THE RESULTING PEALS

The results are presented below in order of their musicality, as measured by the number of 'Combination Roll-Ups' (CRUs). Each peal has been analysed for the starting position which gives (a) the maximum number of CRUs and then (b) the maximum number of 678s for that number of CRUs. Note that (b) is not necessarily the unconditional maximum; for instance, in the case of the 5,024 palindrome it was thought by the conductor, when the composition was rung for the first time, that it was better to sacrifice some CRUs for the sake of 678s and 8765s.

From the compositional angle, the number of CRUs is an arbitrary statistic, but its importance in the enjoyment of a peal prompts the method of classification.

(A CRU is one of the 144 rows in which 7 and 8 are at home, and some combination pair of 4, 5 and 6 are in 5ths and 6ths)

5,120 with 12 short courses (74 CRUs, 56 678s, irregular 2-part)

An interesting discovery of the 2-part tree search on 4 May 1988 was the pair of identically called round blocks given below, which together constitute a 5,120:
     B   M   W   H     2 3 4 5 6       B   M   W   H     3 2 4 6 5
     ---------------------------       ---------------------------
         -       S     4 6 3 5 2           -       S     4 5 2 6 3
         -   -a  -b    2 5 3 6 4           -   -k  -g    3 6 2 5 4
     x           -c    2 5 6 4 3       x           -d    3 6 5 4 2
         S       -d    6 3 5 4 2           S       -c    5 2 6 4 3
         -e      -f    2 5 3 4 6           -b      -j    3 6 2 4 5
     x                 5 4 2 6 3       x                 6 4 3 5 2
     x                 4 6 5 3 2       x                 4 5 6 2 3
     x                 6 3 4 2 5       x                 5 2 4 3 6
     x           -g    6 3 2 5 4       x           -b    5 2 3 6 4
             -a  -h    2 5 6 3 4               -k  -i    3 6 5 2 4
             S   -i    6 3 5 2 4               S   -h    5 2 6 3 4
     x           -j    6 3 2 4 5       x           -f    5 2 3 4 6
         -e  -   S     4 5 2 3 6           -b  -   S     4 6 3 2 5
             -   -     2 3 4 5 6               -   -     3 2 4 6 5
     ---------------------------       ---------------------------
Each is a palindrome, that is, reversing the calling leaves them unchanged. They were produced on the 2-part plan which swops two pairs of bells. The blocks are rich in possible links, singles for bobs, which have been tabulated by the letters a to l. They are in image sets, such as bb, gg and ff, jj. Some such as aa do not link the two blocks but can be useful in conjunction with others. Other palindromes with more singles can be produced but they stubbornly refuse to form a peal, and an asymmetric linking pair of singles is required. After experimentation it was decided to use the palindromic blocks derived by singling bbjjffgg, plus an extra pair cc, because it produces a calling easier to remember, with a repetition of calling for no apparent reason. The result is by happy chance musical, with 74 CRUs (as against 62 in Middleton's), 56 678s and 42 578s, and three 8765s. As the band who first rang it discovered, tittums occurs at the Wrong in the third course.
               5,120 Cambridge Surprise Major

                B   M   W   H     2 3 4 5 6
                ---------------------------
                x           -     2 3 5 6 4
                    S       S     4 5 3 6 2
                    S       -     3 2 5 6 4
                ---------------------------
                    -       S     5 4 2 6 3
                    -   -   S     6 3 2 4 5
                        -   -     2 4 6 3 5
                    -       S     6 5 4 3 2
                    -   -   S     3 2 4 5 6
                        -   -     4 5 3 2 6
                        S   -     3 2 5 4 6
                ---------------------------
                x           S     2 3 4 6 5
                x                 3 6 2 5 4
                x                 6 5 3 4 2
                x                 5 4 6 2 3
                x           S     4 5 2 3 6
                ---------------------------
                x           S     5 4 3 6 2
                ---------------------------
                    -       S     3 2 4 6 5
                    -   -   S     6 5 4 2 3
                        -   -     4 2 6 5 3
                    -       S     6 3 2 5 4
                    -   -   S     5 4 2 3 6
                        -   -     2 3 5 4 6
                        S   -     5 4 3 2 6
                ---------------------------
                x           S     4 5 2 6 3
                x                 5 6 4 3 2
                x                 6 3 5 2 4
                x                 3 2 6 4 5
                x           S     2 3 4 5 6
                ---------------------------
First rung, on handbells, at Imperial College on 6 June 1988 conducted by Roger Bailey (R.W. No.4027 p.622, composition R.W. No.4035 p.819). First rung on tower bells at Bristol Cathedral on 26 August 1988 conducted by Anthony Cox (R.W. No.4042 p.973).

5,120 with 12 Short Courses (73 CRUs, 53 678s)

A series of 32 different palindromic blocks of 5,120 were produced on 26 June 1988, all variations of the same basic blocks. When linking singles (alternative to bobs) have been removed, the following five blocks remain:
         Main Palindromic Block

       B   M   W   H     5 4 2 6 3       B   M   W   H     4 5 6 2 3
       ---------------------------       ---------------------------
       x                 4 6 5 3 2       x           -     4 5 2 3 6
       x           -A    4 6 3 2 5               -   -d    2 3 4 5 6
               -B  -C    3 2 4 6 5           -F      -E    6 4 3 5 2
               S   -D    4 6 2 3 5       x                 4 5 6 2 3
       x           -E    4 6 3 5 2       ---------------------------
           -b  -   S     5 2 3 6 4
               -   -     3 6 5 2 4        Offset Palindromic Blocks
           -       S     5 4 6 2 3
           -   -B  -e    3 2 6 4 5       B   M   W   H     2 3 5 6 4
       x           -d    3 2 4 5 6       ---------------------------
           S       -c    4 6 2 5 3       x           -e    2 3 6 4 5
           -b      -a    3 2 6 5 4               -f  -D    6 4 2 3 5
       x                 2 5 3 4 6           -       -     5 2 4 3 6
       x                 5 4 2 6 3       x                 2 3 5 6 4
       ---------------------------       ---------------------------

                          Pair of Asymmetrical Blocks

        B   M   W   H     5 4 6 3 2       B   M   W   H     5 2 3 4 6
       ---------------------------       ---------------------------
           -   S   -C    2 3 4 6 5           -   -f  -A    6 4 3 2 5
       x           -a    2 3 6 5 4       x           -c    6 4 2 5 3
           -F  -   S     5 4 6 3 2           S   -   S     5 2 3 4 6
       ---------------------------       ---------------------------
They consist of a main one-part palindromic block, two asymmetric image blocks (with mutually reverse callings) and two offset palindromic blocks which are not interchangeable. As presented, the symmetry of the system is that of the transdigit (24) (36)(5). Note that the internal symmetry of the offset palindromes is not the same - one is (23)(56)(4), the other (35)(46)(2).

