[r-t] Falseness groups

[Simon Humphrey]

On reading through this I was startled to find much of it contradicts what
I've intuitively held to be true for many years. Can you give examples of
irregular lead ends where ambiguities in labelling the groups arise?  

I thought the mapping of FCHs into groups was invariant, whatever coursing
order is chosen.  I use Ted Shuttleworth's process (which works with
coursing orders rather than course heads) for producing the groups, and it
seems to me to be independent of the plain course coursing order.
Intuitively, the process should still work if the coursing order was written
in letters "abcdefg".

Perhaps I need to revisit my intuitions.

SH

> RAS wrote:
>  
> Assuming the method is palindromic and is seven leads long,
> then you can divide the false courses into 28 falseness
> groups.  However, it's not necessarily true that only 19 of
> these have in-course tenors-together FCHs.
> 
> Often it's clear how to label the falseness groups, e.g.
> which irregular group corresponds to the regular U group,
> and so on.  But again this is not invariably the case.
> There is always a three-fold ambiguity in this mapping
> meaning that for any irregular method, you can find three
> different ways for labelling the falseness groups which a
> priori are equally good.  (A mathematican would probably
> describe this by saying the automorphism group of the
> falseness group structure is C_3.)
> 
> In practice, it is usually the case that one of the was of
> labelling the falseness groups is 'clearly' the right one
> in some intuitive sense.  But there are a few irregular lead
> ends where two people who both understand falseness groups
> well will come to different conclusions about which way to
> label the groups.
> 
> This ambiguity is precisely the same as exists in
> determining the coursing order in the plain course.  By
> convention we agree that 7532468 is the plain course
> coursing order for a regular method.  But this is just
> convention based on what conductors find helpful.
> >From a theoretical stand-point we could just have easily
> have chosen 5267348 or 2745638.
> 
> We choose 7532468 for several reasons.  The reason that
> ringers meeting a coursing order for the first time are
> usually told is that it is the order the bells come to the
> back.  But that's not strictly true -- think of Superlative.
> 7532468 has several merits over 5267348 or 2745638.  The
> tenors are adjacent the coursing order, and as they're often
> fixed for large parts (or all) of a peal, that means we can
> ignore them.  And the three bells affected by a bob are also
> all adjacent.  But for some methods, we cannot
> simultaneously satisfy both these criteria and this is the
> situation when, in practice as well as in theory, we get
> ambiguity -- both with the plain course coursing order and
> with the falseness group names.


 
> The treble's path is irrelevant.  What is relevant is that
> the treble is a fixed hunt bell (i.e. it is leading at every
> lead head thoughout the composition) and that the method is
> palindromic with a symmetry point about the treble's lead.
> 
> RAS