(1) The question “Is music an art or a science” is, on one level, a silly one, since it is obvious that music contains both elements. Pitches that sound good together are good combinations because whole-number ratios can describe their relationship. Strings, when sounding a octave, will have a length ratio of 1:2; when a fifth, 2:3, and so on. Thus far music seems vaguely science-y. It’s also clearly an art in that the goal of music is the expression of an individual or a community and their feelings. So far, so good.
But there is a more important sense in which music is neither of these things—art or science. The fact that we even feel the need to pit against one another “art” and “science” shows that we are following a paradigm, and that paradigm is one of decidedly modern origins. So the question holds little or no relevance to people living before 1600 because they would not have cared and it did not influence how they thought about music, how they composed it, or how they heard it.
Think about it for a moment: when we say “science” in English, most of the time we’re talking about an academic discipline that uses methods of inductive certainty to arrive at conclusions about nature. Music is not that, but do we believe there is a subtle similarity? Most of us assume that music is something that develops more like science than like literature. We assume that is gets genuinely better over time, more advanced, more complex and effective. That belief doesn’t mean we don’t see, say, 150 years ago as a golden era of music, but even if we did believe that was a golden era, we then must believe today is a dark age and 1000 years ago was too. So when we say music is a science, perhaps what we’re really doing is drudging up a positivist approach to music history. After all, isn’t there some sense in which the music of Beethoven or Brahms or Mozart or Rachmaninoff is just more advanced than Medieval music?
Similarly, when we say “art” in English, what do we mean? Art is “the spontaneous overflow of powerful emotion”; art is for its own sake; art primarily is about satisfying the inner needs of the artist and secondarily about the art’s audience and receivers. The reason we have art around is not functional, it is purely that it deserves to be there. Now, this vision of art may be how we see Classical music, including Bach and composers before his time, but it is not how all of them viewed themselves. Beethoven definitely did buy into this vision of his own art, but Dufay from the 1440s definitely did not. Is it any wonder, then, that we see Beethoven as more advanced? Speaking of buying in or selling out, the very fact that we use the words “sell out” in modern popular music is shows that we think that commercial concerns, people-pleasing concerns, functional concerns pollute musical and artistic ones. But the origins of these ideas go back not to ancient Greece or to human nature but to German and English Romanticism, whose ideas still control our thinking.
(2) So is there a sense in which we can say music is inherently either a science or an art? Perhaps yes, if we return to an older understanding of these two words. Scientia is “knowledge” in Latin; ars is “skill”. Surely music requires both. This, interestingly, puts the emphasis on the act of composing music more than anything: you need knowledge to compose music (knowledge of the rules and the literature) and you need the craft and skill (extensive practice and experience at writing music). These two things bookend, for instance, Tinctoris’ De arte contrapuncti, where he begins by quoting Horace “scribendi recte sapere [i.e. scientia] est principium et fons” (knowledge is the first principle and the fountain of writing well), emphasizing the knowledge; at the end, he gives the opposite side of the coin, “Nam, ut Cicero ad Herenium ait, in omni disciplina infirma est artis praeceptio sine summa assiduitate exercitationis,“ (after all, as Cicero said in Ad Herenium, in every discipline the art’s instruction is weak without the most possible constancy of practice), emphasizing the ars end of things. Music, then, needs both art and science to survive, but only when “art” and “science” are conceived differently from our modern expectations.
But it’s not at all clear that the Medievals actually used these terms to think about music or, if they did, that they agreed upon it. Boethius and Cassiodorus, who both originally categorized music with the three other liberal arts in the Quadrivium (arithmetic, geometry, and astronomy) did so because their conception of music was an overtly Pythagorean and Platonic one. Music was dangerous if sensually enjoyed and the sort of music that intellectuals liked was essentially mind-game stuff: arguing about tuning systems or the best way of mathematically describing a minor 2nd. But this conception of music hardly held sway among actual composers of the Medieval period, who mostly considered Boethius’ treatise on music to be stuffy and irrelevant, if they knew of it at all. It behooved Pythagoras, Plato, and Boethius to think of music and astronomy as part of the same game, since they wanted to view them as the same phenomenon of world harmony or musica mundana (Boethius attacks those who think this music of the spheres is actually sensual or hearable music); but fundamentally, these men thought that music of that sort could only be theorized about and that was the highest task music could have as a science. Obviously the western tradition didn’t go the way they thought, since soon the task of Medieval and Renaissance music became coming as close in human terms to that heavenly ideal as possible, which undoubtedly Plato and Pythagoras would have thought blasphemous.
So if we have anyone to blame for either thinking of music as a liberal art or as one of the sciences, it would probably be Boethius and his school of thought, but it was a school of thought that has held little or no influence on the actual composition of music almost from the very beginning.