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ringing.info
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What’s change ringing? I’ve never heard of it.

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it’s a bell (think church bells) ringing technique surprisingly closely related to group theory in mathematics. Here’s a video explaining theory and practice: https://m.youtube.com/watch?v=f5GmUxl2NaU

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tl;dr:

• Ringing church bells (or handbells);
• every permutation is different;
• bells don’t move more than one place from one permutation to the next (think braiding);
• you need a pattern of changes that produces the sequence of permutations

Take a church tower with usually six bells, but let’s say four, to keep the examples simple.

Now ring those bells in order from high to low:

``````1 2 3 4
``````

Next ring the bells in a different order (a different permutation), but each bell may only (a) swap places with the bell before or after it, or (b) stay in place. For example, you could swap the last two bells:

``````1 2 3 4
---
1 2 4 3
``````

Each permutation of the four bells is called a row: we have just rung two rows. Now you want to keep going: but:

• you don’t want to repeat any rows (permutations)
• your bells are still limited to either swapping places with their neighbour, or staying in place.

and to that you add these artistic constraints:

• you want to ring every permutation of your 4 or 6 bells, or perhaps half or a quarter of all possible permutations, without repeating any permutation
• you want your ringers to be able to remember what to ring – they’re not going to memorize the 6! = 720 permutations, and the place of their bell in each permutation. (A conductor who “calls the changes” helps here; but you’d still want large stretches to be predictable, so that the conductor can limit themself to calling the special bits.)

So you need a predictable pattern (of, say, 24 rows) of which bells stay in place, and which bells swap; and when you reach the end, you swap two bells and repeat the pattern with a different starting row, so you get another 24 permutations out of it; and you do that again until you’ve finally rung all possible rows (or an eighth/quarter/half of them). That pattern is also called a method, and because it determines the sequence of notes you hear you could also call it a compostion.

All the above is explained much better in the video @tgfrerer linked, which is shortish and enjoyable.

Compositions have exciting names like “Kent Treble Bob” or “Double Oxford Minors” or “Grandsire Triples”.

For fun, and because we have an infinite canvas here, here’s you could go through all 24 permutations of 4 bells by swapping exactly one pair each round. Another method/composition could have you swapping sometimes two bells, sometimes one; and with six bells there’s even more possible ways to generate subsequent permutations, eventually generating all of them.

`````` 1 2 3 4   The first row of a peal is traditionally from high to low, a.k.a. rounds
--- } Bell 4 hunts down (towards the front)
1 2 4 3 }
---   }
1 4 2 3 }
---     }
4 1 2 3
---   The back end swaps
4 1 3 2
---     } Bell 4 hunts up (towards the back)
1 4 3 2 }
---   }
1 3 4 2 }
--- }
1 3 2 4
---     } The front end swaps
3 1 2 4
--- } Bell 4 hunts down
3 1 4 2 }
---   }
3 4 1 2 }
---     }
4 3 1 2
---   The back end swaps
4 3 2 1
---     } Bell 4 hunts up
3 4 2 1 }
---   }
3 2 4 1 }
--- }
3 2 1 4
---     } The front end swaps
2 3 1 4
--- } Bell 4 hunts down
2 3 4 1 }
---   }
2 4 3 1 }
---     }
4 2 3 1
---   The back end swaps
4 2 1 3
---     } Bell 4 hunts up
2 4 1 3 }
---   }
2 1 4 3 }
--- }
2 1 3 4  And that's the last of the 24 possible permutations!
(---    ) If we'd continue the pattern, we'd be back where we started
(1 2 3 4)
``````
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I bounced over to Wikipedia, and no, it doesn’t make change ringing any easier to understand.

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Amen. It’s a very jargon-heavy fields; some of the jargon describes a place (whichever bell is in it), and some describes a bell (whichever place it is in); some jargon describes what a single bell does, some of it describes how an entire row changes; and some of it describes a pattern across multiple rows; and some of it describes repetitions/transitions of that pattern.

I think it’s actually hard to understand in a similar way that it is hard to understand how computers work: being simultaneously aware of what is happening at multiple levels of abstraction is difficult, and it’s doubly difficult when you don’t know *any* of the levels yet..

Perhaps it gets easier once your brain has practiced so much that it can recognise patterns at each of those levels? I wouldn’t know, I haven’t got that far.