[r-t] Diamond Delight Major
richard at ex-parrot.com
Mon May 24 11:59:27 UTC 2010
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.
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