Well, the key to the Universe, as Gabriel says to the school children in The Prophesy (which is persumably relevant as it has Viggo Mortensen as Lucifer) is "Mathematics".
Music and Mathematics are very much two sides of the same coin. Both are advanced most often by prodigy savants, whose best work is usual behind them well before middle age. It seems odd, but true genii arise only in those two fields.
Music of course is also Art, and arguably the highest achievement of Human Civalization. A sophisticated, post-Victorian such as JRRT would likely have been in utter awe of the sublime work by the Great Masters over the then previous 250 years, which remains perhaps the superlative flowering of creativity in all of history.
Music also reflects a continuum of themes, motifs, chordal structures and melody. So, it corresponds to Tolkien's perspective on fate. Music sets a tone and rythm. But how it changes and grows is not known until the end. One cannot know it all at once, and the Ainur were given only a glimpse of how the Music would play out, although some such as Manwe, Mandos, Olorin, Elrond and Melkor, no doubt understood more. It is through understanding the Music that one has power in Elfin terms.
And one can make music in agreement with a larger score, and yet still make one's own music. The two themes last heard in the Ainulindale, are manifestly those of Iluvatar's children. Feanor was indeed on the edge of Fate when unlocking great secrets and expanding the Music through the beautifully sad theme, and even the horror and doom that played out through Melkor's challenge was but part of the plan.
The final theme of Men is aptly described, but even in its blaring there is beauty of those that truly can make their own music, and are free creatures of the creator, and are not tied to the rythm and harmonies of the theme of Arda, for better or worse.
Yet, whether discord and disharmony arise from the vanity of men, the evil of the Melkor or the pride of Feanor, it all redounds to the greater tune, and indeed, dissonance is a critical element of many great works of music, especially in the most recent century.
Oh, yeah, this is about Physics. There I can only think about something that Tolkien as a contemporary of Einstein might have absorbed. Music must at some point involve a meter. And yet it carries its own meter, just as one's place and speed within the universe determines the relative nature of time. So, the Valar, as one example, utterly transcend time as we understand it, through there place in the music, and Gandalf did indeed wander beyond time after fighting that winged thing.
Also, of course, what is Physics, but Math?
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