Musicality is a deep and complex subject. In the Western tradition, the philosophy of music, and music theory, are highly sophisticated and systematic disciplines that have stood the test of three millenia, from their Hellenic origins. Thinking about the relationship of music to (and the concept of musicality in) figure skating has really only been around a few scant decades, and mostly in an ad hoc rather than methodical way, so I think it extremely useful to build on these foundations in examining what it means for skating.
The key general concepts of musicality that are particularly applicable to skating, it seems to me, are: rhythm, articulation, fluidity, expressiveness, interpretation, and projection. In my view, Yuna is among the most musical skaters ever (which, in addition to the translucence and electrifying athleticism of her skills, is why I'm such a huge fan), so I use her as illustration.
-Rhythm. What do we mean when we say that a poem is musical? Most prominently, we are referring to its meter (if rigorous) or its sense of beat (if the structure is not so rigid), as well as ancillary techniques to create pace, such as punctuation. Its rhythm, in a word. For activities that do not express themselves in the language of notes (which includes poetry, dance, and figure skating), the foundation of musicality is rhythm.
In skating, it has to do with the consonance of movement with the time of the notes, and that seems fairly basic. But in practice, it is difficult to do well, because it is not (or at least shouldn't be) just limited to whether major elements (e.g. a step sequence or a spiral, or even a jump) are timed to the music's beat. This would be like a pianist who continuously ignored the time signature, except at points of emphasis such as a change in register or a crescendo. Just as in a musical score, a truly rhythmic skater displays a "groove" throughout, in all her movements, not just sporadically but continuously, with her body, arms, head, even her fingers. When I consider Yuna's performances, whether classical (Danse, Meditation, Gershwin, Giselle) or pop (Bond, Fever, Bulletproof) or non-Western (certain sections of Homage to Korea), and whether they are among my favorites of her performances or not, the unerring rhythm and pace never fails to amaze me.
-Articulation. In skating, this has to do with the clarity, the transparency, of each individual movement, in consonance with "movement" in the music (and I find it evocative and revealing that music feels the need to use the metaphor of movement in describing key aspects of itself). I used to get grief all the time as a young kid (took violin and piano lessons) for the lack of precision, the vagueness, of my fingering. On the other end of the scale (so to speak) is someone like a Glenn Gould, or a Jascha Heifetz, who point the way to what articulation means as a performance quality that is in reference to music.
-Fluidity. This quality refers to the physical ease and seamlessness of transition from movement to movement, and from moment to moment, again, in consonance with the "movement" in the music. It is very often the case, I think, that articulation and fluidity are often at odds in skating. The former risks creating physical and mental tension resulting from its requirements for focus and precision, while the latter requires relaxation, and thus the ability to combine these two qualities is rare.
At 2011 Worlds, I understand that Irina Slutskaya commented that on Russian TV that, while she could not fully put into words why Yuna was so special and unique in her musicality and artistry, one aspect that she could put her finger on is that every movement had a 'finished' quality that was incomparable. I surmise that Irina is specifically referring to Yuna's articulation and fluidity of movement here. And in my view, Irina should have keener eyes for this than most, which is at once ironic and understandable, having suffered for perceived shortcomings in these areas vs. her great rivals in the course of her long career. (A thanks to elegance, a Russian member of Yuna's forum).
The above qualities, rhythm, articulation and fluidity, all in consonance with the characteristics of the accompanying music, is what constitutes, in my view, the "technical" aspects of musicality in skating, or musicality proper. This is because these qualities directly refer to qualities in the music itself (specifically the "movement" in the music), and otherwise have no value referent. (In other words, rhythmic in relation to what? Articulated and fluid in comparison to what?). In this, dance and figure skating are similar. There is a reason that dance is inevitably coupled with music, aside from the occasional experimental piece, and that is to partake of these musical qualities. One could, I suppose, argue that articulation and fluidity can be achieved without music, but absent the almost mathematically abstract sub-structure that music confers, they will gravitate toward pure naturalism. The result would amount to a difference in kind (and therefore could no longer be, ipso facto, "musical" qualities, and it is in their musical incarnations that we judge them).
-Expressiveness. Where expressiveness differs as a quality from those above (i.e. rhythm, articulation, fluidity) is that it is not solely and uniquely a characteristic of music. Literature of all types can be expressive, as can speeches, paintings, sculpture, dance, etc. This is because all of these activities have something in common: they are all intentional representations of an emotional state or idea (the definition of expressiveness), and are therefore on equal footing with each other in this respect. Figure skating movement, and dance, through physical movement, can be expressive without music, exactly because all of these disciplines refer to things outside of themselves. Skating, dance and music are in this sense all vessels, that can be filled with the thematic content that they try to represent.
