Subject: Re: [LordPeter] Some change-ringing math - WAS : NINE: Chapter and sections
From: Simon in the little town of St Ives in Huntingdonshire
Date: Mon, 02 Aug 2004 12:06:29 +0100
To: LordPeter@yahoogroups.com

Mr. Venables wrote:

I think square dance calling is an apt description of
what is going on. The ringers have some 'choices' at
the end of each section of 8 bells ringing, and the
caller gives the ringers their next move.

Well, sort of, but it's both simpler and more complicated than that.

One of the principles of method ringing is that  bell can only change places with either of its immediate neighbours -- so if you are ringing in third place this time round, you can only be in second, third or fourth place next time round -- you cannot jump to first or fifth or higher. This limits the number of possibilities at any given point.

The reasons for this are to do with changing the angular momentum of a swinging bell, something which is not easy to do, especially with the heavier bells -- but the only way to move from third place to second is to ring a little sooner than you would if you were staying in third place, and similarly you must ring a little later (which is a little easier) in order to move from third place up to fourth.

In addition. in nearly all cases, a bell may not ring in the same place more than twice, without moving away.

So, in plain hunting, a bell moves from the 'front' (the first place, or the lead) to the back (eighth place if plain hunting on eight bells) and back to the lead again, ringing two 'blows' when in the lead, and two blows when at the back, and one blow in each of the intermediate places. A moment's thought will show that this means that the bells in 2nd & 3rd places swap, the bells in 4th & 5th swap, and the bells in 6th & 7th swap (leaving the bells in 1st & 8th unchanged), and then at the next stroke, the bells in 1st & 2nd swap, and similarly 3rd & 4th, 5th & 6th, and 7th & 8th each swap. And repeat, ad nauseam. After 16 changes each bell will be back exactly where it started from, and the pattern will repeat.

Diagrams on request!

Most methods consist of plain hunting together with occasional variations in order to prevent the pattern repeating. The treble bell -- the lightest and highest pitches, the number 1 bell -- plain hunts all the time. It starts by moving off the lead into 2nd place, and every time it gets back to the lead, just as the other bells are about to get back to their prevous starting place, some of them will vary their path for one blow in order to vary the pattern. So for example, the bell that started in 2nd place and is now coming down 8th, 7th, 6th, 5th, 4th, 3rd might, instead of going back to 2nd place, instead go back up to 4th place, before continuing 3rd 2nd, lead etc, i.e. continuing to plain hunt. This is known as dodging, in this particular case as 'dodging in 3/4 down' (because you are dodging in 3rd and 4th place on the way down from the back to the lead: the bell you dodge with is dodging 3/4 *up*.

The particular pattern of dodges is a feature of the method you are ringing, and can be learnt from a diagram and frequent practice. A ringer remembers them as variations from plain hunting, once they have learnt to plain hunt without thinking about it. All of this is done without any calls from the conductor -- ringers are expected to know what they are doing when ringing (obviously this doesn't apply when ringing at practices when one is learning a method). This pattern, with its dodges, but without any other interruption to the method, is called the 'plain course' of that method.

The feature of a peal is to ring without repeating the same pattern, and in order to do this, the plain course must be varied to swap a couple of bells over, otherwise the method will not allow all the permutations to be reached in a plain course. These variations are of two types: a 'bob' and a 'single'. It is these variations that a conductor must call, at exactly the right place, and they will typically be fairly infrequent, more or less a whole plain course apart, and you then ring more or less another plain course with the bells in this modified order beforre another bob is called and so on. The conductor has to be experienced enough to know when to call the bob to get the method right. Getting it wrong means that the peal will be invalid, because the same permutation of bells will be repeated, or it may totally throw a less experienced ringer, such as Wally Pratt in the opening chapters.

What I gather all the change ringing jargon is about
is that it helps the ringers remember where they are
in the column sequence, so they don't repeat a
previously done row *and* they manage to get *all* the
different possible permutations.

Yes, that's basically the case -- one remembers a basic pattern, then the standard variations (for this method) to that pattern, and then the variations to those variations which occur when a bob or single is called.

