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In the same way homeopathy does work, just not for the reasons many homeopathists think it works.
There is more to reality than we know.
Studies that conclude really radical things are often quickly repeated by peers to confirm results. This is a rather old one and the best that someone has done is say "unlikely", referencing that there is no active ingredient in the preparation, so it "shouldn't work".
http://www.biomedcentral.com/1472-6882/3/7
Mice poisoned with arsenic, given extremely low quantities (almost non-existent) of arsenic as the remedy, had significantly better outcomes than the ones given no treatment. It even further said that in a separate experiment, dilutions of arsenic to low levels gave rats a better outcome too. Nobody has disproved this so far. Assuming there were significant (But tiny) quantities of As in the medication, an effect called hormesis could speak for the outcome, but some of these homeopathic remedies apparently have one or zero molecules of the active chemical in a normal dose.
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Play a chord to a non-musician, followed by a different chord. Ask them which sound was higher pitched. There will be unanimous consensus about which sounds higher. With further testing, we realize what seemed to the listeners to be a single sound is a chord made of three distinct notes, and the dominant note in the higher sound is, in fact, higher, but the other two notes could have been pitched lower than the lower-sounding chords' quieter two notes. So for the most part, the listeners were approximately two thirds wrong. Now imagine if actually, each of the three notes making the chord were actually chords themselves, each actually a set of notes too fine for us to distinguish with our ears or instruments. Once again everything seems right when viewed one way from the current perspective but may be different in an unknown one.
As square waves are actually an infinite number of sines added together, when viewed with the understanding that sines are the raw building block of sound, sine waves are an infinite number of square waves added together, if one recognizes the square as the simplest signal type. Given that the current finer understanding of reality takes "fluid" amounts of energy such as a waveforms' magnitude being any floating point value when viewed from the understanding of relativity, and describes them in quanta, discrete, uniformly sized packets of energy, the square wave (on, or off) seems to be the better candidate for the raw "building block" of sound. When viewing sound energy propagation through air, it simply presents itself as sines, because that is how we view air molecules interacting. How do they intraact?
All our theories are supported by evidence leading back to the theory and vice versa, but the whole system is only correct when viewing it as humans with our limitations of matter/energy manipulation and interaction. It can be correct but it can be wrong when viewed more broadly. The notion of time, which we all plainly understand and see this very second, is completely synthetic and made up as a product of viewing the objective reality in the way that we happen to.
Perhaps the emotional, mental understanding, feel, and thought or perception of the music travels
not as the measurable electrical and mechanical energy representing the sound, but within a yet unmeasurable format such as the spins (or some quality/behavior of particles, I don't know anything about physics) of the matter that forms a solid physical coupling from source component to brain. The measurable electrical and mechanical effects in the wire and air
come as a product of this higher-level propagation.
In a nutshell: If it sounds better it is better. =D