Cambridge Major Tenors Together - The Full Monty

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In 1988, Brian Price completed tenors-together computer searches for palindromic and multi-part peal compositions of Cambridge Surprise Major with bobs and singles, making a number of important discoveries (see New Peals of Cambridge Surprise Major by Brian Price). It is perhaps surprising that these compositions remained undiscovered for so long, given the popularity of the method and the effort that must have been invested by composers with pen and paper since singles had become accepted in Surprise.

At that time, an exhaustive search for all the tenors-together compositions with bobs and singles was beyond Price's reach. But as computing power increases, more problems can be solved in this way, perhaps allowing that missed gem of a composition to be found. It is also possible to provide definitive answers to questions such as: What is the longest length? Or, What is the maximum number of combination rollups (crus) possible? Or, How many different lengths can be obtained?

I first completed a search for all the tenors-together compositions of Cambridge Surprise Major in 1995 using a 90 MHz PC and Single Method Composer (SMC), a search program designed and developed in 16-bit Assembler by myself in 1991. The search took 9 days to complete, but the program only kept the best 500 compositions for analysis. In 1998, I repeated the search using a 400MHz PC and SMC32, which is an improved version of SMC, completely rewritten in 32-bit Assembler and C by Mark Davies.

The following analysis is the combined result of two exhaustive searches. The first for all the tenors-together compositions with a conventional start and finish using normal bobs and singles. The second, rather longer search (which cannot benefit from rotational optimisation), adds the compositions finishing at the treble's backstroke snap. The round-block search took 25 hours to find 9,997 compositions with 255,138 rotations. The second search took 13 days to find a further 15,416 compositions with a snap finish. With today's PCs these searches are even quicker. The current record for completing the round-block search is just one hour 49 minutes using SMC32 version 0.95 on a PC with a 3.4GHhz Pentium IV processor. By comparison, a bobs-only search takes just 1 second.

In the table below, compositions with a similar structure are grouped, by the number of parts, the number of short courses, and their length. The maximum number of crus, maximum musical score, number of compositions, and where known, the composer of a published representative of each group is indicated. The musical score is based on a simple sum of musical counts, namely crus, 5678s, 6578s, 3456s, 6543s, 2345s, 5432s, and 4/5/6 bell runs both at the front and the back of the row. An example composition from each group follows the table.

Using only fourths place bobs, it is clear why Middleton's composition is so important. Only five very similar peal length compositions exist, with 99 rotations. The 5600 is the only five part and the longest length (No.1); two others are shortened forms of this by omitting three Homes (No.2) or by substituting a Before for 2M2W (No.3); and the other two are reversals of each other, originally discovered by James Washbrook and Arthur Heywood (No.4). By modern measures Middleton's is still one of the most musical compositions, containing plenty of runs of four or more bells to compensate for the paucity of 6578s.

In 1947, Price's controversial use of a single in his 5090 (No.29) opened Cambridge up to a much wider variety of composition, although it took another 40 years to discover its full potential. The analysis shows that compositions with singles fall into structural groups of dramatically different sizes from a single composition to thousands of similar variations.

Multipart compositions with singles are limited to just three groups, each with previously discovered examples. The earliest was a two-part, short-course, 5120 by Jim Diserens (No.7). Price's searches revealed a four-part 5120, also exclusively in short courses (No.5), and a musical two-part 5184 with 16 short courses (No.6).

There are 18 groups of one-part round blocks with singles, ranging in length from 5024 to 5344. Price discovered examples of nine of these groups, including the composition with the most i.e. 74 crus (No.18). David Beard found another, which was a 5088 with 31 short courses and only five long courses (No.22). Very recently I discovered that Stephen Yates had produced several tenors together compositions in the late seventies, but of these only a 5088 with three short courses had been published (No.9).

The compositions finishing at the treble's backstroke snap fall into 23 groups of 11 different lengths. It is for their unusual length that such compositions are rung, since they are musically inferior to the round blocks from which they are derived. Examples of only three of these groups have been published. In addition to Price's original 5090 (No.29), there is a similar 5090 by Andrew Tyler (RW 1988 page 940), a 5122 by Price (No.32), and a 5186 discovered by both John Warboys and John Goldthorpe (No.28).

So the question I asked myself in 1995 was "Have I found anything new?" and my conclusion was "Not a lot". However, I did pick just a few compositions which I felt had some merit, namely a slightly more musical 5024 than Brian Price's peal, with six short courses (No.13); a new 5024 with thirteen short courses which has the highest overall musical score in this analysis (No.19); and a 5216 with only one long course and 39 short courses, which has the most crus (118) when those off the back and front are added together (No.24). I also selected two 5250s, which I thought would be useful for 250th anniversaries, one with five short courses (No.35), and the other which is all in short courses until the last course (No.48).

The full results of these exhaustive searches can downloaded from here by anyone wishing to undertake their own analysis.

Graham John
May 2002 (from an original draft in December 1998)