To be clear, I'm not defending vinyl, just pointing out the inaccurate approximation of high-frequency waves encoded at 44.1kHz PCM.
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For example, it is possible to reproduce a perfect 1 kHz sine wave even though the digital data has gaps.
That's all well and good, but 1kHz is somewhere in the neighborhood of two octaves above middle C. I'm not in any way arguing about CD's ability to reproduce sound in this range, but there is a lot of data in the very high frequencies that are byproducts and overtones of instruments that some people can hear, and which are improperly reproduced by the CD format. This is the brittleness of digital audio that some people claim to be able to hear.
All that said, the people that can hear those things are probably far, far, less common than the people that claim they can hear them. It also doesn't speak to the terrible noise floor with vinyl. I would be very interested to hear the playback of complete silence recorded onto vinyl and see what the dB level is.