One Part 23-Spliced Surprise ATW

The Mythical Beast

The composition below is believed to be the first example of a one-part ATW peal of 23 Spliced Surprise Major, with methods spliced between calls. It has the tenors together throughout, in contrast to the usual 7-part plan.

5152 23-Spliced Surprise Major
Composed by Mark B Davies (no.5)

23 Methods: 224 each Abaia, Basilisk, Cerberus, Djinn, Ettin, Fenrir, Gorgon, Hydra, Incubus, Kraken, Lessness, Marshwiggle, Naiad, Ouroboros, Panserbjørn, Roc, Sphinx, Titan, Ungoliant, Valkyrie, Wyvern, Yeti and Zombie S Major; ATW, 157 COM.

 23456   M  W  H
(52436)     -      WZ.
 42356   3  2  -   ZYF.FROWZY.HGLITC.ROW.BUNKDE.YFRO.
 34256      3  -   P.AMPSV.PSVAM.SVAM.
 52643   -  -      V.VA.H
 64523   3  -  -   GLIT.GLITCH.TCHGLI.C.UN.
(42563)     2      ITCHG.TCHGLI.
 52364   -     SS  CHG.OWZYF'DEBUNK'
 43265   -     -   R.Y.
 32465   3     2   BUNKD.KDEBUN.UNKDEB.E.MPSVA.
 56423   -  -  -   FROWZ.LIT.L.
 45623      3  -   ZYFRO.EBUNKD.FROWZY.W.
(24653)     -      KDEB.
 23456   2     -   MPS.SVAMP.AMPS.
 
Contains:
 128 4-runs including 14 xxxx5678
 14 xxxx6578

The following twenty-two new Surprise methods are included:

The Performance

This composition has now been rung, at the first attempt, by a band organised and conducted by Simon Linford:

http://bb.ringingworld.co.uk/view.php?id=988996

The Story

I was inspired to search for a one-part peal of 23-spliced after reading Albert J. Pitman's biography. The "unassuming genius" is rightly known as the father of Spliced Surprise, and I found the story of his quest to cram ever more methods into an ATW composition both fascinating and thrilling (if, in truth, this was merely a sub-plot in his extraordinary composing life). One paragraph near the end of the book had probably the most effect on me (I quote from the offical Central Council biography by Michael B Davies):

"Very soon after his death, the number of Surprise Major Methods with all the work which could be included in a peal increased from 9 to 12, though unusual and carefully chosen methods had to be introduced to achieve this. Then quite suddenly, in the same year as Pitman’s death, there was a major breakthrough by Norman Smith in method-splicing and before very long, the maximum total of 23 methods with all the work would be squeezed into a normal peal length. In December 1966 the first peal of 23-Spliced Surprise Major with all the work was rung. It would have been interesting to see Jack Pitman’s reaction!"

Norman Smith's famous composition is of course a 7-part, achieving ATW by virtue of ringing the 23 methods in the same order, with a part end chosen from a group of order seven (in Smith's original, a lead from the plain course) so as to rotate each bell through every lead of every method. In the last half-century, this brilliant device has swept through the Spliced Major genre, and is now without question the dominant arrangement. But, with its fixed sequence of methods, and split-tenors courses, it is a very different beast to the tenors-together one part pioneered by Pitman.

I set to wondering whether the very existence of the seven-part plan had stifled development of other forms. I noticed that, in the field of Spliced Surprise Royal, several composers had produced minimum-length one-part ATW peals of 14-spliced. To do this they had made use of the fact that the course length of Royal is non-prime: 9 = 3x3. A rolling threesome of methods thus forms three courses (ABCABCABC, BCABCABCA, CABCABCAB) which give a true ATW set when joined with, say, three calls at Home. It is still not necessarily easy to extend this idea to a peal of 14 methods, but it can certainly be done. I believe Roddy Horton was the first to demonstrate this, in 1988.

On eight bells the course length is prime, so no such handy subgroup is available. The only possible group is that of order 7, which gives us the Smith-style arrangement. Nevertheless I quickly found that the seven courses with seven methods starting ABCDEFG, BCDEFGA etc can in theory give us ATW; the difficulty is, we need to move out of the plain course to keep truth, but there are no Q-sets for seven courses capable of providing truth as well as preserving the ATW property. Despite this, I discovered that there did exist unrelated sets of tenors-together coursing orders which could be applied to give the desired results. One example is (53246, 43526, 63425, 25346, 35246, 46325, 32546), but there are many others. These sets of coursing orders seemed to be random in nature, having neither internal group structure nor any consistent linkage to each other. It was certainly not possible to join them together with standard calls. But in finding these "course sets", as I termed them, I had conquered the first of the four major obstacles on the road to my 23-spliced peal. So far, only a couple of weeks had been spent on this potentially-fruitless quest - little did I know what was in store!

The next obstacle was dispatched with relatively little trouble. Clearly, three sets of seven courses gives only 21 methods - too few - whilst four course-sets yields far too many. Graham John had shown, in his post-Horton 14-Spliced Surprise Royal, how different LH groups could be combined to whittle a course-set down to fewer methods, in his case by replacing two a-group methods with one b-group. My research soon revealed that, for my rotating courses, any course structure would work in this fashion, and this realisation was critical to later progress. For example, the LH groups c, b, a, b, f combine to make a five-lead course. If five suitable methods VWXYZ are chosen to represent these LH groups, then seven courses can be had by starting the "V" method at each of the seven positions of the tenors, with the other methods following on in order. Two of these courses will not have the Home position, but this is not of immediate importance. Furthermore, using the coursing order sets I had already established, ATW was always guaranteed. Here is an example, with the coursing orders from the previous paragraph applied to those same LH groups cbabf:

