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.

Let’s look in more detail at how a couple of bells in York­shire Sur­prise Major meet the treble and the in-phase bell. The 4th place bell, and then the 8th, are suf­fi­cient to show what is going on. (The 7th and 6th place bells are respect­ively the mir­rors of these.) First the 4th place bell:

12-4----

214----- 4 meets the treble so does places and dodges with treble (York­shire places in 3–4 down)
124-----
21-4----
2-14----
-241----
2-14----
-241---- 4 com­pletes the dodge with the treble and meets the 2, so passes it, miss­ing a dodge in 1–2 down
-42-1--- which puts it back out of phase, so it can treble bob with the oth­er out-of-phase bells
4--2-1--
4-2-1--- 4 starts treble-bob­bing up, from 1–2
-4-2-1--
4---251-
-4--52-1
--4-251- 4 dodges in 3–4
---452-1
--4-25-1
---4521- 4 encoun­ters the 5 above it (the in-phase bell)
---425-1 so makes places and dodges up with it (York­shire places in 3–4 up)
--4-521-
--45-1--
--541---
--45-1--
--541---
-5-14--- hav­ing dodged with the in-phase 5, 4 meets the treble and plain hunts past it
5-1--4--
-5-1--4- which puts 4 back out of phase, so it resumes treble-bob­bing with the oth­er bells
5-1----4
51----4-
15-----4
51-----4
15----4-
15-----4 4 becomes the 8th place bell

And con­tinu­ing as the 8th place bell:

15-----8

21----8- 8 goes down to 5–6 and dodges
12---8--
21--8---
2-1--8--
-2-18--- where it encoun­ters the treble,
2-1-8--- so make places and dodge with the treble (York­shire places in 5–6 down)
-2-1-8--
--2-18--
---281--
--2-18--
---281-- hav­ing dodged with the treble, 8 encoun­ters the 2 (treble-bob­bing up in phase)
---8251- so passes it, miss­ing a dodge, which puts it back out of phase
--8-52-1
-8--251- 8 resumes out-of-phase treble-bob­bing, dodging 1–2 down
8---52-1
-8--25-1
8---521-
8---25-1 8 dodges 1–2 up
-8--521-
8--5-1--
-85-1--- and meets the in-phase 5
-8-5-1-- so makes places (2nds, 1st)
8-5-1--- to get into phase with the 5
85-1---- and dodges with the in-phase 5 (York­shire places in 1–2 up)
581-----
85-1----
581----- 8 meets the treble so hunts past it, miss­ing the dodge in 3–4 to get back out of phase
518-----
15-8----
51--8--- 8 resumes treble-bob­bing out of phase
15---8--
15--8--- 8 becomes the 5th place bell

There are some oth­er con­sequences of this. When learn­ing York­shire after Cam­bridge, it is com­mon to con­sider the Cam­bridge front­work (either side of mak­ing 2nds place over the treble at the lead end) as divided in two and assigned to the 8th and the 6th place bells. But it is bet­ter, in York­shire, to con­sider it as York­shire places up or down in 1–2 rather than as half the Cam­bridge frontwork.

We can then see that York­shire places are made altern­ately up and down. This begins with the work of the 6th place bell, where all the up places include a dodge with the treble, but all the down places involve a dodge with the in-phase bell. In Major the work is: the low­est set of places down, in 1–2 with the in-phase bell, then 5–6 places up with the treble, 3–4 places down with the in-phase bell, and finally 3–4 places up with the treble, becom­ing the 3rd place bell. Each of these sets of York­shire places is pre­ceded by a missed dodge, where you pass the treble if you’re going down, and the in-phase bell if you’re going up.

After doing the back­work as 3rd place bell you become the 4th place bell, begin­ning imme­di­ately with 3–4 places down with the treble, 3–4 places up with the in-phase bell, 5–6 places down with the treble and 1–2 places up with the in-phase bell. Each set of places is fol­lowed by a missed dodge where you pass the treble or the in-phase bell. The work ends with a 5–6 up dodge, becom­ing the 5th place bell.

