revived an interest in music/equipment, but am only slowly putting the pieces together regarding the PCM/DSD discussions.

There is really very little to discuss. It is basically a PCM world, and DSD is a little placebophile side show that you can safely ignore.

If properly implemented, PCM  and DSD sound exactly alike. 

For about the last 20 years just about all of our DACs have been converting PCM to DSD under the covers prior to turning the data into analog, and nobody but a few technical specialists knew or cared.  The code name for this process is Delta-Signal or Sigma-Delta.

DSD was taken out from under the covers in order to provide IP protection. Some marketing genius decided to mine the same old reliable but fraudulent vein of gold that the placebophiles have been mining for decades, and claim that DSD "Sounded Better".  It doesn't and if you take what I said about almost all of our DACs turning PCM into DSD as a stardard part of our modern way of ding business, to heart, you can see why.

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My main query is regarding the value of a sampled bit. There are plenty of references that state things like '24 bits has a higher dynamic range than 16 bits'.

That is because it is true. But it does not follow that any music sampled with 24 bits has higher resolution than music sampled with 16 bits.  Both processes depend on the same analog data, and the same acoustical event. In general live music has less than 16 bits of resolution.

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Why does a bit sample always have to have the same amplitude value?

It doesn't.  For example the most signfiicant bit of any PCM word has twice the value of the next one.

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Why can't you expand (say) 90dB into 24 bits instead of 16 bits, and get higher resolution?

Because PCM words represent data, they don't define it. On a good day, they don't limit it, either.  

Data is what it is. You can reduce its resolution or preserve it, but you can't increase it without going back to the original physical process that it represents, and changing it.  That's why many of us have a hearty laugh about all those DSD and 24 bit PCM files that are based on analog tapes and legacy PCM files.  Interestingly enough, about half the SACD and DVD-A recordings released through about 2006 were this way, and no golden ear ever noticed it. Many of those recordings are still being sold, and they have been joined by a host of newer recordings that had the same limitations simply because of the usual forces of nature.

Virtually every so-called "Hi Rez" recording has the bits but not the data to be true to its name.

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With DSD, is a 0/1 bit switch the same amplitude as one of the 65535 16 bit bits?

No.

In DSD there is only one bit and it is switched very rapidly on and off to provide the same kind of handling of the various signal levels as we have with 16 or 24 or whatever bits in PCM.

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DSD is quoted as having a better impulse response than PCM.

...As if impulse response was that relevant to sound quality, which in general it is not...

If you had exactly comparable DSD and PCM systems, the impulse response would be the same. But, as implemented, the systems are not the same. So, they have different impulse responses.

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Surely though (at least in theory) PCM can go from 0-65535 in one sample, whereas DSD would take 65535 samples to do the same?

Well, a sample in DSD is not just one bit.  The parity you suggest is real, so a DSD data stream has to have a whole lot more bits in it to do the identical same thing as a comparable PCM data stream.  The PCM data stream weights the bits with binary values, and the DSD stream does not.

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So DSD would have to be at 65535 times the sample rate to get the same response?

True if all things were equal but they are not all equal in the commercial implementations.

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Obviously in practice you wouldn't get these extreme values, but what is the reality of the speed of a transient? DSD would only be good with transients of low amplitude.

Like I said, if all things were equal, but...

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Or have I got everything completely bass-ackwards?

More like comparing apples with oranges than bass ackwards.  If you really are a newbie, you would do well to concentrate on other issues, such as the ones that actually matter for sound quality. Things like acoustics...

There are proponents of both sides.

I like to try to gather information so I can make an informed decision, instead of blindly following one herd or the other - and understanding how these things work hopefully goes a long way to cut through the misinformation.

From the few samples I've downloaded so far, I can understand where the two camps come from, but I'm not sure the difference is worth fighting over.

I'm afraid I'm having problems interpreting this post. 

Surely, either the scale is logarithmic (and double sound pressure is double on the scale), and therefore the folks saying that "anything over 20-bits is a waste of time as it is beyond human endurance" are correct, OR we are capturing an amplitude of -1 to 1 in n resolution, regardless of the amplitude max sound level, then we get a higher resolution to "to express smaller, quieter signals".

Are these two things not contradictory?

All by yourself, as relatively easy as it really is, most people resist doing proper listening tests. I just got called a bunch of dirty names for politely pointing that out on another thread. But know it or not, you signed up to agree to that when you registered here. Please see TOS 8.

Quote from: shakeshuck on 2017-04-23 14:04:11

I'm afraid I'm having problems interpreting this post. 

