Is anyone else into change ringing? I started playing around with swapping adjacent characters in a sequence, and started graphing the edges so it's easier to trace out and play the sequence on my ukulele. It struck me that this is a similar sort of thing to change ringing, though the paths I'm following through the graph don't enumerate all the sequences available
#recreationalmath #math #music
@2ck Yes! 🔔 Years ago I rang a peal of surprise major, though these days I'd struggle to remember Grandsire Doubles.
I love your graph! Seems hard to scale up far, but it's perfect for four bells, where I'm amused to see it's planar 🙂 It can represent all called changes on four bells, though to support minimus methods I think you'd want extra 'X' edges, connecting (e.g.) 1234 and 2143? Nice work!! 👍
@gtw thanks! I looked up the peals you named, but I don't really get it. I guess what I'm doing is like just having a single "track" (not sure on the terminology) since I only exchange one pair of adjacent notes from the last sequence to the next. I'd like to try swapping more though: should be fun.
I had a hunch that my construction would be planar for 4 characters after I started drawing it. What I'm doing is basically a "permutohedron". Wikipedia tells me the kind I'm playing with is isomorphic to a kind of Caley graph, but I'm not sure what the implications are yet of that.
IDK what minimus methods are.
@2ck A "minimus" method is just a method rung on four bells (e.g., "Plain Bob Minimus" is the 4 bell variant of the Plain Bob method).
https://plus.maths.org/content/ringing-changes describes some of the conventional terminology, and after reading that article, for the second time in two days I've seen the graph representation of the group of changes on four bells! But since I saw yours first, I will always feel you invented it, and Polster and Ross independently rediscovered your result 😉
@gtw Thanks for sharing: The article is altogether lovely to read.
I first heard about change ringing in a documentary I no longer remember anything else about. The physicality of the practice, the math, and mental challenge involved all fascinated me but the religious aspect of it made me wary as nonreligious person. Nonetheless, I'm sure I'll look more into it for the math, if nothing else 🙂
@2ck In my experience, ringing is completely secular (it might depend on the tower). I've heard many times the Church of England had banned ringing on Sunday for most of its history, on grounds the (stereotypically drunkard) ringers were a disgrace to the glory of the church (not sure if that's historically accurate).
I hope the band I rang with weren't that much of an embarrassment. Though I have to admit, we were such frequent customers of the local microbrewery, they named a beer after us:
