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

King, Peter R peter.king at imperial.ac.uk
Wed Dec 2 22:18:05 UTC 2015

On Colin Wyld's 24, it is ATW. And having rung it on handbells I can assure you it is quite interesting enough. None of which detracts from Mark's achievement. I had thought along vaguely similar lines but lacked the patience and computational expertise to do this so well done!

-----Original Message-----
From: ringing-theory [mailto:ringing-theory-bounces at bellringers.net] On Behalf Of Mark Davies
Sent: 02 December 2015 21:58
To: ringing-theory at bellringers.net
Subject: Re: [r-t] 1-part tenors together atw compositions of 23-spliced major

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.


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