Positions of pairs of possible linking singles (substituted for bobs) have been labelled so that AA and aa are image pairs, etc., and all the palindromic peals have both such image pairs singled or not. However, we are not obliged to produce palindromes. The fact that a peal is a palindrome is not much help to the conductor and it would perhaps be better to find a one-part peal with some semblance of repetition of calling. The system gives a very large choice - 644 different peals, consisting of the original 32 palindromes plus 306 other callings and their reverses. A printout of these, using a special Basic program, consumed nearly two rolls of paper and took over three hours!

The position of Rounds in the above blocks is that which gives the maximum musicality of 73 CRUs with 53 each of 678s and 578s, and three 8765s. An alternative start with the same statistics is from 32456. Two other slightly less musical starts (with one less 8765) are 23465 and 32465. All these variations have six 5678s on the front. As every different calling consists of the same rows, the choice of calling is independent of musicality, and there is a limited choice of start. A search for incidentally-repeated callings proved futile, and it was decided to give the following palindrome, using singled Q-sets AaCcDdEe:

                                 5,120

                        B   M   W   H   2 3 4 5 6
                        -------------------------
                            -       S   4 6 3 5 2
                            -   -   S   5 2 3 6 4
                                -   -   3 6 5 2 4
                            -       S   5 4 6 2 3
                            -   -   S   2 3 6 4 5
                                -   S   4 6 2 3 5
                        x           S   6 4 3 5 2
                        x               4 5 6 2 3
                        x           -   4 5 2 3 6
                                -   S   3 2 4 5 6
                            S       S   6 4 2 5 3
                            S   -   S   5 2 3 4 6
                            -   -   S   4 6 3 2 5
                                -   S   2 3 4 6 5
                        x           S   3 2 6 5 4
                        x               2 5 3 4 6
                        x               5 4 2 6 3
                        x               4 6 5 3 2
                        x           S   6 4 3 2 5
                        x           S   4 6 2 5 3
                            -       S   2 3 6 5 4
                            -   -   S   5 4 6 3 2
                            -   S   S   3 2 4 6 5
                                S   S   6 4 2 3 5
                            -       -   5 2 4 3 6
                        x               2 3 5 6 4
                        x           S   3 2 6 4 5
                        x           S   2 3 4 5 6
                        -------------------------
First rung at St.Michael's, St.Albans on 17 December 1988 conducted by Philip Mehew (R.W. No.4077 p.555).

The Q-sets singled are all the Home ones, so that there are few Homes not singled, while the only singles at Middle and Wrong (ones integrated into the composition) come together conveniently in pairs. The number of singles is remarkable, considering that a single links two mutually false courses!

5,056 with 8 short courses (70 CRUs, 56 678s, irregular 2-part)

A 5,056 of Cambridge emerged from the 2-part tree search on 17 June 1988 in eight different forms, all giving two separate identically-called round blocks, and not a 2-part peal. Examination showed that none of the singles (always four in each block) were integrated into the composition but formed Q-sets with bobs, and their removal left the following six blocks, all palindromes:
       B   M   W   H     5 4 6 2 3          B   M   W   H     2 3 6 5 4
       ---------------------------          ---------------------------
       x           -a    5 4 2 3 6          x           -e    2 3 5 4 6
           -             2 4 6 3 5              -             5 3 6 4 2
           -   -         3 6 5 4 2              -   -         4 6 2 3 5
               -   -b    5 4 3 6 2                  -   -f    2 3 4 6 5
       x           -     5 4 6 2 3          x           -     2 3 6 5 4
       ---------------------------          ---------------------------
       B   M   W   H     6 5 4 3 2          B   M   W   H     6 2 3 4 5
       ---------------------------          ---------------------------
           -   -   -c    2 3 4 5 6              -   -   -g    5 4 3 2 6
               -i  -a    4 5 2 3 6                  -k  -e    3 2 5 4 6
       x           -b    4 5 3 6 2          x           -f    3 2 4 6 5
           -j      -d    2 3 5 6 4              -l      -h    5 4 2 6 3
           -   -         6 5 4 3 2              -   -         6 2 3 4 5
       ---------------------------          ---------------------------
       B   M   W   H     6 5 4 2 3          B   M   W   H     6 2 3 5 4
       ---------------------------          ---------------------------
           -   -k  -c    3 2 4 5 6              -   -i  -g    4 5 3 2 6
       x           -d    3 2 5 6 4          x           -h    4 5 2 6 3
           -l  -         6 5 4 2 3              -j  -         6 2 3 5 4
       ---------------------------          ---------------------------
The left and right columns differ only by the transdigit (25)(34)(6). The middle blocks are in-course and the positions for singles (substituted for bobs) to link them to the upper and lower out-of- course blocks are labelled a to l. The eight solutions are accounted for by the choice of aaee or bbff to link the top blocks, and ccgg, or ddhh, or iikk, or jjll to link the bottom blocks (remembering that the 2-part tree search can only produce exact 2-part systems). Since tjjll to link the bottom blocks (remembering that the 2-part tree search can only produce exact 2-part systems). Since the blocks are all palindromes, the eight solutions consist of four mutually-reverse pairs.

To make up a peal, it is necessary to use an unbalanced pair of singles. In order to produce as little disturbance from the 2-part structure as possible, it was decided to use the singles at Home aaee and ccgg, plus an unbalanced pair at Wrong, ii.

For the sake of musicality, it was decided to put the odd course at the end rather than at the start with the other two. In the following form, the 6th is observation bell and there are 70 CRUs and 56 678s:

                 B   M   W   H     2 3 4 5 6
                 ---------------------------
                         S   S     5 4 3 2 6
                         -   S     2 3 5 4 6
                 ---------------------------
                     -             5 3 6 4 2
                     -   -         4 6 2 3 5
                         -   -     2 3 4 6 5
                 x           -     2 3 6 5 4
                 x           S     3 2 5 4 6
                 x           -     3 2 4 6 5
                     -       -     5 4 2 6 3
                     -   -         6 2 3 4 5
                     -   -   S     4 5 3 2 6
                 x           -     4 5 2 6 3
                     -   -         6 2 3 5 4
                 ---------------------------
                     -   S   S     5 4 2 3 6
                 ---------------------------
                     -             2 4 6 3 5
                     -   -         3 6 5 4 2
                         -   -     5 4 3 6 2
                 x           -     5 4 6 2 3
                 x           S     4 5 2 3 6
                 x           -     4 5 3 6 2
                     -       -     2 3 5 6 4
                     -   -         6 5 4 3 2
                     -   -   S     3 2 4 5 6
                 x           -     3 2 5 6 4
                     -   -         6 5 4 2 3
                 ---------------------------
                     -   -   S     2 3 4 5 6
                 ---------------------------
First rung at St.Mary's Hendon on 11 March 1989 conducted by Roger Bailey (R.W. No.4069 p.366)