This can be gen­er­al­ized to high­er num­bers of bells. Begin­ning with the 6th place bell, places down are with the in-phase bell, start­ing in 1–2 down and mov­ing one dodging pos­i­tion high­er and earli­er each time we come down to the front: so 1–2 down the first time, then 3–4 down, then 5–6 down etc. Between each of these places down we have to do places up with the treble, begin­ning in the highest intern­al pos­i­tion (5–6 in Major, 7–8 in Roy­al, 9–10 in Max­imus, and so on) and mov­ing one dodging pos­i­tion lower and earli­er each time we leave the front, fin­ish­ing with 3–4 places up.


In the next sec­tion, we exam­ine Pudsey.

Pud­sey is a little dif­fer­ent, partly because it is “Cam­bridge below the treble”. York­shire, remem­ber, is “Cam­bridge above the treble”, and this means that at every lead-end, when (by defin­i­tion) the treble is lead­ing, all the oth­er bells are above the treble. They are there­fore doing the same work as they would in Cam­bridge, and they con­tin­ue doing that until they each pass the treble, at which point they are in the same pos­i­tion as they would be in Cam­bridge. And as the meth­od is sym­met­ric­al, then sim­il­arly as they pass above the treble and approach the lead end then too each bell is in the same place as it would be in Cam­bridge. So when the 4th-place bell, for example, hav­ing done its York­shire work below the treble, passes the treble to go above it, it does so in exactly the same place as the 4th-place bell does in Cam­bridge, and so it does the work of the 4th-place bell in Cambridge.

Pud­sey, how­ever, is “Cam­bridge below the treble”. So at the lead-end, every bell is above the treble and doing some­thing dif­fer­ent from Cam­bridge work, and each bell will pass the treble at a dif­fer­ent point from when it passes the treble in Cam­bridge. Hav­ing passed the treble it rings Cam­bridge – but not as the same place bell as it is in Pud­sey. For example, the 4th-place bell in Pud­sey com­pletes a triple dodge in 3–4 down and then imme­di­ately passes below the treble. It is in the pos­i­tion that the 6th-place bell in Cam­bridge would be, and that is the work it does below the treble, lead­ing and then treble-bob­bing up to 5–6 where it does places to dodge with the treble and pass above it. It’s not par­tic­u­larly help­ful, espe­cially when learn­ing the meth­od, to remem­ber that when you’re the 4th-place bell in Pud­sey that you do the work of the Cam­bridge 6th-place bell when it has passed the treble.

Now we’ll look at the work of each of the bells above 3rd place in Pud­sey and see how they are affected as they meet the in-phase bell and the treble.

1-3----8 8th-place bell

-1-3--8-
1-3--8--
-1-38--- 8 meets the in-phase bell and must pass it
--183---
--81-3-- 8 meets the treble so must dodge with it
--183---
--81-3-- 8 does places to get back out of phase and dodges again
--8-1-3-
---8-1-3
---81-3- keep treble bob­bing out of phase (this is Cam­bridge 4th-place bell work)
--8--1-3
---8--13
--8---31
-8----13
8-----31
-8----31
8-----13
8-----31
-8----13
8----1-3
-8--1-3-
--8--1-3
---81-3- meet the treble before dodging, so pass it
---183-- and meet the in-phase bell so dodge with it
--1-38--
---183--
--1-38--
-1-3-8-- and make places to get back out of phase
1-3-8---
-1-38--- and keep treble-bob­bing out of phase
1-3--8--
1--38--- becom­ing 5th place bell

