What is meant exactly by the description 'more musical'?

Let's look at objective measurements of four audiophile-grade amplifiers mentioned in this thread as "musical" (some of them may be not exact model mentioned, yet shall be close enough in "amp family sound"):

https://www.stereophile.com/content/plinius-sa-reference-power-amplifier-measurements

https://www.stereophile.com/content/plinius-sa-100-mkii-power-amplifier-measurements

https://www.stereophile.com/content/leben-cs300-integrated-amplifier-measurements

 https://www.soundstagenetwork.com/index.php?option=com_content&view=article&id=1505:bhk-labs-measurements-hegel-music-systems-h360-dac-integrated-amplifier&catid=97&Itemid=154

All of them would be characterized by objectivists as highly distorting. And yet these amplifiers find many buyers who consider them thoroughly enjoyable. At one time or another, this or that authoritative reviewer would call them musical.

There could be many common perceptual phenomena at work, as well as individual hearing system differences. Also, preferred most often listened to music genres, and even specific artists.

It is no different from widely differing preferences in food, wine, closing, cars etc.Yes, there are common qualities that have to be present in all of them, yet it's the differences that make them unique enough for a specific buyer to choose.

I once had a conversation with a man who is both an accomplished audio gear designer and a successful businessman. He keeps multiple authentic vintage audio systems, almost all of them objectively highly distorting.

Why? Because each of the systems is best for reproducing a specific genre of music originating in a specific era. If one wants to hear the artist's intent, he better listen on a system that this artist used to approve the master mix.

So, my take is that "musical" has correlation with objective metrics, yet is heavily influenced by specific individual hearing system peculiarities, and specific gear that specific music piece was recorded and produced with.

Dear @mahgister, @rauliruegas, we agree on about 75%, yet there is still a remaining topic of the gear that musicians, recording engineers, mixing engineers, and mastering engineers use.

These music professionals pick the gear according to their own at times very peculiar preferences, and tune the stages of recording/mixing/mastering chain in very specific ways: sometimes for a whole album, sometimes for a specific song, and sometimes just for a short music phrase.

Also, their hearing systems are quite different from each other and from the listeners’, albeit accomplished professionals tend to know well how to account for and somewhat compensate those differences.

To give you a couple of simple examples of just one stage of the chain - mixing studio monitors:

Michael Cretu (Enigma) used large Quested monitors for his album Love Sensuality Devotion. These monitors were known for their high power and low harmonic distortion across the full audio spectrum, yet their woofers were massive and relatively underdamped - they started slowly and kept going for a split second after a bass tone was already over. For the kind of music that Michael Cretu created, this was beneficial. It emphasized the smooth continuous dreamy aspects of his music.

Boris Blank from Yello chose PSI Audio A21-M studio monitor for mixing his group’s album Toy. In addition to also being powerful, full range, and low-distorting, the PSIs are especially known for their precise response in time domain. Their group delay is surprisingly stable across the frequency range, and they start and stop on a dime. Fittingly, songs on this album are full of intricately interwoven sharp transients, which would be significantly more difficult to get right on less precise studio monitors.

When it gets to listening, Michael Cretu’s music would feel more natural on speakers resembling Quested - smooth, eager to fill out short pauses between notes. Boris Blank’s mixes world probably sound less exciting on such "super-smooth" speakers, yet would come to life on sharp-hitting "analytical" speakers. So here you have it - the artists preferences in sound and corresponding gear choices do matter!