Thinking allowed

Thinking about Yorkshire and Pudsey Surprise

I looked recently at the underlying structure of Cambridge Surprise on any number of bells (6 or more), and now I want to do the same with Yorkshire and Pudsey Surprise on any number (8 or more, since they are false on 6 bells, though still ringable as Yorkshire/Pudsey Block Delight Minor). This may well not directly help you to ring these methods, especially if you are just learning them. But understanding the structure of a method helps you know why you’re doing what you are doing, and what other bells are doing around you.

You might think Pudsey is a slightly odd choice to include immediately after Cambridge, but there’s a good reason why. In many ways it is the complement of Yorkshire: the changes each of these methods make, compared with Cambridge, are essentially identical except that they are made in different places.

The basic idea of Yorkshire and Pudsey is similar to Cambridge: the treble always treble-bob hunts in each dodging position (1-2, 3-4, 5-6, 7-8, etc); and wherever possible the other bells treble-bob hunt, but out of phase with the treble.

(See the article on Cambridge structure for a reminder of what it means to treble-bob hunt either in phase or out of phase with the treble.)

But Yorkshire and Pudsey each make one additional change to Cambridge. In each of them there is one bell that treble-bob hunts in phase with and adjacent to the treble, and the other bells have to deal with that bell as well as with the treble. The two methods differ only in which bell is in phase with the treble, and therefore in which places the extra adjustments must be made.

In Pudsey, it is the 3rd-place bell, which treble-bobs up to the back, dodging down with the treble and making places under the treble at the half-lead, and then dodging up with the treble and back down. Except when dodging with the treble at the back it is always one dodging position higher than the treble.

In Yorkshire, conversely, a bell treble-bobs down to the front, dodges up with the treble and makes 2nds place, and then dodges down with the treble and treble bobs out to the back. This bell treble bobs one dodging position lower than the treble. Whereas in Pudsey the work begins and ends when the treble is at the front, in Yorkshire it begins and ends when the treble is at the back, i.e. from the half-lead to the next half lead, and begins as the work of the 5th-place bell, which becomes the 2nd-place bell at the lead-end in the middle of this piece of work.

Yorkshire     Pudsey
half-lead end -----5-1 1-3----- lead end
----5-1- -1-3----
-----5-1 1-3-----
----5-1- -1-3----
treble-bobs down to the front ---5-1-- --1-3--- treble-bobs out to the back
--5-1--- ---1-3--
---5-1-- --1-3---
--5-1--- ---1-3--
-5-1---- ----1-3-
5-1----- -----1-3
-5-1---- ----1-3-
5-1----- -----1-3
51------ ------13
15------ ------31
where it dodges with the treble 51------ ------13 where it dodges with the treble
15------ ------31
makes 2nd place over the treble 12------ ------31 makes (n-1)th place under the treble
21------ ------13
and dodges down with the treble 12------ ------31 and dodges up with the treble
21------ ------13
2-1----- -----1-3
and treble bobs out -2-1---- ----1-3- and treble bobs down
2-1----- -----1-3
-2-1---- ----1-3-
--2-1--- ---1-3--
---2-1-- --1-3---
--2-1--- ---1-3--
---2-1-- --1-3---
----2-1- -1-3----
-----2-1 1-3-----
----2-1- -1-3----
-----2-1 1-3-----
----2--1 1--3----

These two pieces of work are mirror images of each other.

Next, let’s consider one small but important point. In Yorkshire, the bell treble-bobbing in phase with the treble is below the treble. The other bells must change their behaviour (compared with Cambridge) whenever they meet this bell, and by definition that can only happen below the treble, since that’s where this in-phase treble bobbing happens. Whenever a bell is above the treble it behaves in exactly the same fashion as it would in Cambridge. That’s why Yorkshire is “Cambridge above the treble”.

In Pudsey, on the other hand, the bell treble-bobbing in-phase with the treble is above the treble. The other bells must adjust their behaviour when they meet this bell above the treble, so the changes from Cambridge occur above the treble, but below the treble Pudsey is the same as Cambridge.

Now let’s turn to the other bells. They are trying to treble-bob out of phase, so when they encounter these two bells (the treble and the bell in-phase with the treble) then they must adapt their work.

Because the two bells are in adjacent positions, we will dodge with one and plain hunt past the other, though which of these comes first depends on where we meet them. And in addition, we must also make places adjacent to the dodge to switch phase.

There are two possibilities.

We can either plain hunt past a bell, dodge with the other, and then make places and (now back out of phase) dodge again. Or else we do the opposite of this: after dodging out of phase, we make places to get in phase, dodge with one of the in-phase bells and then plain hunt past the other.

Which we do depends on whether we have already dodged when we meet the first of the two bells.

If we meet the first of the two bells after we have dodged, then they have not yet dodged, so we must make places to wait for them, dodge, and then pass through the next dodging position to get back out of phase, and then resume out-of-phase treble bobbing. (In the following diagrams the treble and the in-phase bell are labelled p and q; in Pudsey p is the treble and q the in-phase bell; in Yorkshire p is the in-phase bell and q is the treble.)

when going down
to the front
when going out
to the back
p-q--x-- --x--p-q
-p-qx--- ---xp-q-
p-q-x--- ---x-p-q
-p-q-x-- --x-p-q-
--p-qx-- --xp-q--
---pxq-- --pxq---
--p-qx-- --xp-q--
---pxq-- --pxq---
---xp-q- -p-qx---
--x--p-q p-q--x--
-x--p-q- -p-q--x-
x----p-q p-q----x
-x----pq pq----x-
x-----qp qp-----x
Alternatively, if we meet the two bells before we have dodged, then they have already dodged and one of them is about to come into our current position so we must miss a dodge and go straight on to dodge with the other one, and having done so, make places to get back out of phase and resume out-of-phase treble-bobbing:
p-q--x-- --x--p-q
-p-qx--- ---xp-q-
--pxq--- ---pxq--
--xp-q-- --p-qx--
--pxq--- ---pxq--
--xp-q-- --p-qx--
--x-p-q- -p-q-x--
---x-p-q p-q-x---
---xp-q- -p-qx---
--x--p-q p-q--x--
---x--pq pq--x---
--x---qp qp---x--

There’s one more detail before we have enough information to understand each of these methods. If we are about to meet the treble or in-phase bell at the back, when we are in the topmost dodging position, then rather than missing a dodge or making places to get in phase we add an extra dodge. We’ve already seen this in Cambridge when we were about to meet the treble and we were at the back. Yorkshire here is identical to Cambridge (because we are above the treble), but in Pudsey this also applies when meeting the in-phase bell, so we must do these double dodges when about to meet that bell. And because the method is symmetrical, when we said “about to meet”, the same applies when “reaching the back having just met”, as it does in Cambridge.

In the full article, we’ll look at the details of Yorkshire, then at Pudsey, and then do a final comparison of the two methods.

(more…)

0 Comments