1-3---7- 7th-place bell

-1-3---7
1-3----7
-1-3--7-
--1-3--7 meet the in-phase bell, so add an extra dodge
---1-37-
--1-3--7
---1-37-
----173- and meet the treble so dodge and do places
----71-3
----173-
----71-3
----7-13
-----731
-----713
----7-31
-----731
----7-13 keep treble-bob­bing out of phase (this is Cam­bridge 8th-place bell)
---7--31
--7---13
---7-1-3
--7-1-3-
-7---1-3
7---1-3-
-7-1-3--
7-1-3---
7--1-3--
-71-3--- pass the treble in 2–3 and meet the in-phase bell, so must triple-dodge with it
-173----
1-37----
-173----
1-37----
1-73---- becom­ing the in-phase bell (with anoth­er dodge to do in 3–4 up)

1-3--6-- 6th place bell

-1-36--- meet the in-phase bell after dodging, so make places to get in-phase and dodge with it
1-3-6---
-1-3-6--
--1-36--
---163--
--1-36--
---163--
---61-3- and imme­di­ately pass the treble
--6--1-3 and miss a dodge to get back out of phase (this is Cam­bridge 7th place bell)
-6--1-3-
6----1-3
-6----13
6-----31
6-----13
-6----31
6-----31
-6----13
--6---31
---6--13
--6--1-3
---61-3- meet the treble after dodging so make places and dodge with the treble
---6-1-3
--6-1-3-
--61-3--
--163---
--61-3--
--163--- and pass the in-phase bell
-1-36---
1-3--6-- and miss a dodge to get back out of phase
-1-3--6-
1-3----6
1--3--6- dodge back, becom­ing the 7th-place bell

1-3-5--- 5th place bell

-1-3-5-- treble-bob out of phase to the back
1-3---5-
-1-3---5
--1-3-5-
---1-3-5
--1-3-5- in-phase bell is com­ing uo behind so add an extra dodge to wait for it
---1-3-5
----1-35
-----153 and dodge down with the in-phase bell
----1-35
-----153 meet the treble, so pass it
-----513
----5-31 (and ring Cam­bridge below the treble, as 5th place bell)
---5--13
--5---31
---5--31
--5---13
-5----31
5-----13
-5---1-3
5---1-3-
5----1-3
-5--1-3-
5--1-3--
-51-3---
-5-1-3--
5-1-3---
51-3----
153-----
51-3----
153-----
15-3---- make 2nds place over the treble and become the 2nd-place bell

The 4th-place bell is the reverse of the 7th, and the 2nd a reverse of the 5th.


And finally, we lay out the blue line for York­shire and Pud­sey Sur­prise Major, side by side. From this can be seen that “Pud­sey is not York­shire” or rather, “Pud­sey is not-York­shire”. That is, begin­ning with the work of the 6th-place bell, and con­tinu­ing until you become the 3rd-place bell, when you make places in York­shire, you plain hunt in Pud­sey, and when you plain hunt in York­shire you make places in Pud­sey. And sim­il­arly, after com­plet­ing the 3rd-place bell, for the work that begins with the 4th-place bell, con­tinu­ing until you become the 5th place bell.

York­shire     Pud­sey
12------ 12------
 
21------ 21------
12------ 12------
21------ 21------
2-1----- 2-1-----
-2-1---- -2-1----
2-1----- -21-----
-2-1---- 2--1----
--2-1--- -2--1---
---2-1-- 2----1--
--2-1--- 2---1---
---2-1-- -2---1--
----2-1- 2-----1-
-----2-1 -2-----1
----2-1- --2---1-
-----2-1 ---2---1
----2--1 --2----1
-----21- ---2--1-
----2--1 ----2--1
-----21- -----21-
-----12- -----12-
----1--2 ----1--2
-----12- -----12-
----1--2 ----1--2
---1--2- ---1---2
--1----2 --1---2-
---1---2 ---1---2
--1---2- --1---2-
-1-----2 -1-----2
1-----2- 1-----2-
-1---2-- -1---2--
1---2--- 1---2---
1----6-- 1----6--
 
