[r-t] Spliced Minor

[Richard Smith]

Leigh Simpson wrote:

> Can anyone remind me of the current records for
> spliced minor, in particular the shortest length
> composed of the 147, of the 41, and the shortest
> lengths atw?

The easiest way to produce atw compositions is in whole
courses.  Fortunately, this doesn't mean that you are
restricted to simple course (and lead) splices as there are
whole families of cross course splices available.  The
simplest examples of these are those discovered by PABS
between the Carlisle and Cambridge backworks, and the London
and Norwich backworks.  These are described on his website:

  http://www.saddleton.freeuk.com/comps/ss6.htm

If you allow cross-splicing between three extents
simultaneously, you get more possibilities.  With the 41,
there's only one new splice (though with a number of
variants).  Take three extents: one each of York,
Netherseale and Bacup.  Choose some course from each extent
-- it must be the same course in each extent, e.g. the
plain course -- and replace these courses with Beverley,
Westminster and Warkworth.  The resulting three extents will
still be true.

For reasons that I won't pretend to understand, course cross
splices don't seem to exist between more than three extents.
(Or, to be precise, they do exist, but can always be
expressed as multiple applications of simpler splices.)

Unfortunately, cross splices tend to preserve the number of
courses with each backwork, meaning it is quite difficult to
get an non-integeral number of extents with each backwork.
When dealing with large numbers of methods (e.g. the 147),
this tends to be the limiting factor.  With smaller numbers
of methods, finding enough different splices tends to be the
limiting factor.

The following table show the number of methods with each
backwork in the standard 41, 52 (41 plus single changes),
147 and 178 (147 plus single changes).  The numbers in
paretheses are the number of extents needed to get enough of
each backwork.

  Backwork   41       52       147      178
  --------------------------------------------
  Norwich    12 (2)   15 (3)   26 (5)   29 (5)
  Cambridge  12 (2)   15 (3)   19 (4)   22 (4)
  Carlisle   11 (2)   14 (3)   18 (3)   21 (4)
  London      6 (1)    8 (2)   13 (3)   15 (3)
  Oxford                       17 (3)   22 (4)
  Dover                        19 (4)   25 (5)
  Kent                         21 (4)   26 (5)
  Castleton                    14 (3)   18 (4)
  --------------------------------------------
  Total         (7)     (11)     (29)     (34)

How does this work out in pratice?  In whole courses, this
is the best I have done so far:

   41: 11 extents  (7,920)
   52: 15 extents (10,800)
  147: 28 extents (20,160)
  178: 34 extents (24,480)

The reason the 147 is in fewer than 29 extents is that
Westminster S and Pontefract D have a course splice, despite
having different overworks.  This allows Pontefract, Wath,
Donottar and Carisbrooke to be rung in the four "spare"
Norwich-over leads, removing the need for the fourth extent
with the Kent overwork.  The 178 methods no longer have
enough spare leads for this to be possible.

I'm fairly sure that these 147 and 178 compositions are the
shortest currently known.  The 147 was rung on 23 June 2004:

  http://www.campanophile.co.uk/show.html?Code=19715

I don't think the 178 has been rung, though I gather it has
been attempted on several occasions.


My compostion of the 41 is equal in length to an earlier one
by Richard Pearce.  His composition isn't in whole courses,
and (as I recall) doesn't use the Bv-Ws-Wk / Yo-Ne-Bc splice
that I mentioned above.  Instead, he makes extensive use of
the three-lead splice between London and Wells to get it
down to 11 extents.  Using a combination of both techniques,
it may well be possible to knock an extra extent off this.

Richard Pearce also has a compsosition for the 52 atw.  Off
the top of my head, I can't remember how long it is --
though I have an idea it was shorter than my composition in
whole courses.

RAS