[r-t] Diamond Delight Major

[Richard Smith]

Ted Steele wrote:

>> Are the falseness groups that arise in treble dodging methods the same for 
>> both regular and irregular lead head methods, or does the different lead 
>> head group give rise to different groups in the latter?

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.


>> Same question with regard to other methods that have a 
>> treble path that is not plain hunt.

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