March 21, 2017

Calling Bob Minor

It’s a long time since I have written anything here, but I want to call a quarter peal, and Bob Minor is a plausible method. So I’d better work out how to do it.

This is based on a piece that appeared in Ringing World in 2008, of which I have a copy. But this is reconstructed from memory as part of my usual trick of trying to learn something new.

A quarter peal of Minor is 1260: a peal on seven bells or fewer is 5040 changes, which is the extent on seven bells, i.e. the maximum number of different changes which is 7! or 7×6x5×4x3×2. And a quarter of 5040 is 1260. (A peal on eight or more bells is 5000 changes.)

The basis of this quarter peal is a common touch of Bob Minor that I have called a number of times, which is to call bobs when the tenor is dodging 5-6 down and up (known as ‘home’ and ‘wrong’ respectively). If you call this twice then it comes back to rounds after 10 leads, which is 120 changes. The pattern of lead ends is: bob, plain, plain, plain, bob; and repeat bob, plain, plain, plain, bob. The three plain leads are when the tenor is among the front bells, dodging 3-4 down, making 2nds and dodging 3-4 up. Incidentally, this touch can be extended into a 240 by calling a single at any one of the lead ends, completing the 120, which now doesn’t come round, and then repeating the exact same pattern of calls at the lead end, including the single, and it will now come round at the end of the 240. I’ve called this a few times, and tried to call it a few more!

So we take this 120 of ‘bob, plain, plain, plain, bob; bob, plain, plain, plain, bob’, and omit the last bob. Instead of coming round this permutes the order of bells 2, 3 and 4. Instead of running in at a bob, the 2 dodges 3-4 down, becoming the 4th-place bell. Instead of running out, the 3 makes 2nd place, becoming the 2nd-place bell; and instead of making the bob, the 4 dodges 3-4 up, becoming the 3rd-place bell. So at the end of this part, after 120 changes, the order of the bells is:

134256

Repeat this, and, after 240 changes, the order will be
142356

And again, after 360 changes:
123456

But instead of letting this come round, we call a single, which swaps the 3 and 4:
124356

And now we can repeat that 360 to make a 720. At the end of the next three 120s with the matching single at the end, the order will be:
143256
132456
123456

720 changes is the extent on six bells, all the possible ways of arranging the six bells, i.e. 6! or 6×5x4×3x2 = 720.

The 720 consists of:
wrong, home, wrong, (plain at home)
wrong, home, wrong, (plain at home)
wrong, home, wrong, single at home
and repeat once more.

Or:
bob, plain, plain, plain, bob; bob, plain, plain, plain, plain;
bob, plain, plain, plain, bob; bob, plain, plain, plain, plain;
bob, plain, plain, plain, bob; bob, plain, plain, plain, single
and repeat once more.

To get up to 1260 we need to add another touch of 540.

Let’s go back to that basic block of 60 changes wrong-home-wrong-home. The lead ends look like this:

123456
The next lead would look like this if it were a plain lead:
135264
but we call a bob instead (at ‘wrong’) so, the 3 runs out, the 2 runs in and the 5 makes the bob:
123564 (after 12 changes)
Then there are 3 plain leads:
136245 (after 24 changes)
164352 (after 36 changes)
145623 (after 48 changes)

Then there’s a bob (a ‘home’), so we get
145236 (after 60 changes)

Repeat this, with a single at the end instead of a bob:
145362 (bob here ‘wrong’)
156423
162534
123645
132456 (single here ‘at home’ after 120 changes)

And ring a plain course with a single at the end:
125364 (no bob ‘wrong’)
156243
164532
143625
134256 (single ‘at home’ after 180 changes)

So in 180 changes we have gone from
123456
to
134256

If we repeat this 180 two more times we get:

142356 (360 changes)
123456 (rounds after 540 changes)

To summarize, the 540 is:
wrong, home,
wrong, single at home
(plain at wrong), single at home
and repeat twice more.

We put these two touches together, the extent of 720 and the touch of 540 and that’s 1260 changes, which is a quarter peal. I think I’ve understood it now — committing it to memory is the next task. Then trying it out, and also ensuring that those ringing 2, 3 and 4 can cope with the singles.

(Acknowledgements to Ringing World, 23 May 2008, article by Simon Linford.)

Posted by Simon Kershaw at March 21, 2017 9:45 AM | TrackBack
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