You are assuming something I didn't say.
What I was talking about was the specific topic of taking the track-count into account in determining optimum levels.
I'm still no closer to what you actually meant by "throwing away resolution" during tracking. Can you please explain further?
The rest of your post appears to be littered with things that don't make a lot of sense, including:
"Inter-sample distortion"? Do you mean quantization noise?
No, I do not. I mean inter-sample distortion, yes, a true phenomenon. I'm not going to take the time to explain it so please read this paper:
www.tcelectronic.com/media/lund_2004_distortion_tmt20.pdf
I don't know what "efficiently" means exactly. In any event, both your software and your hardware are going to process each sample at its full bit-depth, even if you don't use all the bits. It's not easier or more efficient for a CPU or software to do 0x00F1 + 0x00F5 (say) than to do 0x0F13 + 0x0F54.
I'm not clear on what you mean by "hardware", but your DAW will most likely process each sample at
more than it's intrinsic bit depth because most DAWs use at least 32-bit floating point precision. Many plugins use 48-bit and now some use 64-bit. In any case, all this does is add resolution
on the bottom for processing (floating point processing exhibits a shifting noise floor which is signal dependent) and does not change the fact that any audio recorded with a modern AD converter will always be 24-bit.
And yes, mathematically it all makes sense on paper. It's binary arithmetic after all. Yet we still have miscalculations due to developer error, particularly in 3rd party plugins and even more particularly when the signal approaches 0dBFS. As explained to me by a plugin developer that I know and trust:
"
Plug-ins internally represent the (audio-) sample values with floating-point values between -1 and +1. Those 2 values, when put on the output of a plug-in, correspond to 0db (+1 is the maximum positive phase, -1 is the maximum negative phase. Think of it as the maximum values of a sine). For ease of explanation I use +1 below, but for -1 it's the same.
Depending on what the plug-in does there's a lot of mathematics inside, additions, multiplications and whatnot. This processing results often in (internal) temporary values bigger than +1. That would 'normally' be not a problem as long as after all those internal processing steps everything's back to -1 ... +1, but...
...a lot, and with that I mean a LOT, DSP algorithms are designed to work ONLY in this range. Some work for all values, some more work for values slightly above +1, some work bad outside that range, some just crash or start to oscillate."
Besides all that, I've personally heard a HUGE improvement in the performance of plugins when operating under -10dBdfs. By performance I mean the cumulative aggregate of perceived distortion at the end of a mix and particularly during mastering. It all piles up and if you have enough of it your mix will suffer and fall apart.
You're ignoring a number of things, particularly that mathematical operations reduce precision; whenever you do any processing of a set of values, you want to carry as much precision as far as you can, and don't truncate precision until you have to.
Precision is not able to truncate. The term precision is limited to the overall operating bit depth of an algorithm. You truncate bits below the LSB (least significant bit) when the first quantization tier is not reached by a given sample. An example would be converting a 24-bit recording of a cymbal hit to 16-bit and at the very end of the sample the audio distorts out (truncation distortion) as the LSB of 16-bit has been reached. A square wave is the result, albeit at a very low level. This is truncation.
Obvious (and perhaps too simple) example: Say you want to find what the sum of two integers is, and (for some reason) you need to roung the result to ten. Now say the integers are 4 and 3. If you round them to the nearest ten before the operation, you'll get 0+0=0. If you maintain the precision until the end, you'll get 4+3=7, which rounds to 10 and is, obviously, considerably more accurate. The same happens in your computer, only you're not rounding by tens, but by bits, and you don't do one calculation but thousands.
Your analysis seems to be based on the assumption that rounding at the end produces more problems than rounding at the beginning. The opposite is the case.
I'm sorry but I disagree and I think that you are taking mathematics on paper as the authority over your ears. This is AUDIO after all. The bare fact is that there is around 120dB of dynamic range in 24-bit audio and slamming your levels at any point WILL introduce distortion at some point, be it at the input of your AD converter, within plugins, or at your DA converter. Furthermore, the issue of analog components in the chain have not even been touched on here either and it's fair to say that manufacturers often skimp on these components in order to save costs and, ironically, the cost for us is distortion. While you may be able to show me on paper that the mathematical theory is correct, the issue still remains that many analog amplifiers exhibit distortion WAY before they reach 0dBFS. This is another reason not to go near full scale, ESPECIALLY with prosumer gear.
Nope. I don't think you understand the math. Actually, it's exactly the opposite: if you were to sum two identical sine waves (same frequency, same level), the result could peak anywhere between double the level and zero, depending on phase. If the "spectral response" is varied, you're going to wind up peaking at double the level of each.
I don't think you got my point in that in the real world, things do not behave like they do in a mathematical equation. A kick drum peaking at -12dB combined with a cymbal peaking at the same level will not combine to double the intensity because they have different spectral responses. This was my point.
With a 24-bit AD converter, there's no overwhelming reason to get pushy about getting super close to 0 dBFS. If you track at (say) -12 dBFS, you're throwing away 2 bits, and you still have 22 bits of precision, which - in the real world - is plenty. You're not going to hear the difference between a 22-bit recording an a 24-bit recording. The downside of pushing for 0 dBFS is that you're either going to go too far, or you're going to spend a lot of time fiddling with levels and retracking stuff that peaked a little more than you expected.
That advice has nothing to do with how many tracks you're planning to include in your finished product.
I'm confused now. Are you saying that the OP SHOULD track at -12dBFS? Please can you explain this then?:
I wouldn't throw away resolution at the tracking stage, particularly since the data path in your software has more resolution anyway.
And just for the record, there's no digital converter out there that can even do 24 bits. Sure, the file results as 24 bits but the best you can hope for is about 21 bits due to limitations in the design of ICs and other analog components. The cost is noise.
Cheers