5,184 with 16 short courses (68 CRUs, 58 678s, 2-part)

This peal in two exact parts, containing 14 long and 16 short courses, was produced by the 2-part tree search on 8 June 1988. It exists in four forms, all containing the same rows but in differing order. They are derived from one another by altering pairs of singles for bobs, or vice versa, and 2 & 3, 1 & 4 are mutually reverse callings.
            Version No.1                      Version No.2

      B  M  W  H     2 3 4 5 6          B  M  W  H     2 3 4 5 6
      ------------------------          ------------------------
            S  -     4 5 3 2 6                S  -     4 5 3 2 6
      x        S     5 4 2 6 3          x        S     5 4 2 6 3
      x              4 6 5 3 2          x              4 6 5 3 2
      x              6 3 4 2 5          x              6 3 4 2 5
      x              3 2 6 5 4          x              3 2 6 5 4
      x        -     3 2 5 4 6          x        -     3 2 5 4 6
         -           5 2 6 4 3             -           5 2 6 4 3
         -  -        4 6 3 2 5             -  -        4 6 3 2 5
            -  S     2 3 4 6 5                -  S     2 3 4 6 5
         S     -     4 5 3 6 2             S     S     5 4 3 6 2
      x        -     4 5 6 2 3             -  -        6 3 2 4 5
      x        S     5 4 2 3 6             -  -  -     5 4 2 3 6
      x        -     5 4 3 6 2          x        S     4 5 3 6 2
         -  -        6 3 2 4 5          x        -     4 5 6 2 3
         -  -  S     4 5 2 3 6          x        -     4 5 2 3 6
      ------------------------          ------------------------
              Repeated                          Repeated

            Version No.3                      Version No.4

      B  M  W  H     2 3 4 5 6          B  M  W  H     2 3 4 5 6
      ------------------------          ------------------------
            S  S     5 4 3 2 6                S  S     5 4 3 2 6
         -           3 4 6 2 5             -           3 4 6 2 5
         -  -        2 6 5 4 3             -  -        2 6 5 4 3
            -  -     5 4 2 6 3                -  -     5 4 2 6 3
      x              4 6 5 3 2          x              4 6 5 3 2
      x              6 3 4 2 5          x              6 3 4 2 5
      x              3 2 6 5 4          x              3 2 6 5 4
      x        S     2 3 5 4 6          x        S     2 3 5 4 6
      x        -     2 3 4 6 5          x        -     2 3 4 6 5
         S     -     4 5 3 6 2             S     S     5 4 3 6 2
      x        -     4 5 6 2 3             -  -        6 3 2 4 5
      x        S     5 4 2 3 6             -  -  -     5 4 2 3 6
      x        -     5 4 3 6 2          x        S     4 5 3 6 2
         -  -        6 3 2 4 5          x        -     4 5 6 2 3
         -  -  S     4 5 2 3 6          x        -     4 5 2 3 6
      ------------------------          ------------------------
              Repeated                          Repeated
Version 4 rung on handbells at Imperial College on 20 July 1988, conducted by Roger Bailey (R.W. No.4033 p.778, composition R.W. No.4071 p.424). First rung on tower bells at Netherton, conducted by Martin Fellows (R.W. No.4077 p.554).

Like the 5,056, this peal can be broken down into palindromic blocks. However, the singles at Middle and Wrong are integrated into one of the blocks and cannot be altered. There is a 2 part block and hence exact 2-part peals can result.

   B   M   W   H     6 3 4 2 5          B   M   W   H     6 5 2 4 3
   ---------------------------          ---------------------------
   x                 3 2 6 5 4          x                 5 4 6 3 2
   x           -a    3 2 5 4 6          x           -e    5 4 3 2 6
       -             5 2 6 4 3              -             3 4 6 2 5
       -   -         4 6 3 2 5              -   -         2 6 5 4 3
           -   -b    3 2 4 6 5                  -   -f    5 4 2 6 3
   x                 2 6 3 5 4          x                 4 6 5 3 2
   x                 6 5 2 4 3          x                 6 3 4 2 5
   ---------------------------          ---------------------------
   B   M   W   H     4 5 6 2 3          B   M   W   H     2 3 6 4 5
   ---------------------------          ---------------------------
   x           -c    4 5 2 3 6          x           -g    2 3 4 5 6
           S   -a    2 3 5 4 6                  S   -e    4 5 3 2 6
   x           -b    2 3 4 6 5          x           -f    4 5 2 6 3
       S       -d    4 5 3 6 2              S       -h    2 3 5 6 4
   x           -     4 5 6 2 3          x           -     2 3 6 4 5
   ---------------------------          ---------------------------
   B   M   W   H     6 3 2 4 5          B   M   W   H     6 5 4 2 3
   ---------------------------          ---------------------------
       -   -   -c    5 4 2 3 6              -   -   -g    3 2 4 5 6
   x           -d    5 4 3 6 2          x           -h    3 2 5 6 4
       -   -         6 3 2 4 5              -   -         6 5 4 2 3
   ---------------------------          ---------------------------
The top two sections are parts of a 2-part palindrome which is in- course. The bottom blocks are out-of-course palindromes, while the middle blocks are palindromes which are mixed, and link to the top and bottom blocks. In order to produce a 2-part peal aa and ee have to go together, and so on, giving four distinct peals, but there are many more irregular peals and a number of versions emerged in the one-part palindromic search. As all variations can have the same rows, the only musical choice is where to start the calling.

In order to get the maximum of 68 CRUs the fixed bell (here 6) must not be 2 or 3. Of the possible starts, the one given appears to be the best with 68 CRUs, 58 678s, 55 578s and three 8765s (a few other starts give the same statistics). In comparison, the full Middleton's has 62 CRUs.

