[r-t] A new search technique, and some new peals of Bristol

[Mark Davies]

I've been busy these last few months composing some new peals of 
Bristol, with the aid of a new search technique.

Philip kindly included my 5056 no.1  (now available at
<http://bronze-age.com/bristol/series2.html#series2_5056no1>) in his 
"compositions of the decade" articles. This composition was produced 
using my earlier technique of hand-composed blocks linked by computer 
search, and at the time of composition (in 2007) I thought it was 
unique, for a tenors-together arrangement, in achieving the property of 
"no duffers" - that is, no undesirable coursing orders between Middle 
and Wrong (whilst maintaining a high number of courses in the peal - 
here, nineteen).

Over the last three months I have discovered this not to be the case. It 
is possible to set up a search space in SMC32 which allows *only* the 
non-duffer courses to be visited. (My particular definition of 
"no-duffer" is a course including either little-bell music of back=bell 
rollups). It turns out that this space is searched relatively quickly 
and produces not one, but millions of excellent results.

And, to my amazement, I found that the best of this new batch manage to 
outstrip the 5056 by some margin. Consider for example these three new 
peals:

   Peal        LB4  LB5  5678  4567  6578  courses
   5024 no.4   140   42   72    10    24   19
   5088 no.7   148   43   72     2    24   19
   5152 no.3   138   38   72     2    13   20

By comparison:
   5056 no.1   134   40   72     2    20   19

(Note that the "6578" score only includes 6578 off the back, whereas 
"5678" and "4567", like LB4 and LB5, include the rollups in both 
directions off front and back.)

 From these numbers you can see that the new 5024 and 5088 dramatically 
exceed the music counts of the 5056. Interestingly, these three peals 
also include all seven near-misses, something I had not realised until 
recently.

The 5152 is remarkable in having the full 20 courses, so an average of 
only 1.05 course-end calls per course, while *still* managing to avoid 
duffer courses. It is unique in having this property and achieving all 
72 5678/8765 rollups - no other 20-course composition comes close. I 
think it is quite remarkable that this arrangement exists.

These new peals can be found individually at:

   <http://bronze-age.com/bristol/series5.html#series5_5024no4>
   <http://bronze-age.com/bristol/series5.html#series5_5088no7>
   <http://bronze-age.com/bristol/series5.html#series5_5152no3>

There is also a more detailed description of the new series, plus some 
other interesting compositions, at:

   <http://bronze-age.com/bristol/series5.html>.

Finally, I have also made some interesting discoveries in the field of 
split-tenors compositions. Earlier this year I found a way of joining 
the four best leads from the seven cyclic courses into a peal using an 
elegant and musical linking block. The results, paired up with the best 
tenors-together courses produced using another "no duffers" search, can 
be found at:

   <http://bronze-age.com/bristol/series4.html>

These peals are also available on <http://www.compositions.org.uk/>, but 
I have made a new home for all my Bristol compositions at 
<http://bronze-age.com/bristol/>. This describes the genesis of each 
compositional series, including details of the techniques I used and how 
they have evolved over the years.

Interested to hear people's views, and also any feedback if you ring one 
of these new arrangements.

MBD