As a diversion from looking at bobs and calls in Grandsire Triples,
this time we'll examine Kent Treble Bob. This method plays a couple of
significant roles in NINE, being the method rung to welcome in the New
Year at the start of the book (and therefore responsible for the later
events of the book); and also being the method chosen by Deacon in
constructing his cypher, and which eventually leads us to the
emeralds.
So far, most of what we have looked at -- with the exception of
Stedman -- has been based on plain hunting, in which a bell leads, and
then moves successively up from place to place to the back, rings two
blows at the back, and then hunts down through each place to the lead
again. In methods based on plain hunting the treble bell always plain
hunts, and the other bells generally plain hunt, with the necessary
variations to prevent the same changes being rung more than once.
Treble bob methods, however, are not based on plain hunting, but on
treble bob hunting, or 'treble bobbing'. In a treble bob hunt, a bell
dodges in every other place, i.e. in 1-2 up, 3-4 up, 5-6 up, etc, and
similarly in 5-6 down, 3-4, down, 1-2 down. On 6 bells we can draw a
diagram like this:
X----- // dodge 1-2 up
-X---- //
X----- //
-X---- //
--X--- // dodge 3-4 up
---X-- //
--X--- //
---X-- //
----X- // dodge 5-6 up
-----X //
----X- //
-----X //
-----X // dodge 5-6 down
----X- //
-----X //
----X- //
---X-- // dodge 3-4 down
--X--- //
---X-- //
--X--- //
-X---- // dodge 1-2 down
X----- //
-X---- //
X----- //
X----- // and start again, dodge 1-2 up
-X----
X-----
-X----
etc etc
We can see that it takes twice as long for the treble to get back to
the lead -- since obviously it is ringing two blows in every place
(though not consecutively).
We can do this for each of the bells, so that they all treble bob, and
the start will look something like this:
123456
214365
123456
214365
241635
426153
241635
...
But hold it right there!
A moment's inspection will show that this is not a valid set of changes,
because we repeat every pair of rows. So we cannot have every bell
treble bobbing like this.
In order to create Kent Treble Bob, we will look at this in sections,
considering in turn each of the places at which the treble is
dodging. Remember that the treble must always treble bob, and its
course is not allowed to change, just as in Plain Bob the treble
always plain hunts, no matter what the other bells are doing.
So first we will look at the section in which the treble is dodging
1-2 up. This is what we have if all the bells treble bob:
123456
214365
123456
214365
The treble must continue to treble bob, i.e. to dodge in every other
place, and so we cannot alter what the 2 does, because it is dodging
with the treble. So instead we have the bells in 3rd and 4th places
each makes 3rds place and then 4ths place, or vice versa:
--34--
--34--
--43--
--43--
at the end of which they are in fact in the same position as if they
had dodged:
123456 // 1 dodges 1-2 up; 2 dodges 1-2 down;
213465 3 makes 3rds & 4ths up; 4 makes 3rds & 4ths down;
124356 5 dodges 5-6 up; 6 dodges 5-6 down
214365
Next we look at the section where the treble is dodging 3-4 up, which
if all the bells were treble bobbing would look like this:
214365
241635
426153
241635
426153
This time, we cannot alter the bells dodging 3-4 up or down, because
that's where the treble is. Instead we have the bell in 2nds place
make 2nds and lead again:
214365
241635 // 2 makes 2nds place; 4 leads;
426153 1 dodges 3-4 up; 6 dodges 3-4 down;
421635 3 dodges 5-6 up; 5 dodges 5-6 down
246153
This time we have altered the order of the front two bells.
Now we consider when the treble is dodging 5-6 up. Again. we have the
bell at the front make 2nds place, but we can leave the other pairs
dodging:
246153
264513 // 2 make 2nds, 6 leads;
625431 4 dodges 3-4 up, 5 dodges 3-4 down;
624513 1 dodges 5-6 up, 3 dodges 5-6 down
265431
And so we continue, looking next at when the treble is dodging 5-6
down. Again we have the bell at the front make 2nds place and lead
again, and we let the other bells dodge (or treble bob hunt):
265431
256341 // 2 makes 2nds, 5 leads;
523614 6 dodges 3-4 up, 3 dodges 3-4 down;
526341 4 dodges 5-6 up, 1 dodges 5-6 down
253614
Now the treble moves to dodging 3-4 down. We keep the bell at the
front making 2nds:
253614
235164 // 2 makes 2nds, 3 leads;
321546 1 dodges 3-4 down; 5 dodges 3-4 up;
325164 6 dodge 5-6 up, 4 dodges 5-6 down
231546
And finally we have the treble dodging 1-2 down. So we finally have to
let the bell at the front dodge, and once more we have the bells in
3-4 make 3rds and 4ths up or down:
231546
213456 // 1 dodges 1-2 down; 2 dodges 1-2 up;
123465 3 makes 3rds & 4ths up; 4 makes 3rds & 4ths down;
214356 5 dodges 5-6 up; 6 dodges 5-6 down
124365
and then we start again with the bells in these new positions:
142635 // 1 dodges 1-2 up; 4 dodges 1-2 down;
416253 2 dodges 3-4 up; 6 dodges 3-4 down;
142635 3 dodges 5-6 up; 5 dodges 5-6 down
416253
Now 4 is the bell at the front that will keep making 2nds, and so on.