Surely, either the scale is logarithmic (and double sound pressure is double on the scale), and therefore the folks saying that "anything over 20-bits is a waste of time as it is beyond human endurance" are correct, OR we are capturing an amplitude of -1 to 1 in n resolution, regardless of the amplitude max sound level, then we get a higher resolution to "to express smaller, quieter signals".

Are these two things not contradictory?

It relates to the operating voltage range of the recording and playback device, it is on the analog side.

Let's ignore the digital part, now I have an analog tape recorder, mixer or anything which are purely analog. If you look at the manual and find the specs, it will say something like max level: +20dBu, 8V RMS and so on. If you feed a +30dBu, or a 10V signal to these devices, will result in distortion. Anything, unless digitally synthesized and will never be played on speakers or headphones, are limited by the analog part.

Now the bit depth part is simple, it simply refer to how this +20dBu or 8V signal can be divided into 65536 steps, for example, when recorded in 16-bit. Now if you play the recorded file from a consumer device, like a mobile phone, which is less powerful, for example, only 0.5V, and the phone has a 16-bit DAC, then this 65536 steps are just remapped to a less powerful state.

It is just like a 1080p mobile phone vs a 1080p TV.

I once (years ago) brought up the subject of CD burning, and that in an experiment I had done the newly burned CD sounded better than the stamped original. I didn't know why, it just did as far as I was concerned. I was pounded for my efforts, as "science says it isn't so", quoted Reed-Solomon etc, etc.
Recently I found out that Reed-Solomon is only effective if the disc is tracking properly, and mistracking could easily have been the reason for the difference in sound. I have seen many discs where the punched centre hole is completely misaligned with the data layer on the disc.

Quote from: shakeshuck on 2017-04-23 15:33:28

I once (years ago) brought up the subject of CD burning, and that in an experiment I had done the newly burned CD sounded better than the stamped original. I didn't know why, it just did as far as I was concerned. I was pounded for my efforts, as "science says it isn't so", quoted Reed-Solomon etc, etc.
Recently I found out that Reed-Solomon is only effective if the disc is tracking properly, and mistracking could easily have been the reason for the difference in sound. I have seen many discs where the punched centre hole is completely misaligned with the data layer on the disc.

I fear you imagine things like you will imagine other things relating to the sound of DSD if you only find a written argument you feel that convinces you. Waste of time.

Recently I found out that Reed-Solomon is only effective if the disc is tracking properly, and mistracking could easily have been the reason for the difference in sound.

All by yourself, as relatively easy as it really is, most people resist doing proper listening tests.

Quote from: shakeshuck on 2017-04-23 15:33:28

Recently I found out that Reed-Solomon is only effective if the disc is tracking properly, and mistracking could easily have been the reason for the difference in sound.

Hogwash.

Quote from: Arnold B. Krueger on 2017-04-23 14:45:42

All by yourself, as relatively easy as it really is, most people resist doing proper listening tests. I just got called a bunch of dirty names for politely pointing that out on another thread. But know it or not, you signed up to agree to that when you registered here. Please see TOS 8.

I didn't realise that I'd taken sides. I thought I'd deliberately been libertarian about the whole thing; not offending anyone or poking any cages by sitting on the fence. Now I'm being chastised for it?

I once (years ago) brought up the subject of CD burning, and that in an experiment I had done the newly burned CD sounded better than the stamped original. I didn't know why, it just did as far as I was concerned. I was pounded for my efforts, as "science says it isn't so", quoted Reed-Solomon etc, etc.

Recently I found out that Reed-Solomon is only effective if the disc is tracking properly, and mistracking could easily have been the reason for the difference in sound.

I have seen many discs where the punched centre hole is completely misaligned with the data layer on the disc.

Because of my own experiences, I don't try to tell anyone which side of the fence to sit on, that's up to them. I am happy for anyone to believe what they like until science changes its mind and proves otherwise.

Quote from: Arnold B. Krueger on 2017-04-23 14:45:42

All by yourself, as relatively easy as it really is, most people resist doing proper listening tests.

This is not necessarily as easy as you make out. My first post on HAudio was in the ABX section for Foobar, which was making comparisons impossible as ReplayGain wouldn't set the levels between PCM and DSD correctly (possibly due to the noise, but I won't speculate as I get told off for doing that).

So I HAVE tried a proper listening test, and the technology failed me.

Quote from: greynol on 2017-04-23 16:05:09

Quote from: shakeshuck on 2017-04-23 15:33:28

Recently I found out that Reed-Solomon is only effective if the disc is tracking properly, and mistracking could easily have been the reason for the difference in sound.

Hogwash.

Why do CD ripping programs have authentication databases if they get it right every time?