Musical Reductionism

Some thoughts triggered by reading the bust-up at Musical Perceptions and Mathemusicality over whether music should be analysed harmonically. Since I know nothing about Westergaardian theory I won’t comment on whether it can explain everything harmonic theories do and more. But James Cook’s (JC from here on, because I’m lazy) comment at the latter link rang bells in my head — the debate seemed to parallel philosophical debates about reductionism. Scott Spiegelberg (SS from hereon) first takes Cook to be saying that harmony doesn’t exist, and Cook denies that he espouses such a doctrine, although he had led SS down the wrong path in saying ‘I don’t believe there is such a thing as “harmony”’. The philosophical parallel is, of course, with eliminativism. JC further clarifies his non-eliminativist stance thus:

Please note that I did not say harmony was unimportant; I said it was logically superfluous. This should be a signal that I don’t believe this debate is actually about different ways of hearing music; it’s about different choices of theoretical vocabulary used to express one’s hearing of music. The point is that so-called “harmonic” phenomena admit a much better description in terms of Schenkerian/Westergaardian operations on basic tonal structures.

[...]

More generally, it should not be assumed that just because one criticizes a certain theory, one therefore is not interested in the phenomena that the theory purports to address. When I say that harmony doesn’t exist, it’s as if I said that phlogiston doesn’t exist — which doesn’t mean I think there’s no such thing as combustion.

So it would seem that JC thinks the argument should be about whether harmony is a good way to explain music. How exactly does he think Westergaardian theory is a better explanation? One point he mentions is that there are some musical phenomena that can be explained by Westergaardian analysis but not by harmonic analysis. In other words, Westergaardian theory is more complete than its harmonic competitors. Another point that has been mentioned on several occasions is that JC, along with many other composers and listeners, thinks that Westergaardian theory tracks their actual compositional thoughts and intentions more closely — they hear music in Westergaardian, not [traditional] harmonic, terms. This, however, has to be weighed against the fact (attested to by SS and other participants in the debate, and consistent with my limited acquaintances with musicians) that many other composers or listeners take a harmonic perspective to music, so harmonic theories track their musical experiences closely. Should we then abandon harmonic analyses for Westergaardian analyses? After all, at this point they seem pretty much even on the ‘natural perspective’ front, but Westergaardian analysis is purportedly more complete.

To answer (or at least feel my way towards an answer to) that question, I returned to the parallel with reductionism. The Standard Model in physics is more complete than quantum electrodynamics, quantum chromodynamics, or electroweak theory, and is the most complete and accurate physical theory we have today. Nevertheless, it’s not the case that all physical calculations are done using the Standard Model only. We use the Standard Model only when the phenomena in question are at a level where Standard Model-specific effects become important, and that is not the case for most physical phenomena under investigation today. We are happy to use the less complete theories as long as they can adequately account for the phenomena we apply them to. Nobody has suggested completely abandoning the less complete theories for the Standard Model, but it is reasonable to suppose that if Standard Model-specific effects are found to feature significantly in most observable physical phenomena, that the Standard Model will be the theory of choice in most physical calculations. In other words, eliminating the use of a theory requires more than showing that it is incomplete for certain phenomena — old theories that do account for enough phenomena adequately still warrant usage, and one would certainly not condemn these theories as fairy-tales just because they are less complete than some other theory.

Which is why I think there is no call to label harmony as something that ‘belongs instead with gods, witches, phlogiston, and élan vital in the hallowed hall of Bad Theories — those that are such that to retain them after they have been “reduced away” would actually obscure the true explanation for the phenomenon they were invented to explain.’ JC might object that QED, QCD and so on are at least consistent with the Standard Model in their domains of application, whereas harmony is, in some sense, inconsistent with Westergaardian theory, and hence should be completely abandoned. But we do not think Newtonian mechanics has the same theoretical status as ‘gods, witches, phlogiston, and elan vital’, even though it is inconsistent with modern physical theories. This is because Newtonian mechanics explains enough to warrant some respect (and continued use) as a theory. (Phlogiston is an interesting case because it did explain enough as well, but it turned out to be ‘more convenient’, in the light of our other theories about mass and so on, to reject it as an ontological entity. The literature on the phlogiston issue is extremely large and someone like me who has barely read anything about it probably has a view to crude to be worth mentioning, but it is this: I wouldn’t consider it an incapacitating blow to a theory to be compared to phlogiston.) Similarly, the purported greater completeness of Westergaardian theory does not necessarily warrant abandoning harmonic analyses. Incomplete theories can be perfectly usable within certain domains, and complete theories are not necessarily more usable — we wouldn’t describe organic chemistry in terms of the Standard Model because chemical theories are more usable, albeit less complete. If I have been successfully erecting buildings based on Newtonian mechanics, I wouldn’t abandon the theory just because one day physicists told me that some Standard Model thingy is more accurate and complete than Newtonian mechanics — Newtonian mechanics has worked so far for me, so why should I bother? Why can’t we use both theories, according to what the situation demands? For something like music, where listeners’ perceptions count for a lot in deciding which theory is the ‘best’, the continued perception of harmony by a significant group of listeners is strong reason not to be an eliminativist about harmony.