[r-t] 1-part tenors together atw compositions of 23-spliced major

[Mark Davies]

Oh dear, this has rather let the cat out of the bag - I was really 
waiting until after it had been pealed to announce it. (There is a band 
lined up to go for it in January).

Not to worry, I suppose now is as good a time as any. Thank you Philip, 
Don, Rob and Roddy for the kind words. As described on my web page, this 
has been in the making for the last two years. The creation of the 
theoretical solution was probably the most exciting composing work I've 
ever been involved in; but the fitting of real methods to the framework 
turned into the worst year of my life. When I started out I had no idea 
just how painful it would be! Nevertheless, I was determined that the 
task would not defeat me, and I am reasonably pleased with the quality 
of composition that has eventually emerged. Hopefully we will soon see 
what it is like in the tower.

Philip asks what scope there is for further development, particularly in 
the area of the leadhead groups of the methods. In fact, the composition 
plan is entirely flexible with respect to leadhead groups, so long as 
all (but one) are of the same type (2nds or 8ths). This condition is 
necessary because the coursing orders must be joined in whole courses; 
the lone g-group is only possible in this arrangement because one method 
is unbobbed. Initially I had a more even distribution of the groups a-f, 
however my conductor thought this was making what was already likely to 
be a fiendish task for the band just a little too difficult, so on 
request I increased the frequency of the a, b and f groups.

In correspondence with Graham John (who has also done much pioneering 
work in this area) I have determined that there are other types of ATW 
set which might, in theory, be linked into a peal. Some of these may 
allow callings which do not require whole courses, and this would open 
up the possibility of mixed 2nds and 8ths place methods. I have not yet 
summoned the energy to pursue this avenue very far.

Don is correct that the existing composition is "every lead different". 
In fact this was one of the pruning criteria I used, allowing me to 
reject search branches without that property. One astonishing thing 
about the method-population part of the project was that I started off 
despairing that there were any methods at all that would fit the 
composition, and ended up with the understanding that the best way to 
find solutions was to make almost unrealistic quality demands for the 
method properties. Such is the power of pruning; or, as I like to think, 
the harder you squeeze the compositional universe, the more spills out.

I was aware of Richard Smith's whole-course 23-spliced, however I must 
admit that I had pushed this to the back of my mind. From the outset I 
was clear that I must have the methods spliced within the course. I 
didn't know about Colin Wyld's 24-spliced, and this is also technically 
a very interesting composition. It's not immediately clear to me how you 
would obtain ATW with it, but in any case I suspect it does not have the 
method variety to inspire the ringer in the tower. I shall however 
modify my "first 23-spliced" claim!

Now the composition has effectively been published, I am happy to answer 
any other queries people might have.

MBD