Musical Speakers - If you like that sort of thing.

I love it when people will post that a particular speaker may not be the most neutral or accurate or resolving, but it sure is musical. Ummm...why do audiophiles want speakers that are less musical? "My speakers make most music sound like rubbish, but they're the best I've ever heard".
In broad terms the purpose of home audio reproduction is to recreate, as closely as reasonably possible, the perception of hearing a live performance. So-called "accuracy" that does not serve this goal is either irrelevant or incomplete.

Cannot define live sound as that depends on so many things that it is impossible to get a base point.

Many live events sound aweful and others heavenly.

Great sound to my ears is what this passion is all about. The only base standard that works is one's own preference.
The longer I'm at this the more I could care less.about neutrality.

I want it to sound good to my ears at even the loudest volumes.

I want my music full, rich and never thin and fatiguing. Full bodied and room filling are also a must.The bass can be little loose or the highs a little rolled off etc...

In the end it better sound good to me even if it has to add or subtract from the recording to sound pleasing.

We have similar wants. I've been swapping in and out various bits of gear over the last year, always dissatisfied with what I had heard. I began to realize what I really wanted, and thankfully my last two or three moves are working out well. Full bodied sound that projects forward towards me is a must. I like lots of detail too, or perhaps that's clarity. But to me it is a must that I be able to follow every instrument's line. If instruments bleed into each other than how can the melody of a song come through? It'll just sound muddy.

But I do value neutrality. The best speakers I've heard achieved what I wanted, but they were also quite neutral. At least when it comes to highs. I don't like elevated highs that become edgy and shrill. But generally I like knowing that my speakers are relatively neutral, as speakers that have large dips and peaks I'd imagine can really make certain albums sound poor, depending on the levels used on those particular songs.

But of course many things are important. Another big one is driver integration. I think it's the main strength of my Quad 12L2. You don't hear two separate drivers, but rather one piece of music where everything fits together, and the various instruments sound like they are playing off each other the way they should.

To address the OP, musicality to me means whether I am moved or not. Some speakers sound boring. Those that do not are what I'd call musical. Does the emotion, rhythm, and melody come through?
I generally agree that there are two aspects to this hobby, but I would frame them somewhat differently. For me, the two aspects are 1) the "illusion" aspect and 2) the "pleasure" aspect. I think of the first as being a more intellectual endeavor. Based on the information my ears are receiving, how much do I have to suspend my disbelief that I have been transported to the recording venue? The second is more emotional. Regardless of realism or lack thereof, is what I'm hearing stimulating the pleasure centers of my brain, or is it grating on my nerves? I decided years ago (after some difficult and expensive lessons) that my first concern must be with the pleasure aspect. So, for example, if a piece of equipment excels as creating an illusion of a soundstage, but the string section on that soundstage is reminiscent of fingers on a blackboard, then to heck with the illusion. I prefer a more euphonic blob of undifferentiated sound. That said, this is just the starting point. From the euphonic blob, future improvements should go toward enhancing the illusion while maintaining the pleasure. One could work in the reverse order, but why suffer while reaching for the ultimate goal, which is a pleasurable musical experience that creates the illusion of being in the original recording space?
One of the most basic truths in life is that we all like different things. It's no different in the world of music reproduction. As many eloquently explained above, many audiophiles like to be able to extract the smallest detail embedded in the record or CD and that's what tickles their brain. Others, like myself, want to be able to listen to the sound of music and be excited not by detail, but by the sound as a whole; the sum of its parts will put me in a different realm of experience; it's almost like being in a trance. I don't want to analyze; I want to experience. At the most basic level, it is a simple tap test; I've auditioned many a speaker where I could hear the artist's take a breath in and guess the length of the guitarist's nails, but was unmoved. The same music through a different speaker would make me tap my foot and nod my head saying, "yeah." That's musicality to me.