5,184 with 16 Short Courses (68 CRUs, 58 678s)

During a run for producing palindromes on the mainframe Cyber on 26 June 1988 a number of blocks of 5,184 were found, four of which were versions of the 2-part 5,184 produced earlier by 2-part search using Basic. These had been predicted. But ten others were not, and analysis showed that they were slightly different. They had the same four smaller blocks and linkages but the main palindrome differed from the former 2-part palindrome in having a Plain/Bob Q-set bobbed. The new bob-Home apex was on the opposite side of the Q-set to the old plain-Home apex. The positions of these bobbed Homes are labelled q below.
     B   M   W   H     4 5 2 3 6       B   M   W   H     5 4 6 3 2
     ---------------------------       ---------------------------
         -   -         3 2 6 5 4       x           -C    5 4 3 2 6
             -   -A    6 5 3 2 4               S   -a    3 2 4 5 6
     x                 5 2 6 4 3       x           -b    3 2 5 6 4
     x           -q    5 2 4 3 6           S       -D    5 4 2 6 3
             -   -b    4 3 5 2 6       x           -     5 4 6 3 2
     x                 3 2 4 6 5       ---------------------------
     x                 2 6 3 5 4
     x                 6 5 2 4 3       B   M   W   H     3 4 2 5 6
     x           -B    6 5 4 3 2       ---------------------------
         -       -q    6 2 5 3 4       x           -d    3 4 5 6 2
     x                 2 3 6 4 5               S   -B    5 6 4 3 2
     x           -a    2 3 4 5 6       x           -A    5 6 3 2 4
         -             6 3 2 5 4           S       -c    3 4 6 2 5
         -   -   -q    4 5 2 3 6       x           -     3 4 2 5 6
     ---------------------------       ---------------------------
     B   M   W   H     6 2 3 5 4       B   M   W   H     2 6 5 3 4
     ---------------------------       ---------------------------
         -   -   -C    4 5 3 2 6           -   -   -d    4 3 5 6 2
     x           -D    4 5 2 6 3       x           -c    4 3 6 2 5
         -   -         6 2 3 5 4           -   -         2 6 5 3 4
     ---------------------------       ---------------------------
This structure enables the smaller blocks to be assembled in 2- part fashion using either Q-sets Cd or cD, leaving the main block to be irregular, but the process is helped by the fact that in the main block, preceding positions B and a, are two courses with the same calling (Before, Before and Home) which can be absorbed into the similar blocks. The choice of Q-sets Cd or cD then gives the following two peals:
              5,184                             5,184

    B   M   W   H   2 3 4 5 6         B   M   W   H   2 3 4 5 6
    -------------------------         -------------------------
        -           4 3 6 5 2             -           4 3 6 5 2
        -   -   -   2 5 6 3 4             -   -   -   2 5 6 3 4
        -   -       3 6 4 5 2             -   -       3 6 4 5 2
            -   -   4 5 3 6 2                 -   -   4 5 3 6 2
    x               5 6 4 2 3         x               5 6 4 2 3
    x           -   5 6 2 3 4         x           -   5 6 2 3 4
            -   -   2 3 5 6 4                 -   -   2 3 5 6 4
    x               3 6 2 4 5         x               3 6 2 4 5
    x               6 4 3 5 2         x               6 4 3 5 2
    -------------------------         -------------------------
    x               4 5 6 2 3         x               4 5 6 2 3
    x           S   5 4 2 3 6         x           S   5 4 2 3 6
    x           -   5 4 3 6 2         x           -   5 4 3 6 2
        S       S   2 3 4 6 5             S       -   3 2 4 6 5
        -   -       6 4 5 3 2         x           -   3 2 6 5 4
        -   -   -   2 3 5 4 6         x           S   2 3 5 4 6
    x           S   3 2 4 6 5         x           -   2 3 4 6 5
    x           -   3 2 6 5 4             -   -       6 4 5 3 2
    x           -   3 2 5 4 6             -   -   S   3 2 5 4 6
            S   S   4 5 2 3 6                 S   S   4 5 2 3 6
    -------------------------         -------------------------
        -       -   6 2 5 3 4             -       -   6 2 5 3 4
    -------------------------         -------------------------
    x               2 3 6 4 5         x               2 3 6 4 5
    x           S   3 2 4 5 6         x           S   3 2 4 5 6
    x           -   3 2 5 6 4         x           -   3 2 5 6 4
        S       S   4 5 2 6 3             S       -   5 4 2 6 3
        -   -       6 2 3 5 4         x           -   5 4 6 3 2
        -   -   -   4 5 3 2 6         x           S   4 5 3 2 6
    x           S   5 4 2 6 3         x           -   4 5 2 6 3
    x           -   5 4 6 3 2             -   -       6 2 3 5 4
    x           -   5 4 3 2 6             -   -   S   5 4 3 2 6
            S   S   2 3 4 5 6                 S   S   2 3 4 5 6
    -------------------------         -------------------------
These peals have the same rows, and hence the same musical qualities, as the 2-part 5,184 and are probably of theoretical interest only. The question arises - is there a second P/B Q-set in the 2-part palindrome? Yes, there is, but if both Q-sets are bobbed one of the resulting blocks is not linkable with the others.

5,184 with 2 Short Courses (64 CRUs, 54 678s)

In a series of runs on the Cyber mainframe on 31 July 1988, a family of twelve one-part palindromes were produced, together with their twelve half-reverses. They all have 2 short and 22 long courses, length 5,184 changes, bobs at Home for both apices, and a maximum of 64 CRUs with 54 678s.

One of the palindromes is given below on the left, annotated with the numerous Q-sets available for producing variations. A and a are P/B Q-sets at Middle and Wrong, while the rest are B/S Q-sets. The apices, both at bobs Home, are denoted by *. The palindrome quoted has Q-set C singled, its other singles being integrated into the composition.

The Q-sets allow of a large number of non-palindromic variations. A not very successful attempt to produce a more tractable calling is on the right.

              Palindrome                        Variation

     B   M   W   H     2 3 4 5 6       B   M   W   H     2 3 4 5 6
     ---------------------------       ---------------------------
             S   -     4 5 3 2 6               S   -     4 5 3 2 6
          A      -     3 4 5 2 6               -   -     3 2 4 5 6
         -B   a  SC    5 6 4 2 3               S   -     4 5 2 3 6
             -b  -     4 2 5 6 3           -       -     6 2 5 3 4
         -       -D    3 5 2 6 4       x           -     6 2 3 4 5
     x           -E    3 5 6 4 2           S   -   -     3 4 5 2 6
         S    a  S     2 6 5 4 3           S       -     5 6 4 2 3
         -F  -         4 5 3 6 2               S   -     4 2 6 5 3
         -   S   -e    2 6 5 3 4                   -     6 4 2 5 3
             -f  -D    5 3 2 6 4           -   -   S     5 3 2 4 6
         -             2 3 4 6 5           -   -         4 2 6 3 5
         -   -   -*    5 6 4 3 2           -   S   -     5 3 2 6 4
         -   -         3 4 2 6 5               -   -     2 6 5 3 4
             -   -d    2 6 3 4 5           -             5 6 4 3 2
         -F      -E    5 3 6 4 2           -   -   -     2 3 4 6 5
         S   -         4 2 6 3 5           -   -         6 4 5 3 2
         -   -f  S     3 5 6 2 4               -   -     5 3 6 4 2
          A  S   -e    6 2 5 3 4           -       -     2 6 3 4 5
     x           -d    6 2 3 4 5           S   -         4 5 3 6 2
             -   -     3 4 6 2 5           -   -   S     6 2 3 5 4
         -B      SC    6 5 4 2 3               S   -     3 5 2 6 4
          A  -b  -     4 2 6 5 3       x           -     3 5 6 4 2
              a  -     6 4 2 5 3               -   -     6 4 3 5 2
         S       -*    2 3 4 5 6           -       -     2 3 4 5 6
     ---------------------------       ---------------------------
The palindromic version was first rung at SS. Mary and Edward, Barrow Gurney, on 21 December 1988 conducted by R.C. Kippin (R.W. No.4058 p.103).

