If an amp sounds more musical than another I can only conclude that this particular amp is adding something to the original signal above and beyond the original recording.
You are missing the point of the term "musical". It refers exactly to the opposite of what you think it does. Live unamplified music is the ideal form that we try to mimic with our stereo systems. Calling a system "more musical" often means that it more closely approximates the natural sound heard live. Calling a system "cold and sterile" means that it does not sound natural like live- usually because it strips away the natural harmonic information that should be present and/or adds electronic artifacts to the sound.
Good live unamplified sound is effortlessly dynamic, open, harmonically rich, and free of artifice. Stereo systems tend to restrict dynamics, reduce resolution, and add all kinds of electronic artifacts that get woven into the music and make it hard, sharp, thin, bright, etc... Human hearing is very sensitive to all of these omissions and commissions. Calling something musical usually implies omitting less of what should be there and avoiding more of what shouldn't