You might think it’s unlikely for any interesting mathematics to arise from incense appreciation, but that’s only because you’re unfamiliar with the peculiar character of Muromachi (室町) era Japanese nobles. There has never been a group of people, in any time or place, who were so driven to display their sophistication and refinement. It wouldn’t do to merely put out a few sticks of incense; no, you would have to prove that your taste was more exquisite, your judgment more refined, your etiquette more oblique.