Obviously, it will get much, much, *much* worse with 8
colors or bells : There are 8x7x6x5x4x3x2x1 = 15,840
different ways (changes) to ring the 8 bells in
sequence without a repeat. There are 15,840 x 15,839 x
15,838 x 15,837 x ... x 5 x 4 x 3 x 2 x 1 different
ways to write all those changes down!

Indedd, and a full 'extent' (i.e. all combinations) on 8 bells takes a very long time, and has not been done very many times in the history of bellringing. The stamina required to ring 8 bells for many many hours (perhaps a dozen or more) without any comfort breaks or refreshment or rest is too great for most ringers to even attempt -- especially as you would need to gather 8 such ringers together.

I take it that the various titles (e.g., Kent Treble
Bob) are ways to choose *one* particular order out of
all these ways (15,840 x 15,839 x ...x 3 x 2 x 1 in
the case of Kent Treble Bob), *and* to have it make
some sense to the people doing the ringing!

Treble Bob methods are another class of methods. In these methods the treble does not plain hunt (as it does in the simpler methods). Instead it dodges (or bobs) in every other place, so that it dodges in 1/2, 3/4, 5/6, 7/8 up and then in 7/8, 5/6, 3/4, 1/2 down. That is, instead of ringing in 1st place, 2nd place, 3rd, 4th, 5th, 6th, 7th, 8th, 8th, 7th, 6th etc, as in plain hunting, it rings 1st, 2nd, 1st, 2nd, 3rd, 4th, 3rd, 4th, 5th, 6th, 5th, 6th, 7th, 8th, 7th, 8th, and then 8th, 7th, 8th, 7th, 6th, 5th, 6th, 5th etc. This is known as 'treble bobbing'. I can just about do this, sometimes without making mistakes! Meantime the other bells perform more complicated manoeuvres of their own.

In the code example given in the text (in the section:
Lord Peter follows his course bell to lead), bells 1
and 2 do 'plain hunting' in the change ringing jargon
- all the way through the example: they go diagonally in one direction, drop down a row, then diagonally in
the other. But notice that bells 3, 4, and 5 start out
'hunting,' then do 'funny stuff' about 2/3 way down. I don't know what the jargon description of the 'funny
stuff' is - whether it is dodging or passing or what.
I wonder if 'called with a double' means that a bell
begins two rows in sequence, or ends two rows in
sequence. 

Haven't got to this bit of the book yet -- I'll have a look and report back later.

I think that it is pretty impressive to devise methods to select one particular specimen out of all
the head-spinning number of ways available, *and* have
non-mathematical villagers be able to keep it in their
heads.

Originally, change ringing was developed in the 17th century, by educated young men who took up as a hobby what was largely the preserve of uneducated villlagers, namely the unskilled, or rather the unscientific, ringing of church bells. These young men applied 'scientific' or mathematical principles to bellringing and devised the basic outline of change-ringing as it has continued to exist in England ever since. In a few more rural (rustic?) parts of the country, especially in the west country (the abode of the stereotypical 'yokel'), the less 'mathematical' method of ringing apparently largely persists. This is 'call changing' in which every change in the order of ringing is called by the conductor. Even here, though, I gather that the changes are rung to a very high level of precision, with high quality 'striking', a topic which merits a separate email.

Not until the end of the 19th century though did anyone publish the diagrams such as are to be found in NINE, and which are now commonplace in ringing, and which help the learner to visualize the path of their bell in a method (the so-called 'blue line' which traces the path of a single bell in such a diagram). Before then, the complicated jargon was the only way of explaining what was happening to the novice. It must have been much harder to learn before this. Most towers probably stuck to some relatively simple methods such as Bob Minor or Bob Major, or Grandsire Triples, and so there was no need to learn lots of different methods. Only in the mid and late 19th century did it become more common for ringers to be able to ring a lot of methods, when bellringing became much more organized on a local and national level with the creation of diocesan associations culminating in the formation of the Central Council of Church Bellringers (the CCCBR).

Mr. Venables, apologizing if s/he has made anyone
reach for aspirin...

simon, tower captain in the little town of St Ives in Huntingdonshire
who realizes this is probably more than most people want to know about bellringing!

-- 
Simon Kershaw
simon@kershaw.org.uk
in the little town of St Ives in Huntingdonshire