Note that the presence in the above two peals of a full course following a bob at Home allows the peal to be shortened, after E.J. Lindley's variation of Middleton's, by starting two rows after the Wrong and ending with a single at Home, thus cutting the peal down to 5,054 changes (the variation of Middleton's, shortened to 5,022 by starting two rows after the Wrong position and ending with a single at Home, was the idea of Edwin Lindley; he gave it to me on 6 September 1947 at the Cambridge University Guild tour; it has subsequently been accredited to Speed).

5,184 with 2 short courses (64 CRUs, 47 678s)

On 31 July 1988 the one-part palindromic search produced two palindromes which were mutual reverses, but were not related to other solutions. On analysis the block was found to break up into three by bobbing four singles (Q-sets C and D) but the other singles were integrated into the composition.

The palindrome is given below, the two apices (both bobs Home) being marked *, while Rounds is in the position which attains 64 CRUs, 47 678s and 45 578s. An alternative start with the same statistics is from 32456. Starting and finishing after the Wrong does not produce any significant improvement.

                    5,184 Cambridge Surprise Major

                     B   M   W   H     2 3 4 6 5
                     ---------------------------
                          A  S   -     4 6 3 2 5
                         -       S     3 5 6 2 4
                             S   -     6 2 5 3 4
                     x           -B    6 2 3 4 5
                         S   -   -     3 4 5 2 6
                         S       SC    6 5 4 2 3
                         -   -   SD    2 3 4 5 6
                         -       -     6 4 3 5 2
                         S   -   S     5 3 2 4 6
                         S    a  -B    2 6 3 4 5
                         S   -   S     4 3 5 6 2
                          A  -   -*    5 6 4 3 2
                         -    a  S     4 2 6 3 5
                         -   S   -b    5 3 2 6 4
                          A  S   S     6 2 3 5 4
                         -   S   -     4 5 2 3 6
                             -   SD    3 2 4 5 6
                         -   -   SC    5 6 4 2 3
                             S   -     4 2 6 5 3
                         -   S   -b    3 5 2 6 4
                     x           -     3 5 6 4 2
                         S       S     2 6 5 4 3
                             -   -     5 4 2 6 3
                         S    a  -*    2 3 4 6 5
                     ---------------------------
The disposable Q-sets are labelled above as follows: P/B Q-sets at A (Middle) and a (Wrong), B/S Q-sets at B, b, C and D (all at Home). Ten non-palindromic variations were found by varying these Q- sets. They are given below. All contain the same rows as the palindrome and have Rounds in the corresponding position. They all have 24 singles, and either 32 bobs or (if A or a be bobbed) 35. Some have a slight measure of repetition of calling which might assist the conductor but there is little to choose between them:
         No.1   Q-sets BC                  No.2   Q-sets ABC

    B   M   W   H     2 3 4 5 6       B   M   W   H     2 3 4 5 6
    ---------------------------       ---------------------------
        -       -     6 4 3 5 2           -       -     6 4 3 5 2
        S   -   S     5 3 2 4 6           S   -   S     5 3 2 4 6
        S       S     6 2 3 4 5           S       S     6 2 3 4 5
        S   -   -     3 4 5 2 6           S   -   -     3 4 5 2 6
        S       S     6 5 4 2 3           S       S     6 5 4 2 3
        -   -   -     3 2 4 5 6           -   -   -     3 2 4 5 6
        -   -   S     5 6 4 2 3           -   -   S     5 6 4 2 3
            S   -     4 2 6 5 3               S   -     4 2 6 5 3
        -   S   -     3 5 2 6 4           -   S   -     3 5 2 6 4
    x           -     3 5 6 4 2       x           -     3 5 6 4 2
        S       S     2 6 5 4 3           S       S     2 6 5 4 3
            -   -     5 4 2 6 3               -   -     5 4 2 6 3
        S       -     2 3 4 6 5           S       -     2 3 4 6 5
            S   -     4 6 3 2 5           -   -   -     5 6 4 3 2
        -       S     3 5 6 2 4           -       S     4 2 6 3 5
            S   -     6 2 5 3 4           -   S   -     5 3 2 6 4
    x           S     2 6 3 4 5           -   S   -     4 6 3 2 5
        S   -   S     4 3 5 6 2           -       S     3 5 6 2 4
            -   -     5 6 4 3 2               S   -     6 2 5 3 4
        -       S     4 2 6 3 5       x           S     2 6 3 4 5
        -   S   -     5 3 2 6 4           S   -   S     4 3 5 6 2
            S   S     6 2 3 5 4           -   S   S     6 2 3 5 4
        -   S   -     4 5 2 3 6           -   S   -     4 5 2 3 6
            -   -     2 3 4 5 6               -   -     2 3 4 5 6
    ---------------------------       ---------------------------