Now this is a bit complicated, but having worked out a single lead
(i.e. a chunk from when the treble leads to when it leads again) we
have enough information to determine the entire plain course of Kent
Treble Bob Minor -- all we have to do is to do the same thing again
with the bells in a different starting order.
To try and make things a little simpler we can break the course up a
little differently.
First we notice that the bell which dodges 1-2 down with the treble
stays at the front, alternately making 2nds place and leading, until
the treble comes back to lead again, whereupon it dodges 1-2 up and
goes out. Whilst at the front it will ring in 2nds place over each of
the other bells in turn. For some reason this bell is said to be 'in
the slow' (a shortened form of the older expression 'in the slow
hunt').
When not 'in the slow' the bells treble bob hunt, except that (a) we
only dodge in 1-2 if it's with the treble, otherwise we plain hunt in
1-2; and (b) if the treble is in 1-2, then the bells in 3-4 make 3rds
and 4ths places up or down, rather than dodging. (But if the treble is
in 3-4 or 5-6, then the bells in 3-4 always dodge.)
(However, the net effect of making places is exactly the same as if
they had dodged, so if either or both forget to make places and dodge
instead, then after the dodge they will still be in the right place!)
We can now put all this together and write out a skeleton plain course
of Kent Treble Bob Minor, indicating the treble and one other bell, and
we add comments on what this other bell is doing:
1X---- // dodge in 1-2 down with the treble
X1----
1X----
X1---- // lead and make 2nds until the treble has
X-1--- treble bob hunted to the back and down to the
-X-1-- lead again
-X1---
X--1--
X---1-
-X---1
-X--1-
X----1
X----1
-X--1-
-X---1
X---1-
X--1--
-X1---
-X-1--
X-1---
X1---- // the treble has arrived in 1-2 down, so dodge with it instead
1X---- of making 2nds
X1----
1X---- // that's the end of 'the slow'
1-X--- // in 3rds place and the treble is below 3rd, so make 3rds place
-1X---
1--X-- // and make 4ths place
-1-X--
--1-X- // dodge 5-6 up
---1-X
--1-X-
---1-X
----1X // dodge 5-6 down
----X1
----1X
----X1
---X-1 // in 4th place, treble is above 2nd, so dodge 3-4 down
--X-1-
---X-1
--X-1-
-X-1-- // and plain hunt down to the lead and out again
X-1---
X--1--
-X1---
-1X--- // in 3rds place and the treble is below 3rd, so make 3rds place
1-X---
-1-X-- // and make 4ths place
1--X--
1---X- // dodge 5-6 up
-1---X
1---X-
-1---X
--1--X // dodge 5-6 down
---1X-
--1--X
---1X-
---X1- // in 4ths place, treble is above 2nd, so dodge 3-4 down
--X--1
---X1-
--X--1
-X---1 // and plain hunt down to the lead and out again
X---1-
X----1
-X--1-
--X1-- // in 3rds place, treble is above 2nd, so dodge 3-4 up
--1X--
--X1--
--1X--
-1--X- // dodge 5-6 up
1----X
-1--X-
1----X
1----X // dodge 5-6 down
-1--X-
1----X
-1--X-
--1X-- // in 4ths place, treble is above 2nd, so dodge 3-4 down
--X1-- // note we are dodging with the treble, so next time we are
--1X-- // in 3-4 down the treble will be in 1-2 up
--X1--
-X--1- // and plain hunt down to the lead and out again
X----1
X---1-
-X---1
--X--1 // in 3rds place, treble is above 2nd, so dodge 3-4 up
---X1-
--X--1
---X1-
---1X- // dodge 5-6 up
--1--X
---1X-
--1--X
-1---X // dodge 5-6 down
1---X-
-1---X
1---X-
1--X-- // in 4ths place, treble is below 3rd, so make 4ths place
-1-X--
1-X--- // and 3rds place
-1X---
-X1--- // and plain hunt down to the lead and out again
X--1--
X-1---
-X-1--
--X-1- // in 3rds place, treble is above 2nd, so dodge 3-4 up
---X-1
--X-1-
---X-1
----X1 // dodge 5-6 up
----1X
----X1
----1X
---1-X // dodge 5-6 down
--1-X-
---1-X
--1-X-
-1-X-- // in 4ths place, treble is below 3rd, so make 4ths place
1--X--
-1X--- // and 3rds place
1-X---
1X---- // rounds
That's all there is to a plain course of Kent Treble Bob Minor. We can
extend this to a course of Kent Treble Bob Major, by adding two more
bells and two more dodging places at the back, in 7-8 up and 7-8 down.
The slow becomes a bit longer because we have to wait for two more
bells to lead while we make 2nds.
simon
who by writing this out has made a big step towards actually ringing it!