So indeed, if I mock up reconstruction using SoX (resample to some ungodly high rate and keep things at 32 bits), the difference between the reconstructions of the original file and the 8-bit version end up peaking at -42. I picked a hell of a day to quit drinking. Thanks for that; I'll keep trying to digest what's happening, because I'm totally not grokking it.
Let's try an analogy: Let's say we take an adult man and amputate one of his legs above the knee. The difference between the man before and after the amputation isn't just the difference between the gap (nothing) which now exists and the part of his leg which has been amputated, there's quite a big difference in what's left of the man himself: For starters he's got a severe wound to deal with and it's also going to cause other changes/differences in his body, metabolic (and probably numerous other) changes for example. Furthermore, there are also going to be significant differences between this adult amputee and the same man had he been born with a congenital defect which resulted in exactly the same gap/nothing above the knee. Likewise in digital audio, there's a difference between running out of resolution/bits when recording and chopping off resolution/bits which did once exist. In fact, truncation error is double the quantisation error in terms of the RMS of the error signal.
I've looked around for a few mins and can't find a quote of the actual math to back this up but I seem to remember that the RMS of quantisation error is just under 0.3 LSB (and therefore about 0.575 LSB for truncation). The LSB in the context of this discussion being the 8th bit, not say the 9th or 16th bit which has been truncated (and then padded with zeros).
I also looked around for an actual example, so you can hear for yourself, which will hopefully help you to get your head around it. I came up with
this example (which is actually a link from the previous article posted). While we can't in practise create an 8bit recording (with only quantisation error) for comparison with an 8bit version truncated from a 16bit version, this example does demonstrate well the difference between a 16bit original and the various different ways of arriving at 8bit versions; truncation, dithering and noise-shaped dithering. However we get to 8bit from 16bit though, there is ALWAYS going to be error in those remaining 8bits, regardless of the fact that they're identical to the 8 MSBs in the 16bit original.
One last point. While the same math applies to bit reductions of any depth, there are additional factors to consider when doing a bit reduction from 24bit to 16bit. Additional factors which are commonly ignored and which significantly change the result!
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... but yeah practical tests tend to agree with Greg(he probably altered our reality just to be right, you know him).
Hmm, it's true that I in effect do often try to alter the perceived reality but I don't think I'm doing it just to be right, I'm doing it to get closer to what is really going on under the hood. Having said this, my perception of what is going on under the hood has it's limits and is not perfect, so maybe in effect it is just about me being wanting to be right, hmmm?! On the other side of the coin, many of the questions/discussions revolve around issues which I investigated as long as 20 years or so ago and in many cases have continued to improve my understanding ever since.
The fact is that under the hood, digital audio is ultimately of course all math, much of which requires requires a quite highly educated mathematician to fully understand. Furthermore, even a great mathematician who would find digital audio math simplistic, wouldn't have the years of audio engineering experience necessary to be sure they're actually taking into account ALL the math relevant to a particular issue/topic of discussion. Us pro audio engineers are not mathematicians though, we're only ultimately concerned with the perceptual results of employing the math. So like the more educated consumers, we have to rely on layman's terms and analogy, although with experience we should have a far better understanding of what underpins those layman's terms and analogies. Ultimately though, if we desire to go further down the rabbit hole, we have to trust/consult others, of which there are incredibly few who are willing to speak publicly, have enough independence from marketing, a deep enough understanding of the math and a broad enough understanding of practical audio to stand a good chance of considering ALL the relevant math. Bob Katz, Paul Frindle, Dan Lavry and just a few others have fit the bill for me over the course of many years.
So when I see a misapprehension due to the inevitable, inherent inaccuracies of layman's terms and analogies, I'll try to come at the issue from a different angle and with some different analogies, to hopefully create a more comprehensive understanding. This approach could easily be seen as "trying to alter your reality"! I could in theory just quote the math but I don't think that would help most here and besides, I commonly don't know the math (because it's proprietary) and even when I do, I often don't understand it comprehensively enough to discuss it in mathematical terms. So while I might sometimes allude to the underlying math, I try to avoid going too far down that hole.
G