          No.3   Q-sets bC                  No.4   Q-sets abC

    B   M   W   H     2 3 4 5 6       B   M   W   H     2 3 4 5 6
    ---------------------------       ---------------------------
        -       -     6 4 3 5 2           -       -     6 4 3 5 2
        S   -   S     5 3 2 4 6           S   -   S     5 3 2 4 6
        S       -     2 6 3 4 5           S   -   S     4 2 6 3 5
        S   -   S     4 3 5 6 2           -   S   S     3 5 2 6 4
            -   -     5 6 4 3 2       x           -     3 5 6 4 2
        -       S     4 2 6 3 5           S       S     2 6 5 4 3
        -   S   S     3 5 2 6 4               -   -     5 4 2 6 3
    x           -     3 5 6 4 2           S   -   -     2 6 3 4 5
        S       S     2 6 5 4 3           S   -   S     4 3 5 6 2
            -   -     5 4 2 6 3               -   -     5 6 4 3 2
        S       -     2 3 4 6 5           -   -   -     2 3 4 6 5
            S   -     4 6 3 2 5               S   -     4 6 3 2 5
        -       S     3 5 6 2 4           -       S     3 5 6 2 4
            S   -     6 2 5 3 4               S   -     6 2 5 3 4
    x           -     6 2 3 4 5       x           -     6 2 3 4 5
        S   -   -     3 4 5 2 6           S   -   -     3 4 5 2 6
        S       S     6 5 4 2 3           S       S     6 5 4 2 3
        -   -   -     3 2 4 5 6           -   -   -     3 2 4 5 6
        -   -   S     5 6 4 2 3           -   -   S     5 6 4 2 3
            S   -     4 2 6 5 3               S   -     4 2 6 5 3
        -   S   S     5 3 2 6 4           -   S   S     5 3 2 6 4
            S   S     6 2 3 5 4               S   S     6 2 3 5 4
        -   S   -     4 5 2 3 6           -   S   -     4 5 2 3 6
            -   -     2 3 4 5 6               -   -     2 3 4 5 6
    ---------------------------       ---------------------------

         No.5   Q-sets BD                  No.6   Q-sets ABD

    B   M   W   H     2 3 4 5 6       B   M   W   H     2 3 4 5 6
    ---------------------------       ---------------------------
        -       -     6 4 3 5 2           -       -     6 4 3 5 2
        S   -   S     5 3 2 4 6           S   -   S     5 3 2 4 6
        S       S     6 2 3 4 5           S       S     6 2 3 4 5
        S   -   -     3 4 5 2 6           S   -   -     3 4 5 2 6
        S       -     5 6 4 2 3           S       -     5 6 4 2 3
            S   -     4 2 6 5 3               S   -     4 2 6 5 3
        -   S   -     3 5 2 6 4           -   S   -     3 5 2 6 4
    x           -     3 5 6 4 2       x           -     3 5 6 4 2
        S       S     2 6 5 4 3           S       S     2 6 5 4 3
            -   -     5 4 2 6 3               -   -     5 4 2 6 3
        S       -     2 3 4 6 5           S       -     2 3 4 6 5
            S   -     4 6 3 2 5           -   -   -     5 6 4 3 2
        -       S     3 5 6 2 4           -       S     4 2 6 3 5
            S   -     6 2 5 3 4           -   S   -     5 3 2 6 4
    x           S     2 6 3 4 5           -   S   -     4 6 3 2 5
        S   -   S     4 3 5 6 2           -       S     3 5 6 2 4
            -   -     5 6 4 3 2               S   -     6 2 5 3 4
        -       S     4 2 6 3 5       x           S     2 6 3 4 5
        -   S   -     5 3 2 6 4           S   -   S     4 3 5 6 2
            S   S     6 2 3 5 4           -   S   S     6 2 3 5 4
        -   S   -     4 5 2 3 6           -   S   -     4 5 2 3 6
            -   S     3 2 4 5 6               -   S     3 2 4 5 6
        -   -   -     6 5 4 2 3           -   -   -     6 5 4 2 3
        -   -   S     2 3 4 5 6           -   -   S     2 3 4 5 6
    ---------------------------       ---------------------------

          No.7   Q-sets bD                  No.8   Q-sets abD

    B   M   W   H     2 3 4 5 6       B   M   W   H     2 3 4 5 6
    ---------------------------       ---------------------------
        -       -     6 4 3 5 2           -       -     6 4 3 5 2
        S   -   S     5 3 2 4 6           S   -   S     5 3 2 4 6
        S       -     2 6 3 4 5           S   -   S     4 2 6 3 5
        S   -   S     4 3 5 6 2           -   S   S     3 5 2 6 4
            -   -     5 6 4 3 2       x           -     3 5 6 4 2
        -       S     4 2 6 3 5           S       S     2 6 5 4 3
        -   S   S     3 5 2 6 4               -   -     5 4 2 6 3
    x           -     3 5 6 4 2           S   -   -     2 6 3 4 5
        S       S     2 6 5 4 3           S   -   S     4 3 5 6 2
            -   -     5 4 2 6 3               -   -     5 6 4 3 2
        S       -     2 3 4 6 5           -   -   -     2 3 4 6 5
            S   -     4 6 3 2 5               S   -     4 6 3 2 5
        -       S     3 5 6 2 4           -       S     3 5 6 2 4
            S   -     6 2 5 3 4               S   -     6 2 5 3 4
    x           -     6 2 3 4 5       x           -     6 2 3 4 5
        S   -   -     3 4 5 2 6           S   -   -     3 4 5 2 6
        S       -     5 6 4 2 3           S       -     5 6 4 2 3
            S   -     4 2 6 5 3               S   -     4 2 6 5 3
        -   S   S     5 3 2 6 4           -   S   S     5 3 2 6 4
            S   S     6 2 3 5 4               S   S     6 2 3 5 4
        -   S   -     4 5 2 3 6           -   S   -     4 5 2 3 6
            -   S     3 2 4 5 6               -   S     3 2 4 5 6
        -   -   -     6 5 4 2 3           -   -   -     6 5 4 2 3
        -   -   S     2 3 4 5 6           -   -   S     2 3 4 5 6
    ---------------------------       ---------------------------

          No.9   Q-sets ACD                 No.10  Q-sets aCD

    B   M   W   H     2 3 4 5 6       B   M   W   H     2 3 4 5 6
    ---------------------------       ---------------------------
        -       -     6 4 3 5 2           -       -     6 4 3 5 2
        S   -   S     5 3 2 4 6           S   -   S     5 3 2 4 6
        S       -     2 6 3 4 5           S   -   S     4 2 6 3 5
        S   -   S     4 3 5 6 2           -   S   -     5 3 2 6 4
        -   S   S     6 2 3 5 4               S   S     6 2 3 5 4
        -   S   -     4 5 2 3 6           -   S   -     4 5 2 3 6
            -   S     3 2 4 5 6               -   S     3 2 4 5 6
        -   -   S     5 6 4 2 3           -   -   S     5 6 4 2 3
            S   -     4 2 6 5 3               S   -     4 2 6 5 3
        -   S   -     3 5 2 6 4           -   S   -     3 5 2 6 4
    x           -     3 5 6 4 2       x           -     3 5 6 4 2
        S       S     2 6 5 4 3           S       S     2 6 5 4 3
            -   -     5 4 2 6 3               -   -     5 4 2 6 3
        S       -     2 3 4 6 5           S   -   -     2 6 3 4 5
        -   -   -     5 6 4 3 2           S   -   S     4 3 5 6 2
        -       S     4 2 6 3 5               -   -     5 6 4 3 2
        -   S   -     5 3 2 6 4           -   -   -     2 3 4 6 5
        -   S   -     4 6 3 2 5               S   -     4 6 3 2 5
        -       S     3 5 6 2 4           -       S     3 5 6 2 4
            S   -     6 2 5 3 4               S   -     6 2 5 3 4
    x           -     6 2 3 4 5       x           -     6 2 3 4 5
        S   -   -     3 4 5 2 6           S   -   -     3 4 5 2 6
        S       S     6 5 4 2 3           S       S     6 5 4 2 3
        -   -   S     2 3 4 5 6           -   -   S     2 3 4 5 6
    ---------------------------       ---------------------------
The original palindrome is, of course, its own reverse; of the ten variations the pairs of mutual reverses are 1, 3; 2, 4; 5, 7; 6, 8; 9, 10.