Practically speaking, the affect of skating and dance without music may be less precise, simply because the languages of skating and dance are less precise. But in contrast to qualities of musicality proper (as defined above), this is a difference of degree, not kind. The overlap of expressiveness with musicality most often occurs when the skater (or dancer) chooses to use the thematic representation contained in the music as the sole and strict guide for emotional representation in the skate. But despite what the PCS definitions may imply, it does not have to be so, aesthetically speaking.
I was chatting online (on a different forum) some time ago about Michelle's Scheherazade program, and the first version I watched was the 2001 Goodwill Games performance. There seemed to me something missing, or odd, in its atmosphere. The awkward edit of the music didn't help. But then I saw the skate at 2002 US Nationals, and a proverbial lightbulb went off in my head:
"The edit of the music seemed to be the culprit, and I thought that its shortcomings were particularly evident in the Goodwill skate. But as I kept re-watching the Nationals skate, it suddenly occurred to me that there was a kind of interior logic here: as you said, Michelle was facing doubts and criticism, both external and internal, at this period in her career. Did she still have the goods? Was she washed up? It now seemed to me that first part of the program, with its dark, dangerous, and foreboding mood, was allusive of the public questions she was enduring and her own fears. In her Goodwill skate, I felt that she wasn't quite able to shake this mood and it clings to the skate to the the end. At the Nationals, however, I saw something different: the second "act" of the skate, where Scheherazade's character is introduced, showed me a reflective Michelle who was now accepting her predicament with peace and grace, acknowledging to herself that she cannot stop the wheel of time and age. The third and last act then becomes an almost heroic stance: she may not be what she once was, the jumps not as effortless and easy at this stage, but she will do what she loves, and do it with every fiber of her being. The older Beowulf on blades. She becomes joyful now (the hand gesture I mentioned at 3:52 acting as the spark), a spirit of fire, and from 4:00 the blazing crescendo of her final movements (which called to mind Yuna's finish in Danse Macabre) sweeping her to her Valhalla. The key to understanding this skate, it seems to me, is that Michelle wasn't telling Scheherazade's story, she was telling her own. For me, the incomprehensible became comprehensible. A program that began at the Goodwill Games with badly edited music became, to me, a triumph; Michelle remolded it to her own ends at the Nationals skate, making the program's weakness into a strength by force of will and internal purpose. The music may have been from Scheherazade, but the text could have been Sinatra's "My Way" . Her tears at the end of her program said it all."
Michelle's Scheherazade at Nationals was for me a kabbalistic lesson in miniature; there was a text within the text, an intensely private meaning that overwhelmed and subsumed the ostensible themes and emotional representations of the musical score. The music was subservient to the emotional intentions of the skater, not the other way round. I see a similar dynamic of private gnosis in certain of Yuna's performances, including her ATS Summer version of Meditation de Thais, and, in spite of flaws in execution, her Homage to Korea performance at Worlds.
-Which leads to Interpretation. Like expressiveness, this is not musicality strictly defined, but a placeholder for the choices one makes, in the emotional affect that is to be pursued (the expressive intent), in the first place, and in the details of the movements that will act as the carriers of this thematic representation, in the second. One can thrust the arms out powerfully, with a beaming laugh, to express joy. Or do it with less force, a reflective smile on ones face. Such nuances shade the viewer's perception, and in the best performances, results in a coherent emotional meaning. Interpretation is that which mediates between musicality and expressiveness, (very) metaphorically akin to the force-carrying particles of quantum theory. The interpretive nuances of Yuna's Meditation EX at ATSS, subtle, detailed, authentic and hypnotic, is an example of the importance of interpretive choices. As in viewing any artistic project, however, fullest appreciation of interpretive selection requires some knowledge of both the musical program and the performer's history.
-Projection. In my view, this is the intensity/energy level at which one captures the viewer's attention, and is powered by force of personality. However, it has no thematic content of itself. By analogy, both a car crash as well as a last-minute swerve away from danger can be so riveting that you can't take your eyes off them. At its best, projection serves as an accelerant, that can heighten the expressive effect. Although only fifth or sixth on my personal list of Yuna programs, her Bond SP is a pretty clear example of the sheer wattage that she can bring to bear.
Finally, as a general point, my own view is that, at a certain level of aesthetic achievement, both natural talents and many thousands of hours of effort are necessary. Thus, the question of whether musicality in skating is natural or learned is a distinction without a difference.