[r-t] A palindromic composition question

[Glenn Taylor]

I'd very much appreciate anyone's thoughts/contributions on the following
topic:

 

 

Consider a palindromic composition (for argument's sake on 8 bells). The
apex of the palindrome occurs either between a lead-head and lead-end, or at
the half-lead. This in turn means that every lead L of the extent either has
an image lead L', or is its own image in the case of a half-lead apex. Given
the details of the bells that cross at the apex (which for major is
typically three crossing pairs, together with one working bell and the
treble being fixed) it is then a straightforward task to calculate L' for
any given L. - and just as any course C is made up of 7 leads, it will be
found that their 7 image leads each belong to the same image course C'.

 

So what?

 

.         Q1. For a given method and given apex details is it possible for a
lead L to be false with L' ?

 

My instinctive response is that the answer has to be 'yes' - but I can't
construct a simple example.

 

 

.         Q2. Assuming that the answer to Q1 is indeed 'yes', then is there
an efficient method for identifying such false pairs (L, L') without having
to generate all pairs to find out?

 

 

 

In an ideal world (ha!) the answer to Q1 would be 'no', as this renders Q2
unnecessary. Currently my algorithm runs along the following lines:

 

.         For each course C, generate and store its image course C'

 

.         For each course in turn:

-          For each lead of this course:

o   Generate its false courses (including tenors parted falseness), together
with incidence

o   If none of the false courses found = C' then

Skip to the next course

else

Investigate whether the incidence is with the image lead, and eliminate
(L,L') if so

 

Because each course has an image pair (or is its own image) then the work
can be approximately halved if a "dealt with" flag is set for course C' once
C has been processed, and is tested before any unprocessed course is
generated.

 

 

 

Is this the best I can hope for.or am I missing something obvious (or not
obvious)?

 

 

Glenn

 

PS. I've read the article by Brian Price, but the potential for L being
false with L' is not raised as far as I can see.

 

 

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