5,024 with 6 Short Courses (62 CRUs, 39 678s)

The following one-part palindrome was produced on the Cyber mainframe at Imperial College on 3 July 1988. It contains six short courses, the minimum number for the shortest peal length of 5,024, and they are discreetly separated!
      B   M   W   H   2 3 4 5 6         B   M   W   H   2 3 4 5 6
      -------------------------         -------------------------
          -   -       5 4 6 3 2             -   -       5 4 6 3 2
              -   -   6 3 5 4 2             -       S   6 2 4 3 5
      x               3 4 6 2 5                 -   S   3 4 6 2 5
              -   S   2 6 3 4 5             -   -   -   5 2 6 4 3
          -   -       4 3 5 6 2         x           S   2 5 4 3 6
      x           -   4 3 6 2 5             S   -   -   4 3 6 5 2
          -   S   S   2 5 3 6 4         x               3 5 4 2 6
      x           -   2 5 6 4 3             -   -   S   2 6 4 5 3
          -   -   S   4 3 6 5 2             -           4 6 3 5 2
          -       S   6 2 3 5 4         x           -   4 6 5 2 3
              -       5 6 3 2 4             -           5 6 3 2 4
          -   -#  -   4 2 3 6 5             -   -   -   4 2 3 6 5
                  -   3 4 2 6 5             -   -       6 3 5 2 4
          -   -       6 2 5 4 3                 -   -   5 2 6 3 4
          -       S   5 3 2 4 6         x               2 3 5 4 6
              -   S   4 2 5 3 6                 -   S   4 5 2 3 6
          -   -   -   6 3 5 2 4             -   -       3 2 6 5 4
      x           S   3 6 2 4 5         x           -   3 2 5 4 6
          S   -   -   2 4 5 6 3             -   S   S   4 6 2 5 3
      x               4 6 2 3 5         x           -   4 6 5 3 2
          -   -   S   3 5 2 6 4             -   -   S   3 2 5 6 4
          -           2 5 4 6 3             -       S   5 4 2 6 3
      x           -   2 5 6 3 4                 -       6 5 2 4 3
          -           6 5 4 3 2             -   -#  -   3 4 2 5 6
          -   -   -   2 3 4 5 6                     -   2 3 4 5 6
      -------------------------         -------------------------
The right-hand version was first rung by the Cambridge University Guild of Change Ringers at St.Andrew, Shifnal on 25 August 1988 conducted by Bernard Taylor (R.W. No.4039 p.909, composition R.W. No.4071 p.424).

The left-hand version starts at the bob Home apex, and has 62 CRUs, the maximum number for this composition, but only 39 678s. The right-hand transposition, which starts just after the mid-course apex, has seven less CRUs but the advantages of 59 678s (including 16 5678s) and six 8765s.

The maximum of 62 CRUs with 59 678s, 16 5678s and six 8765s may be attained by starting and finishing the peal two rows after the Wrong at #, in course 32546, with the first two calls being bobs at Home.

5,120 with 40 short courses (56 CRUs, 60 678s)

Four 5120s in short courses were produced by the 1-part palindromic search in quick succession, with starting apex at bob Before. They are all related by P/S Q-sets. The basic block has 6 singles in it:
                          B    H    2 3 4 5 6
                          -------------------
                          x         3 5 2 6 4
                          x    S    5 3 6 4 2
                          x    -    5 3 4 2 6
                          x         3 2 5 6 4
                          x      a  2 6 3 4 5
                          x         6 4 2 5 3
                          x    -    6 4 5 3 2
                          x      b  4 3 6 2 5  ++
                          x    -    4 3 2 5 6
                          x         3 5 4 6 2
                          x    S    5 3 6 2 4
                          x         3 2 5 4 6
                          x    -    3 2 4 6 5  **
                          x      c  2 6 3 5 4
                          x    -    2 6 5 4 3
                          x         6 4 2 3 5  **
                          x      d  4 3 6 5 2
                          x    S    3 4 5 2 6
                          x         4 2 3 6 5
                          x         2 6 4 5 3
                          x    S    6 2 5 3 4
                          x      a  2 3 6 4 5
                          x         3 4 2 5 6
                          x    -    3 4 5 6 2
                          x      b  4 6 3 2 5  ++
                          x    -    4 6 2 5 3
                          x         6 5 4 3 2
                          x    S    5 6 3 2 4
                          x         6 2 5 4 3
                          x    -    6 2 4 3 5  **
                          x      c  2 3 6 5 4
                          x    -    2 3 5 4 6
                          x         3 4 2 6 5  **
                          x      d  4 6 3 5 2
                          x         6 5 4 2 3
                          x    -    6 5 2 3 4
                          x    S    5 6 3 4 2
                          x         6 4 5 2 3
                          x         4 2 6 3 5
                          x         2 3 4 5 6
                          -------------------
There are four pairs of positions, labelled aa to dd, where plain Homes can be singled in Q sets and used as shunts. The other three palindromes are produced by singling aadd, or bbcc, or all four pairs. Other irregular variations are produced by, for instance, singling aacc. It is interesting to observe how the upper and lower sets of positions of the Q-sets are within an open-ended palindrome of 14 courses.

Both apices of the palindrome are at bobs before. This peal and its variations are not related to other palindromes with apices at Home.

Musically, this composition differs from all the other short- course peals. Every variation has either 56 or 48 CRUs. Some are distinguished by having 16 5678s on the front. The choice for musical start is between the two alternatives

56 CRUs, 60 678s, 48 578s, 3 8765s, 16 5678s on the front; marked ++
56 CRUs, 60 678s, 42 578s, 6 8765s, 8 5678s on the front; marked **

In all these arrangements, the 6th will be the pivot bell of the complete palindrome.

