Yeah, and at a certain point, that mathematical abstraction becomes a bit of a distinction without a difference, because as you approximate a just interval better and better, the longer your notes have to be before someone can really detect any difference in how the harmonics are beating against each other. There's a kind of uncertainty principle where in order for a note's pitch to be really precisely defined/measured, it has to be very spread out in time -- something like a clap has a very poorly-defined pitch, and the longer the notes get, the more precisely their frequencies can be measured. Exactly where you start regarding pitches as the same will depend on the music you're trying to make, and things like distortion can also get involved in making it easier or harder to hear and feel.

@@cgibbard I was just going to say the same thing . . . Indeed, it is like how the Uncertainty Principle works in particle physics: kzfaq.info/get/bejne/jJucksiZ07ObY6s.html