Although this is an interesting exercise, it really isn't the same as comparing digital audio at different bit depths. 24 bit records don't just add 8 more bits below the current 16.

By truncating the least significant bits, your are cutting information out, but only certain parts -- the quiter parts. A true 12 bit recording doesn't totally lose some of the sound, it just has effectively less resolution across the entire sample. So, by taking a 16 bit recording and truncating the bottom 4 bits, you are keeping ALL of the resolution contained in the most significant bits. Take a single piano note, struck loudly. By truncating bits, the beginning will likely sound identical, but the 'fade' will stop suddenly once it reaches a certain level. If the entire note was done at 12 bits from scratch, you wouldn't get that sudden crop, but rather less resolution in the dropping sound levels.

Think of a still image, with 24 bits per pixel (8 bits each for RGB), then truncate 6 bits off to make an 18 bit per pixel image. If the original image consisted of only very bright pixels (narrow dynamic range), you probably couldn't tell the difference. If the image instead had a very broad dynamic range (bright sky fading to a dark horizon), you would lose fainter details. If the image were resampled to an 18 bit depth, instead of simply cropping, some of those lost details would be retained, at the expense of banding as the sky faded.

Stereophile magazine had a good CD out a few years ago for TRUE comparisons of recordings at different bit depths, called Testmasters. They recorded a solo piano along multiple paths at the same time. Same performance, same microphones, same levels. Along some paths, analog mastering was used. Various digital paths were used, including straight 16 bit, 24 bit with dithering, various dithering techniques, etc, HDCD, and so on. It's easy to compare each technique by skipping tracks around.

It is also easy to tell the difference between straight PCM and 24 bit dithered down to 16 bits -- not to mention the differences that would most likely be evident if the experiment were re-created today with a medium like DVD-A, which would allow true 24 bit recording to be directly compared.