I've been exploring the music relations of superparticular intervals recently and their implications for just intonation and the Harmonic Series. I'm worried that this sort of thing is too mathematically involved to post here and still remain relevant. At the same time, I'm not sure how many people on the mathematics site have sufficient musical background to help. Is this sort of musical theory appropriate for this site?
Yes, all branches of music theory are on-topic here. However, more obscure systems may need a certain amount of explanation from the asker to be accepted.
You can usually gauge this by the number of existing questions in the relevant tag on the site. So, a question about 12-tone harmony needs very little background, as would one about just intonation. But if, for example, you've developed your own system of music theory, you'd likely need to do quite a bit of explanation before your question would make sense to this audience.
In your case of "superparticular intervals" -- that was the only term I wasn't familiar with, and a quick google showed that it can simply be explained as "harmonic ratios of the form
n+1/n", which an asker could easily include in their question on the topic.
Ultimately it depends on the question, but I would think unless your question is exceedingly specific to mathematics, Music would be a good place to start.
Seems like this would be a good place for it, but I wonder how many experts really exist in that area that use either site. That's super niche. But I'll say this... one non-obvious area it applies is for synthesizers and synthesis (additive, subtractive, FM). There are synthesizers that actually take mathematical formulae as patches, directly into the user interface (!). Does that make a possible point for the sound design SE, instead, maybe?