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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.

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Thinking about Yorkshire 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 Sur­prise on any num­ber (8 or more, since it is false on 6 bells).

The basic idea of York­shire 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.)

In York­shire there is an excep­tion to this out-of-phase treble bob­bing: start­ing when the treble is dodging at the back, one of the bells treble-bobs in phase with the treble and one dodging pos­i­tion below it, mak­ing 2nd place over the treble at the lead-end, and con­tinu­ing in phase until the treble reaches the back again.

Everything else in York­shire is a con­sequence of this change from Cambridge.

The bell that starts doing this in-phase treble bob­bing is the 5th-place bell, from the half-lead when it has passed the treble at the back, and con­tinu­ing as the 2nd-place bell until the half-lead as it approaches the back. For brev­ity, I call this piece of work the in-phase bell, because it is treble-bob hunt­ing in phase with the treble. (This isn’t a short­hand I have come across else­where, but it is a con­veni­ent term.)

Because the treble and the in-phase bell are in adja­cent dodging pos­i­tions, the oth­er bells meet the in-phase bell imme­di­ately before or imme­di­ately after meet­ing the treble, They must either pass it or dodge with it, just as they do with the treble.

Remem­ber that in Cam­bridge places a bell dodges with the treble in the middle of the work, mak­ing places either side of that dodge in order first to get in phase with the treble, and then to get back out of phase. But in York­shire there is imme­di­ately anoth­er in-phase bell to deal with: so if we have dodged with the treble we must cur­tail Cam­bridge places to pass the in-phase bell. Or altern­at­ively, if it’s the treble that is passed, then we must dodge with the in-phase bell and make places to change phase. This changes Cam­bridge places into York­shire places and also adds them in pos­i­tions where in Cam­bridge you just plain hunt past the treble.

Let’s see what that means in practice.

(more…)

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