53246  43526  63425  25346  35246  46325  32546  
12345678 V13457286 V16738452 V17826543 V18674325 V15283764 V14562837 V
17856342 W18672453 W15284736 W14365827 W12543678 W16437285 W13728564 W
16482735 X12563847 X14326578 X15237486 X13758264 X17845623 X18674352 X
14263857 Y15324678 Y13647285 Y12758364 Y17836542 Y18572436 Y16485723 Y
13527486 Z14738562 Z17865324 Z18674235 Z16482753 Z12356847 Z15243678 Z
12345678134572861673845217826543186743251528376414562837

Each of the seven columns has a fixed coursing order, as given by the column heading; every column has the methods in the same order, VWXYZ, with the respective LH groups being cbabf; but we start each column with a different position of the tenors. The result is a combined set of 35 leads which gives ATW for both the tenors and the front bells for each of the five methods. The same approach works for any complete course structure, for any number of methods from two to seven.

I now had a sightline to the 23-spliced peal. I would build four course sets, each with seven distinct coursing orders from one of the ATW sets. In the first course set I would use a course structure giving five leads, whilst in the others I would have six leads. This would total to 23 methods, and by this arithmetic I would have 23-spliced ATW. But one final obstacle remained (or so I thought at the time): linkage. The coursing orders from a single course-set would not link together. Could I find four sets of seven coursing orders that could be cross-linked into one complete round block? The problem was made more difficult because not all calling positions were available in every course set. For instance, in the five-method example given above, the fifth column does not have either the Wrong or Middle position, so can only be linked into a finished tenors-together composition via the Home. Other columns are similarly constrained.

At the time, I thought this would be the real stumbling block, solutions either not existing or being impractical to find with any algorithm I could design. However, it quickly became obvious that the search space was in fact inexhaustible. With 28 courses, each needing to be rung in their entirety, singles as well as bobs were required to obey the Q-set rules, but the task now became to identify the best and most worthwhile solutions. Realising early on that cross-falseness between courses would become a major issue, I soon settled on the idea of minimising the number of negative coursing orders, and it proved possible to reduce these to one. For this constraint, only a handful of solutions existed, and of these, one had the interesting property that a potential calling position in one course-set remained unused. This meant that one method could remain unbobbed throughout the peal, and so, by choosing the LH groups of the course set containing it carefully, I was able to introduce a lone 8th's place method. (Naturally, it would have been possible to use 8th's place methods throughout with 6th's place calls, but I had from the outset decided against this, at least for the first published peal). Furthermore, this one solution seemed to contain the best and most musical coursing orders. The universe was smiling on me - perhaps.

By now I had spent a couple of months in feverish thought, problem-solving and software development. The brief description above does not detail the many blind alleys I investigated nor the time I spent recovering from stupid mistakes. But although the path had not been altogether smooth, I had overcome the three major obstacles and was now in possession of a theoretical solution. It just remained to put methods to the 23 placeholder letters of the arrangement I had discovered. How hard could that be? Suffice it to say that the next 18 months were spent in this final battle. The problem was simple enough to state: find a set of 23 good methods which were true to my 28 courses. I wanted good methods, insofar as possible, so that the finished composition would be one that people would want to ring, rather than remaining a theoretical exercise. The methods would need to have appropriate LH groups, in order to make up a valid course structure for each of my course-sets (but here there was almost too much choice - many hundreds of such course structures existed, with no clear way to identify which were preferable). And of course the cross-falseness between my 28 coursing orders had to be be navigated.

As 2014 drew to a close it became clear that the rung library did not contain sufficient variety of methods to populate my composition. In one sense, ditching the libraries and constructing new methods dramatically increased the size of the problem: instead of a mere five-thousand-odd possibilities for each method, I would now have several hundred thousand. Raising this very large number to the power of 23 gives some idea of the problem space. There was still no guarantee that any worthwhile solutions existed, but my instincts told me to trust the changeringing universe - in my experience, it usually has more to give than you could reasonably expect, if only you can explore it deeply enough.

To tackle the problem, I developed several new ideas, including the "stalactitic search", whereby methods are simultaneously grown from the leadhead (the stalactites) and the halflead (the stalagmites), obviously in the hope that they will meet up in the middle. I also found the concept of what I termed method "slices" useful: a single slice of a method being the 28 rows with the treble in the same position (and hence all those rows which can be false against each other, and against other method slices at the same level). With the right data structures, it proved possible to grow methods slice-by-slice instead of row-by-row. As the months passed results gradually began to appear, poor at first but slowly improving as I refined and tuned the algorithms. In the end I found that the most effective technique was to prune as viciously as I could, targeting the search at the types and variety of method and the quality of music that I hoped was achievable. This "Super-pruned Stalactitic Search" has so far been the most fruitful of the dozen or so different algorithms I developed over many months to attack the problem.

This first published composition shows, I hope, that the changeringing universe has indeed delivered. It contains 22 new methods, chosen for variety and interest as well as their ability to provide music within the composition, plus one old favourite - Lessness. The new methods are named for mythical beasts; but the beast that is the 23-spliced one-part is mythical no longer.

A note on some predecessor compositions

Two peals of non-7-part 23/24-spliced predate this composition. The first is Colin Wyld's 6-part 24-spliced, composed in the 1980s:

http://www.cantabgold.net/users/pje24/wyld24.pdf

This is not a one-part, but it does successfully give ATW for 24 methods. Library methods are used, grouped into closely-related variations.

The second peal is by Richard Smith, and is a one-part 23-spliced ATW arrangement. However methods are not spliced between calls; this style of composition is sometimes described as sliced, or laminated. It was produced in 2005 - see towards the end of this page:

http://wiki.changeringing.co.uk/Compositions_of_the_Decade_5_-_Major

The "Mythical Beasts" plan is not closely related to either of these compositions.