-1--6--- -1--6--- 3–4 d: Y plain hunt; P places
1--6---- 1---6---
-16----- -1---6--
-61----- --1--6--
6--1---- ---16---
-61----- --1--6--
6--1---- ---16--- Y places in 1–2; P plain hunt
6---1--- ---61---
-6---1-- --6--1--
-6--1--- -6--1---
6----1-- 6----1--
-6----1- -6----1-
6------1 6------1 both: lead and treble-bob
6-----1- 6-----1-
-6-----1 -6-----1
6------1 6------1
-6----1- -6----1-
--6----1 --6----1 3–4 u: Y plain hunt; P places
---6--1- ---6--1-
----61-- --6--1-- 5–6 u: Y places
----16-- ---61---
----61-- ---6-1--
----16-- --6-1---
---1-6-- --61----
--1-6--- --16----
---16--- --61----
--1--6-- --16----
-1--6--- -1--6--- 5–6 u: P plain hunt
1----6-- 1----6--
-1----6- -1----6-
1------6 1------6
1-----7- 1-----7-
 
-1-----7 -1-----7
1------7 1------7
-1----7- -1----7-
--1----7 --1----7
---1--7- ---1--7-
--1--7-- --1----7 8–7 d: P extra dodge
---17--- ---1--7- 6–5 d: Y plain hunt
---71--- ----17--
--7--1-- ----71-- 6–5 d: P places
---71--- ----17-- 4–3 d: Y places
--7--1-- ----71--
--7---1- ----7-1-
---7---1 -----7-1
---7--1- -----71-
--7----1 ----7--1
---7---1 -----7-1
--7---1- ----7-1- 4–3 d: treble-bob
-7-----1 ---7---1
7-----1- --7---1-
-7---1-- ---7-1--
7---1--- --7-1---
7----1-- -7---1--
-7--1--- 7---1---
--71---- -7-1----
--17---- 7-1-----
--71---- 7--1----
--17---- -71-----
-1-7---- -17-----
1-7----- 1--7----
-17----- -17-----
1--7---- 1--7----
1-3----- 1-3-----
 
-1-3---- -1-3----
1---3--- 1-3-----
-1---3-- -1-3----
--1-3--- --1-3---
---1-3-- ---1-3--
--1---3- --1-3---
---1---3 ---1-3--
----1-3- ----1-3-
-----1-3 -----1-3
----1-3- ----1-3-
-----1-3 -----1-3
------13 ------13
------31 ------31
------13 ------13
------31 ------31
------31 ------31
------13 ------13
------31 ------31
------13 ------13
-----1-3 -----1-3
----1-3- ----1-3-
-----1-3 -----1-3
----1-3- ----1-3-
---1---3 ---1-3--
--1---3- --1-3---
---1-3-- ---1-3--
--1-3--- --1-3---
-1---3-- -1-3----
1---3--- 1-3-----
-1-3---- -1-3----
1-3----- 1-3-----
1--4---- 1--4----
 
-14----- -14-----
1-4----- 1--4----
-1-4---- -14-----
--14---- -41-----
--41---- 4--1----
--14---- 4-1-----
--41---- -4-1----
-4--1--- 4---1---
4----1-- -4---1--
4---1--- --4-1---
-4---1-- ---4-1--
4-----1- --4---1-
-4-----1 ---4---1
--4---1- ----4-1-
---4---1 -----4-1
--4----1 ----4--1
---4--1- -----41-
---4---1 -----4-1
--4---1- ----4-1-
--4--1-- ----41--
---41--- ----14--
--4--1-- ----41--
---41--- ----14--
---14--- ---1--4-
--1--4-- --1----4
---1--4- ---1--4-
--1----4 --1----4
-1----4- -1----4-
1------4 1------4
-1-----4 -1-----4
1-----4- 1-----4-
1------8 1------8
 
-1----8- -1----8-
1----8-- 1----8--
-1--8--- -1--8---
--1--8-- --18----
---18--- --81----
--1-8--- --18----
---1-8-- --81----
----18-- --8-1---
----81-- ---8-1--
----18-- ---81---
----81-- --8--1--
---8--1- ---8--1-
--8----1 --8----1
-8----1- -8----1-
8------1 8------1
-8-----1 -8-----1
8-----1- 8-----1-
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