Yes... bit depth is about dynamic range, but its more about 'smoothness' of your sampling, and the number of discrete levels you can represent.
If you draw a wave signal on graph paper, then draw points every cm - we sample these values. The x axis (time) is your sample rate, the y axis is the amplitude - and if 1cm is the smallest fluctuation you can measure you won't need many bits to store those numbers. More bits = more accurate sampling of the input wave's signal level (amplitude)
Next, best of breed converters can't physically deliver more than about 22 bits of dynamic range - so why isn't 24 a bit DAW ok for that? CD uses only 16 bits, we're going to compress it down, anyway?
The answer is about the the smallest subtle difference you can keep within the numeric pipeline of the DAW's signal processing chain ... it does mathematical calculations -
I might have a chain of plugins -
input -> A -> B -> output
and the numbers flowing out of them are
1.000 -> 1.001 -> 1.002 -> 1.002
We can see that, because A and B are doing subtle shimmery sexy tape emulation, by adding really small amounts of second order harmonic distortion, internally their maths need to have more precision, but the DAW's pipeline (here, only 5 decimal floating point!) is cutting off all their subtle [0.000045] and [0.000013] stuff!
And that is going to sound crap!
So, here we have only a 4 digit DAW (a sample range of 9.999 to -9.999 in 0.001 steps). The number of steps we need to represent that is 20/0.001 = 20,000 - so a 15-bit DAW would be needed for this (2 to the power 15 is 32768, 2^14 is only 16384 discrete levels, not enough to store enough permutations). This is one reason old 16 bit digital guitar gear sounds so crappy.
To go back to the truncation issue, chopping stuff off as predictably as this, always, in the same place, has a monotony about it, and mathematically it causes a nasty spike in the signal, so to mask the effect of this, we brick wall filter and add a random +/-.001 signal at the output, to make some of the chopped off stuff visible - an amazing idea called DITHER!
So, if we can keep full resolution all the way down, and just dither and truncate once at the end, we lose less information.
1.000000 -> 1.001945 -> 1.002716 -> 1.003
Using nonsense numbers in this example, but can you see how quite often, with lower bit depth, we might frequently get the 'wrong' result compared to what a 'perfect' pipeline would do.
I think the best analogy here is the colour depth in a photograph.
- Get a nice photo with beautiful colours (maybe lots of fades from one colour to another = subtle timbre)
- Save a copy at the same res as '1.gif', reducing the colour depth to say 64 colours (so starts to look 'bandy')
- Run the original through the a series of photoshop plugins, e.g. adjust levels, contrast, sharpen, denoise etc.
- Now run the 1.gif through the same process, each time saving to 64 colour GIF format, to reduce the colour depth in your DSP pipeline.
- Lastly, save the original as 2.GIF (same colour depth) and compare the end results
You should see that the same processing gets a better end result if your plugins are able to work against a full depth source, then only render down once at the end... this is because of rounding error in small numbers represents loss of information.
In sound, colour depth equates to tibre or tonal colour, esp of bass tones. Lack of it means frequencies have are cut out, leaving spikes either side, see mp3.
So, at the top end of the scale, the dynamic range, headroom in the mix bus. At the low end of the scale, the numerical accuracy and our ability to not destroy small signals as they are operated on by faders, processors, scalars, summers. The more numbers and more resolution you store the better the end result, but more CPU needed to crunch and retrieve the bigger numbers - so you may need to have more powerful hardware - but it's worth it.
I think rounding errors have a huge effect on audio and one of two reasons analogue sounds best - Neve component bandwidth is always well over 100khz (sample rate needed to capture it is > 300k), and the dynamic range in current models is big because of 90v rails.
Most converters won't do that, but internally Pro Tools swaps its bus range into macro / micro modes to achieve an effective 56-bit pipeline, which is why Avid claim HD sums as nicely as a Neve.