Ok time for some debunking. I think a big part of the problem is that it is hard to grasp the size of the decibel system especially when it comes to measuring audible noise.
For starters, low level noise is not equal in transmission power relative to higher signals in newer hardware. New digital audio information is represented in a logarithmic scale rather than the old system which was linear, the old system was called unsigned if you want to look into it (check out 8-bit unsigned digital audio). There is a downwards gating effect that happens in the newer system, lower level bits are attenuated more than higher bits when converting back to analog, the new system is called mu-law.
Some were mentioning noise levels of analog gear and gain from reamped guitars. Analog noise or rather the signal to noise ratio of analog gear remains the same regardless as to which bit-depth you use, bit-depth is only reducing the amplitude of noise created from quantization errors when converting to digital.
What does quantization error noise sound like? Its nasty, if it is audible you would notice, its a very digital square wave triangle wave hybrid if you input a single sine wave. The more wideband your signal is (closer to white noise), the less apparent the quantization distortion becomes. You also don't really care if a signal that is close to white noise has a very slight increase in white noise because all you are doing is getting an infinitesimally small bump in gain, and in the end you use dithering which injects white noise relative to the amount of quantization distortion present. A larger amplitude signal causes more quantization distortion, a more band limited signal causes more quantization distortion. Dithering actually erases those errors, and actively changes its amplitude so that the white noise it injects goes unnoticed in quieter sections.
So keep this in mind, the signal to noise ratio of your analog gear, including preamps and compressors and other outboard gear is the same not matter which bit-depth you use.
Mic preamps and high gain guitar amps don't have that much gain in retrospect, at max gain (gain dimed) a guitar amp typically will have a gain around 64dB. That's at full gain, the gain knob due to cascade staging acts more logarithmic, so having the gain set half way is closer to 32dB, not 61dB as you might expect. And most of us aren't running out 5150s half way on the gain, which is still overkill.
With a guitar amp having a robust and somewhat over the top 32dB of gain does that mean your noise floor audibly comes up 32dB? No, remember mu-law means the actual represented analog voltage for small level noise is still attenuated relative to high amplitude signals. Quantization noise typically would therefore be half that, depending on proper tracking levels.
While mic preamps may have a gain of 60dB, how frequently do you have to crank the gain all the way up to get proper tracking? If you do because you have a quiet source and a low output mic, well you should use a different mic but regardless of bit-depth the white noise and some 50Hz/60Hz noise will be equally proportioned to audio amplitude, bit-depth be damned.
Back to dithering so a moment, with sensitive sources like overheads or high gain guitar heads during reamping, if you don't hear nasty harmonic distortions when you increase gain and you cannot hear noticeable white noise (that isn't mic pre/comp analog noise) when the drummer is playing, then you don't have a problem.
Now even with all that in mind the full scale system that is used to measure audio is in power gain, not voltage gain (although they result in the same measurement), and for refreshers you get only 6dB increase of gain for every doubling of power. For example, noise sitting at -80dBFS would be 1/100,000,000 the output power of a full wave signal. Now I don't know anyone at ambient listening levels could hear that noise or the effects of such noise.
16-bit has a dynamic range of ~96dB depending on quality and 24-bit has a dynamic range of ~144dB, the only thing that this means is you can have quantization noise that is up to, theoretically speaking, 48dB quieter. Quantization distortion in an entire mix may reach -60dBFS in 16-bit and its 24-bit equivalent would be -108dBFS. -60dB is 1/1,000,000 the power of full scale, and -108dB is roughly 1/60,000,000,000 Now the noise output power at 16-bits is a lot more, but considering it is still very small for a very high amount of noise how many people would be able to hear an extra one millionth of full wave power additional "similar to white" noise in a full mix at ambient listening conditions? Then can you really hear it when you dither and the noise is drastically reduced upwards of 20dB on top of the fact that output power is in mu-law which makes noise even quieter than the figures I posted?
The chances of you hearing a difference is slim to none. The big reason why many who have done shootouts hear a difference is you are hearing white noise from mic preamps because when you record in 16-bit there is a subliminal urge to track hotter to get maximum signal to noise ratio in the box, but inadvertently do more damage because you are getting hotter levels by giving your analog gear more gain. The higher you turn up the gain on a compressor or mic pre you are decreasing the S/N ratio. That's the extra noise you are hearing is because you tracked too hot. Then because you tracked to hot your converters have higher harmonic distortion which makes the tone sound "pushed". If you backed off an other tracking levels you will find that you won't pick up on quantization distortion especially if you dithered.
Put it this way it is hard to hear quantization noise with 8-bit mu-law. Also keep in mind professional reel to reel tape at its best had an equivalent noise floor to 13-bit unsigned digital. Everyone rants and raves about the vibes that tape adds, it adds a whole hell of a lot more noise than 16-bit quantization distortion could ever dream of.
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Also, for the guys that keep saying they record in 32-bit floating point, you are not actually recording audio in 32-bit. The audio is 24-bit but the audio engine is processing the numbers in floating point to provide more headroom in the processing phase of audio. 32-bit uses the first 24-bits as a binary number and the next 7-bits as an exponent, the last being a parity bit. That allows the values to exceed 24-bit values and still retain all the information. That only implies inside the DAW because if the master bus exceeds 24-bits, clip-city.
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My reasons for recording my demo's/tracks in 16-bit has less to do with computing power, although my 4 year old 3.0GHz AM3 Dual Core can barely track with 4 instances of X50v2 and Superior Drummer 2.0 with stock Andy Sneap Library, at any latency. I can however mix without much of a hitch. My main reason is that 24-bit audio takes up 50% more space than 16-bit. I am tight on disk space and can't afford to go out an buy a Hard Drive every time my current one gets full, it would be a nice luxury.