> But that's very different from claiming that western music is derived from the universal mathematical properties of the harmonic series,
Western (classical) music is marked (one might even say "distinguished") by its attention to harmonicity, which in turns is rooted in ideas about consonance and dissonace. These ideas are absolutely rooted in the mathematical properties of the harmonic series. As noted elsewhere in the comments, the work of Plomp & Levelt and then Sethares has shown how human perception of consonance (with dissonance being its reciprocal) is rooted in the averaged amplitude-weighted sum of the pair-wise disonnances between all the partials.
Sethares showed shocking ignorance towards the history of the actual usage of dissonance and consonance by practicing musicians and theorists in the history of Western music. The most obvious being that the category of dissonance and consonance has shifted over time. The most famous example being the perfect 4th, which has a simple ratio of 4:3 and should be a consonance but was treated as a dissonance against the bass for most of music history in the west (even though Sethares' graph categorise it clearly as a consonance, contrary to common practice). At around around the same time, the thirds and sixths began to be considered as consonances either, whereas previously they were regarded as dissonant and were used sparingly (composers generally avoided thirds in the final chord until around the end of the 15th century).
There's nothing inherently "good" or "bad" about dissonances and consonances, the Western ear has been trained to recognise instability in dissonances and stability in consonances, hence the ancient prohibition of dissonances in the final chord of the piece (a rule that has since been discarded). The trajectory of classical music in the 20th century shows that people can indeed get used to music which do not take that as granted. In fact, the almost unspeakable secret about dissonances is that they sound as good, even better than consonances. How else can the suspension play such an important part in western music up until then?
Sethares is of course free to define consonance and dissonance in his idiosyncratic way unconnected to common usage, but of course his definition and discoveries would then be of no use to those who use the ordinary definition.
I find this line of argument to be self proving. It seems like a variation of begging the question.
If you define a term in such a way that it is completely culturally determined, you can then prove this concept is subjective and culturally determined?
The 4th against the bass changes the perception of the root. This is why it was avoided. Using the word dissonance to refer to this is just confusing.
The definition I use and is used in the work you are rebutting is consistent, has a physics explanation and is largely cross cultural.
At best all that is going on here is a disagreement about the definition of a word.
At worst this discussion is some sort of proxy for a metaphysical disagreement about postmodernism and the subjectivity and cultural framing of all reality.
I don't think this is a fair interpretation of Plompt & Levelt's work, which is by far the more important of what's under discussion (IMO), and I don't think it's a particularly good interpretation of the work by Sethares that interests me. Why not? Because the interesting work is not about musical practice but listener perception, about audio psychology, not compositional style.
They are related to the mathematical properties of the harmonic series, but they are definitely not rooted in it.
If it was true that western musical ideas of consonance is rooted in simple harmonic ratios, and that our musical scales were based on the harmonic series, then we should be seeing subminor thirds (6:7) and supermajor seconds (7:8) everywhere. They are way more "consonant" than major seconds (9:10), or minor seconds (15:16). But in reality, they are seen as exotic and wrong.
Unfortunately, nobody said "western musical ideas of consonance is rooted in simple harmonic ratios". The whole point of Plomb & Levelt's work (recommended if you have no read it) is that provides an explanation for consonance that has simple harmonic ratios as an existential but insufficient component. From their work, what matters is not the ratios of the two fundamentals, because there are essentially no natural tones that consist of only the fundamental (1). Instead, consonance/dissonance is a result of the sum of the consonsance relationships between each pair of partials in the two tones.
Sethares extended their conclusions a bit by noting that since the partial spectrum is the definition of timbre, the most consonant/dissonant intervals would vary by timbre, which they claimed is observed in the real world.
(1) Indeed, the first step of their work, defining the "human dissonance response curve" relies on being able to use a signal generator to create pure sine tones.
Western (classical) music is marked (one might even say "distinguished") by its attention to harmonicity, which in turns is rooted in ideas about consonance and dissonace. These ideas are absolutely rooted in the mathematical properties of the harmonic series. As noted elsewhere in the comments, the work of Plomp & Levelt and then Sethares has shown how human perception of consonance (with dissonance being its reciprocal) is rooted in the averaged amplitude-weighted sum of the pair-wise disonnances between all the partials.