You're right, of course. My wording is was bit poor.
What I should have said that harmony is less ad hoc; it has less "degrees of freedom".
With regards to melody, there are tons of tuning systems that are quite close to the usual twelve-tone equal temperament. It would be hard to give a convincing argument that one of these sounds better than all others.
Contrast this to the system of harmony where the basic principle is that ratios of small integers sound good together. This is not the only possible system of harmony, but it does seem to represent some kind of local optimum. And this makes it more amenable to the kind of purely theoretical reasoning that the article is trying to do.
What I should have said that harmony is less ad hoc; it has less "degrees of freedom".
With regards to melody, there are tons of tuning systems that are quite close to the usual twelve-tone equal temperament. It would be hard to give a convincing argument that one of these sounds better than all others.
Contrast this to the system of harmony where the basic principle is that ratios of small integers sound good together. This is not the only possible system of harmony, but it does seem to represent some kind of local optimum. And this makes it more amenable to the kind of purely theoretical reasoning that the article is trying to do.