[r-t] Long Lengths of Bristol (was: Brian D Price Long Lengths)

[Richard Smith]

Philip Earis wrote:

> The composition for 28512 Bristol (ie 891 leads) is the longest I've
> seen in the method. Can anyone do better?  Rod Pipe has a list of 973
> mutually true leads on his website
> (http://www.ringing.info/peter-border-main.html#major) that he and Peter
> Border came up with, but no composition.  Richard Smith has also been
> working on the problem, extending the known number of mutually true
> leads.  Perhaps he'd like to comment?!

I have manged to find a number of sets of 975 mutually-true
leads of Bristol, however, like Rod Pipe and Peter Border,
I've been unable to join them up.  There doesn't appear to
be much structure to this set of leads -- unlike Rod and
Peter's leads, which form a seven-part structure, mine are
just in a one-part arrangement.

I've had a couple of a discussions with Rod about how many
mutually-true leads we think should be possible in
principle.  Rod is of the opinion that the number should be
a "nice" fraction of the extent.  975 is 65/84 of an extent
-- hardly a round number, though perhaps better than
973 which is 139/180.  980 leads would be 7/9 of the extent,
but to me this is implausibly high.

My personal opinion is that 975 leads is probably the
maximum, and that there is no good reason to suppose the
maximum to be a "nice" fraction of the extent.  I still need
to spend more time trying to get a set that might join
together to form a composition.  If it is possible to
join the leads, it would produce a 31,200.

The other style composition I've been looking at is
compositions in whole courses.  (Compared to Brian's
nine-part compositions, these have considerably fewer
calls.)  Unfortunately fourths-place bobs don't really lend
themselves to joining together compositions in whole
courses, so instead I've used 16 bobs and 1678 singles.

The longest composition entirely in whole courses that I've
produced is a 26,880 on a three-part plan:

  http://www.ex-parrot.com/~richard/major/long-lengths/26880_B8_1.txt

It doesn't seem possible to get more courses than this even
if you look at one-parts and ignore whether the courses can
be joined together.

Finally, given Brian's enthusiasm for (and success with)
nine-parts, I've done an exhaustive search of nine-parts
using just 16 bobs.  The longest such touch possible is a
26,208:

  http://www.ex-parrot.com/~richard/major/long-lengths/26208_B8_1.txt

With just 14 bobs, it is not possible to get a nine-part of
any length.  (This is because there is no suitable call to
add/remove from every third part to turn a three-part into a
nine-part.)  It is, however, possible to get nine mutually
true parts using 14 bobs.  Three 16 bobs can be used to join
these together into a 27,072:

  http://www.ex-parrot.com/~richard/major/long-lengths/27072_B8_1.txt


Richard