[r-t] Scientific triples

[Philip Earis]

Colin:
"I can suggest a few possibilities..."

Excellent.  


"I haven't worked out the specific arrangements but there is the potential for 40+ methods. The second has no calls except changes of method and triple changes throughout.  I will submit these when I can get the formatting sorted out"

Top work.  I'm really looking forward to seeing these.



-----Original Message-----
From: ringing-theory-bounces at bellringers.net [mailto:ringing-theory-bounces at bellringers.net] On Behalf Of Wyld Family e-mail
Sent: 27 April 2009 23:01
To: ringing-theory at bellringers.net
Subject: Re: [r-t] Scientific triples

I don't think there is anything inherently spliceable about methods based on
the same mathematics as Scientific however I can suggest a few
possibilities: -

It may be possible to generate three ten change (or five six change) methods
which together generate each of the cosets corresponding to the thirty
changes in the lead of Scientific.  The 24 courses of each of these three
methods would contain different changes and if joined together would
generate a peal.  Whether this is actually feasible I haven't tried to find
out.

Course splices are possible.  I know of two different methods which contain
exactly the same changes.  Neither is very exciting indeed one is the seven
part touch of original triples that was probably John Carter's starting
point.  More practically every assymetric method may be spliceable with its
inverse i.e. the method rung backwards.  To achieve this it is necessary to
use a double.  Starting with Scientific I have called the inverse
New-Scientific (on the same basis that Grandsire rung backwards is New
Grandsire) but if anyone rings it they can of course choose their own name.
The place notation is: -

1.7.1.7.1.7.1.5.1.5.1.7.1.7.1.7.1.7.1.5.7.1.7.1.5.1.7.1.3.7

The double is called at either lead end and the place notation is 347
replacing the final 7ths place.  It is possible to have the call and change
of method at another point in the lead so that it is not necessary for a
bell to ring for 4 blows in the same position but for this example I have
stuck to calls and changes of method at the lead end although that means 4
blows in 3rds when the change is from New-Scientific to Scientific.
Whenever a double is called there is a change of method and whenever there
is a change of method there must be a double.  The first composition is a
regular 7 part.  This has more changes of method than the bare minimum but
since a regular 7 part of Scientific (or any other method based on the same
mathmatics) is impossible without the use of the call that affects all 7
bells (5.1.5 becomes 5.7.5) I thought it would be interesting.  I have only
listed the methods since every change coincides with a double.

S, 2N, 3S, N, 4S, 2N, 5S, N, 2S, 3N (there is a call at the part end so that
the next part can start with Scientific)   Part end 5362714

For those looking for more changes of method, and something more challenging
to call, the following has two changes of method fewer than the maximum.  I
could not resist the temptation to produce a palindromic composition which
entailed splitting a block into two losing the two changes of method.  The
basic block is made up of 8 leads with calls and changes of method at every
lead end.  To save space I have only shown the number of lead ends to the
next plain lead end without a change of method so 1 means a plain lead
immediately and 2 means one call followed by a plain lead.  All sequences of
calls are an odd number.  Because of this plain leads alternate between
Scientific and New-Scientific (except for the 8 occasions where there are 2
plains together).

1,2,8,2,8,2,8,2,1,2,8,2,8,4,1,2,8,2,4,4,1,8,1,2,8,4,8,2,1,8,1,4,4,2,8,2,1,4,8,2,8,2

I originally sent the compositions above in February but for technical 
reasons
at this end it did not get through.  Since then I have produced two more 
compositions
based on combinations of 12 lead, 4 lead, 3 lead and 2 lead splices.  I 
haven't worked
out the specific arrangements but there is the potential for 40+ methods. 
The second
has no calls except changes of method and triple changes throughout.  I will 
submit
these when I can get the formatting sorted out.

Thanks Philip for an interesting idea.

Colin Wyld



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