[r-t] ringing-theory Digest, Vol 89, Issue 11
Philip Saddleton
pabs at cantab.net
Fri Feb 10 14:34:39 UTC 2012
You are not mistaken.
Put another way, the standard calling defines which Q-sets are bobbed
(those where a given bell is unaffected except where another bell is
also unaffected).
Let's define sufficient conditions for a method with a hunt bell such
that any touch where the hunt bell is unaffected and all the elements of
a Q-set are either bobbed or plained is guaranteed to be true:
- the lead has palindromic symmetry
- the changes at the apices are even
- the bob occurs at an apex and is also even
- there are not two rows in a half-lead with the treble in the same
place and of the same parity
[With these conditions, given any row the rows either side of it are
uniquely determined - the parity determines its position in the half
lead, and if it is at an apex the Q-set rule determines the change at
the apex. This is what I would described as a "rule-based" composition.]
Now with these conditions, the standard calling for Minor is true. It
will also give an extent if:
- the hunt bell rings twice in each place in a half-lead
- the plain course is five leads long
- the bob affects three bells
[These guarantee that calling a bob whenever one bell is unaffected
gives a two course touch of 240 with each other working bell unaffected
once: omitting this bob and repeating twice gives a 720.]
Philip
Don Morrison said on 10/02/2012 12:30:
> Oh, and assuming you define the standard calling in terms of a
> suitable pair of bells being affected or not instead of simply with
> Wrongs and Homes, I believe it is true for any set of lead ends
> corresponding to a five lead course, so long as the method has the
> usual symmetry, has the treble the right number of blows in each
> position, and the method has the correct flow of in- and out-of-course
> rows; Plain Bob-ness is not required. If I'm mistaken about that, I'm
> sure we'll hear it soon!
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