For a scientific world in which it is recognized that a previously accepted theory will be overturned by another more complicated theory in time, there arises a question of belief, as scientifically-minded people must recognize the evolving situation yet distinguish between theories they presently accept and those which they never did. The dominant idea behind this distinction has become, courtesy of philosopher Karl Popper, that of falsifiability. Basically this means that if it is possible under certain conditions to falsify (disprove) a theory, and it has not yet been falsified, then we accept it as valid. This is actually a descriptive paradigm, because it is supposed to describe how scientists behave. As the dominance of the scientific worldview has spread, the idea of falsifiability has filtered into other disciplines, and has become especially well-entrenched in the daily lives of people who are not scientists themselves but do follow its cult. The latter describes an increasing number of professionals in all areas, including music & the arts. Ultimately this makes falsifiability an important issue in music, if only because of its audience, and especially in early music.
Now that the German scientific model of career evaluation is dominant in universities throughout the world, academics in art & music must present a thesis rather than demonstrating scholarship per se. This makes falsifiability one of the primary movers in art music, and even partly explains the popularity of the "authenticity" phenomenon itself. The first issue is that for events of the past, falsifiability only takes us so far. Beyond a certain point, and with a few circumstantial exceptions, details of performance cannot be known. In other words, there are various "theories of performance" which are simply unfalsifiable (short of inventing a time machine), yet which are presented under the general rubric of thesis & argument. There is no new information to use, and there is nothing else the notation can tell us. We are left to accept or reject them based on other factors, and one factor which has indeed been influential is whether they reflect a kind of science-like determinism used to defuse criticism concerning a lack of individual thought. Beyond that, even if we know exactly how the composer or someone else heard or envisioned a piece of music, do we necessarily care? Art is not about whether an airplane will fly or crash, and to continue the analogy, we cannot even agree on which of the two we prefer.
Another area in which science-like ideas intrude into aesthetics is in so-called proofs of the superiority of one set of musical constraints. Ordinarily this means Western tonality, and uses integer interval ratios and pure mathematics as a way to conflate paradigms and suggest some sort of credibility for the broader argument. In other words, although the ratios and their relationships certainly fit within the doctrine of falsifiability, the notion that music should use them in particular ways does not. Citing physiology and brain response is just another way to imply aesthetic conclusions in a "scientific" way, while surreptitiously positing what are usually naïve assumptions on what the goals of art actually are. Even music which does fit the desired patterns did not arise from anything so simpleminded, and in fact this raises the question of whether scientific philosophy is even as rich as aesthetic philosophy. When I did science, I approached it with an underlying aesthetic philosophy, and that behavior was by no means unique among my peers. Remember that falsifiability as a concept is descriptive. Of course, given the ubiquity of science, there is no reason it should not be an inspiration for the arts, but then art will encompass everything, and that includes aspects of human nature which scientism not only neglects but willfully discards.
So what if a piece of music or a performance were actually falsified? What might that mean? At one level, this was exactly the contention of the early "authenticity" movement, but of course arguments became much trickier when the traditional performers actively defended themselves. Ultimately, the movement was about inventing new criteria and saying they were being falsified by others. Unlike the physical world, however, they simply aren't binding. In fact, the scarcity of information allows one to play "connect the data points" in the most circuitous fashion, and in many cases there is no possibility that another point can be placed on the diagram to falsify the picture (especially if one gets to decide what the diagram is about!). Suppose we are more concrete and ask about cases where a performer specifically claims to be doing something, but that this can be proven false. I am less fond of such things, but am not sure I want to draw any kind of line here. What if the performance remains artistically stimulating? History is full of artists who thought they were following someone else but ended up creating something new & exciting. I guess the lesson here is that one should think clearly about which propositions are falsifiable and which are not, but that this concern needs to be measured against a broader aesthetic matrix.
Scientific theories of art will always meet up against this fuzzy barrier, precisely because the human artist as actor will seize upon the boundaries and subvert them. This is what makes art such a powerful endeavor, and guarantees that it will continue, even if various forces seek to make it subservient to commerce. When it comes to auxiliary questions such as authorship or pitch, we cannot rely on the "objectivity" after which science chases. While we can happily debate authorship without real consequences, we must determine pitches in order to create a performance. This is an individual aesthetic choice, and while some might view that statement as an abdication of responsibility, it can also be viewed as an intensification of that responsibility. Artistic decisions are ultimately more challenging precisely because they do not have a hard reality upon which they can rest.