Double-blind tests have made this abundantly clear.

If you really can hear a difference, you've either got particularly poorly compressed files, or are in a tiny minority of us.

Lossless (when used properly and able to algorithmically guarantee what comes out == what goes into the compression toolchain) avoids the whole issue altogether, and that's what's valuable about it.

Focusing on whether compression captures every nuance of uncompressed sound is the wrong battle. The real battle is against careless distributors and bad artifacts introduced by poor compression settings and often incorrectly coded compression utilities used throughout the music industry.

(ie we on hn might all be using Lame or the Fraunhofer mp3 encoders, but a lot of music producers/distributors will be using custom / closed source encoders, or even audio workstations with the encoder implemented in hardware, and those might or might not be encoding mp3 correctly.)

Whether it's because of the math or because of poorly done encoding is only of academic interest. It happens regardless of the cause. Using a lossless encoding resolves the issue entirely.

Higher bit rates (and probably improved encoders) help though.

It's not a problem in any other codec though. You probably couldn't hear the difference in AAC or Opus.

Do you have a reference for the MP3 issue?

The highest frequency band doesn't have its own quantization level meaning it's hard to control the bitrate when there's detail in it.