Flac 16 bit or 24 bit Qobuz

[blaked]

2. I admit it may come over as a bit philosophical or a matter of semantics but what @blaked means is that even if there is noise+signal, the signal is still in there, with less bits you get (more noise)+signal, but the signal is still in there...

Yes, exactly, particularly when using dither since the noise is not correlated with the signal.

 

[71 dB]

You need infinite perfection to make it happen, no?

Yes, if you demand total noise free signal, but that's ridiculous. If you want say 100 dB of dynamic range, you calculate how many bits you need: About 100 / 6 bits ≈ 17 bits. If you are fine with 60 dB of dynamic range, you don't need more than 10-11 bits and so on...

 

[gregorio]

If that's the case, PRECISION is greater with more STEPS over the given range.
Quantization noise, ultimately, is a byproduct from lack of PRECISION.

Yes, to the first sentence, it’s entirely correct! Unfortunately though, the second sentence is incorrect, quantisation noise is not a “byproduct” from lack of precision, it is the ENTIRE result …

And the greater the bit depth, the more PRECISION, along with greater Dynamic Range and a lower Noise Floor.

No, that is entirely wrong! That more “PRECISION” is absolutely not “along with” greater dynamic range and a lower noise floor. In effect, the higher precision is converted into a lower noise floor (greater dynamic range), so you cannot have “more PRECISION along with” a lower noise floor, the lower noise floor is the result of that “more precision”, there is no other result of more precision. If more bits provides more precision and the result of that is not a lower noise floor, where do you think the lower noise floor comes from? And if you do think the lower noise floor is the result of more precision, then what else apart from a lower noise floor do you think more precision results in?

If I'm understanding all of this correctly, what is the mathematical justification that I would ever want to drop from 32 or 24 bit audio to 16 bit, unless I have a format constraint?

You’re not understanding all of this correctly. There is no mathematical justification but then we can’t hear mathematics or devise a technology that allows us to. The only thing we can actually hear is acoustic sound, which means there is a scientific justification for dropping from 32 or 24bit, because according to the laws of physics, the LSBs (Least Significant Bits) cannot even be resolved into analogue signals, let alone acoustic sound! What is the dynamic range of your DAC? I guarantee it’s not the 144dB of even 24bit. Your DAC has probably no more dynamic range than about 120dB or so, which is equivalent to 20bit. Those last 3-4bits (with 24bits) are not “justified” because analogue audio does not support them (due to thermal noise) and even fewer are supported by actual acoustic sound.

You need infinite perfection to make it happen, no?

Ah, you are thinking about digital audio in terms of analogue signals but of course digital audio is entirely different, that is why it was invented, because it is not limited by the restrictions of analogue audio! An analogue signal is analogous to the acoustic sound, hence why it’s called an analogue signal. This means that any noise, distortion, interference or whatever that is applied to the analogue signal will be reflected in the sound reproduced from it (assuming it’s of significant magnitude to be reproduced as sound). This is not the case with digital, we can for example apply relatively huge amounts of noise or distortion to a digital signal and absolutely none of it will be present in the signal when converted back to analogue. This is because we’re effectively dealing with numbers (just zeroes and ones) which are just conceptual/representative and are not subject to the physical rules/laws of analogue signals or acoustic sound. A digital signal is NOT analogous! Your concept of precision with regard to analogue audio is different to the concept of precision in the digital domain. Your concept of precision with an analogue signal can be accomplished beyond audibility with just 1 bit, because in effect with digital, precision is always perfect, regardless of how many bits you have, even just 1 bit. In digital audio, digital noise is effectively a separate entity, so you always have perfect precision with some amount of noise depending on the number of bits, the higher the number of bits, the lower the digital noise accompanying that perfect precision.

G