Intransitive continuity put me in mind of some methods of musical tuning. Note that I'm not a musician and this is cobbled together from various YouTube videos and snatches of music theory, but to quote Wikipedia:
(If anyone with a stronger grasp of music theory wants to educate me on how what I've said is complete gibberish, please do so!)
As I tenuously understand it, setting up a tuning scale is like trying to flatten a globe into a map: there are many different ways to do it, and all of them involve fudging somewhere. From what I gather, some tuning systems go for stronger local continuity where closely-related intervals are more "pure" at the expense of global coherence (so notes from more-distant octaves sound increasingly out-of-tune with each other), while others (such as the equal temperament common in Western music) smear the discrepancies out across the scale so that everything is just a tiny bit off from each others, but notes from distant octaves still work together, since the difference is small enough that most people don't notice.It is impossible to tune the twelve-note chromatic scale so that all intervals are pure.
(If anyone with a stronger grasp of music theory wants to educate me on how what I've said is complete gibberish, please do so!)
Statistics: Posted by Philadelphus — 10 Dec 2023 23:18