5,122 with 4 short courses (55 CRUs, 50 678s, irregular 2-part)

A solution of a 2-part touch of 4,992 in two separate round blocks, admitting of a true coda, was produced on 7 December 1988 in three forms. The basic blocks are palindromes. One cannot link them without asymmetric calls:
  B    M    W    H     2 3 4 5 6     B    M    W    H     2 5 6 3 4
  ------------------------------     ------------------------------
       -    S    -a    6 5 3 4 2          -    S    -b    4 3 5 6 2
        e   S    -b    3 4 5 6 2           g   S    -a    5 6 3 4 2
  x              -     3 4 6 2 5     x              -     5 6 4 2 3
            -    -     6 2 3 4 5               -    -     4 2 5 6 3
       S     f   -*    3 5 2 4 6          S     h   -*    5 3 2 6 4
        e   S    -     2 4 5 3 6           g   S    -     2 6 3 5 4
       -         -     6 5 4 3 2          -         -     4 3 6 5 2
  x              -c    6 5 3 2 4     x              -d    4 3 5 2 6
       S     f   -d    3 4 5 2 6          S     h   -c    5 6 3 2 4
       S    -    S     2 5 6 4 3          S    -    S     2 3 4 6 5
        e   -    -*    6 4 2 5 3           g   -    -*    4 6 2 3 5
       -     f   S     2 3 4 5 6          -     h   S     2 5 6 3 4
  ------------------------------     ------------------------------
a, b, c, d are B/S Q-sets   e, f, g, h are P/B Q-sets   * are apices
The coda of 130 rows must follow a bob at Home substituted for the final single, and no transpositions of this are allowable. There seems little point in using one of the two pairs of P/B Q-sets as they do not produce a more regular calling (one cannot use both) and singling the pair of bobs at b gives the peal with the most irregularity at the start:
                   5,122 Cambridge Surprise Major

                      B   M   W   H    2 3 4 5 6
                      --------------------------
                          -   S   -    6 5 3 4 2
                              S   S    4 3 5 6 2
                              S   -    5 6 3 4 2
                      --------------------------
                      x           -    5 6 4 2 3
                              -   -    4 2 5 6 3
                          S       -    5 3 2 6 4
                              S   -    2 6 3 5 4
                          -       -    4 3 6 5 2
                      x           -    4 3 5 2 6
                          S       -    5 6 3 2 4
                          S   -   S    2 3 4 6 5
                              -   -    4 6 2 3 5
                      --------------------------
                          -       S    2 5 6 3 4
                          -   S   S    3 4 5 6 2
                      --------------------------
                      x           -    3 4 6 2 5
                              -   -    6 2 3 4 5
                          S       -    3 5 2 4 6
                              S   -    2 4 5 3 6
                          -       -    6 5 4 3 2
                      x           -    6 5 3 2 4
                          S       -    3 4 5 2 6
                          S   -   S    2 5 6 4 3
                              -   -    6 4 2 5 3
                      --------------------------
                          -       -    3 2 4 5 6
                      --------------------------
                      Rounds 130 changes later
First rung at Christchurch, Ebbw Vale on 10 June 1989 conducted by Robin Churchill (R.W. No.4079 p.595).

This composition is curious in that the 'observation bell', the 2nd, makes fourths at sixteen of the 35 bobs, in a regular pattern, and is unaffected at all the singles.

The peal has 55 CRUs, 50 678s, 14 5678s, one 8765 and eight 5678s at the front.


5,120 with 40 short courses (52 CRUs, 48 678s)

All the remaining peals produced have the above statistics. Analysis showed that for various starts: The optimum music is produced by starting positions giving 52 CRUs, 10 each of 5678s and 6578s, six 8765s and twelve 5678s on the front. In all the short-course peals below the alternative starts for these statistics are marked **.

4-part Peal

The following peal was produced by the 4-part tree search on 18 February 1988. It subsequently emerged from the 2-part tree search. It is not a palindrome, but a portion of it is, duplicating a section of one of the 2-part palindromes in short courses.
                                5,120

                        B     H      2 3 4 5 6
                        ----------------------
                        x            3 5 2 6 4
                        x            5 6 3 4 2
                        x     -      5 6 4 2 3
                        x     S      6 5 2 3 4
                        x     -      6 5 3 4 2
                        x            5 4 6 2 3  **
                        x     S      4 5 2 3 6
                        x            5 3 4 6 2
                        x     -      5 3 6 2 4
                        x     S      3 5 2 4 6
                        ----------------------
                           3 times repeated
The above version has 6 as fixed bell, and has the maximum of CRUs and 678s, but starting from rounds at the point marked ** is more musical, with 4 as fixed bell.

Rung on handbells at Imperial College on 15 June 1988 conducted by Roger Bailey (R.W. No.4031 p.731, composition R.W. No.4035 p.819).

2-part Palindromes (singles at both apices)

These two palindromic peals were produced by the 2-part search, and they also emerged later during the palindromic 1-part search.
                  No. 1                           No. 2

          B     H      2 3 4 5 6          B     H      2 3 4 5 6
          ----------------------          ----------------------
          x            3 5 2 6 4  **      x     -      2 3 5 6 4
          x     -      3 5 6 4 2          x            3 6 2 4 5  **
          x            5 4 3 2 6          x            6 4 3 5 2
          x     -      5 4 2 6 3          x     S      4 6 5 2 3
          x     S      4 5 6 3 2          x     -      4 6 2 3 5
          x            5 3 4 2 6          x            6 3 4 5 2
          x            3 2 5 6 4          x     S      3 6 5 2 4
          x            2 6 3 4 5          x            6 2 3 4 5
          x     S      6 2 4 5 3          x     -      6 2 4 5 3
          x     S      2 6 5 3 4 *        x     S      2 6 5 3 4 *
          x     S      6 2 3 4 5          x     -      2 6 3 4 5
          x            2 4 6 5 3          x            6 4 2 5 3  **
          x            4 5 2 3 6  **      x     S      4 6 5 3 2
          x            5 3 4 6 2          x            6 3 4 2 5
          x     S      3 5 6 2 4          x     -      6 3 2 5 4
          x     -      3 5 2 4 6          x     S      3 6 5 4 2
          x            5 4 3 6 2          x            6 4 3 2 5
          x     -      5 4 6 2 3          x            4 2 6 5 3
          x            4 2 5 3 6          x     -      4 2 5 3 6
          x     S      2 4 3 6 5 *        x     S      2 4 3 6 5 *
          ----------------------          ----------------------
                 Repeated                        Repeated
These are given with apices at half-way and end. In all the most musical variations (marked **) the fixed bell will be the 4th.

The apices are all at singles Home, and are marked with single asterisks *. At the first apex of each, 3,4 cross over and the other working bells 2, 6, 5 make places; at the second apex, 5,6 cross over, and the overall transdigit of the first part is (2)(34)(56).

1-part Palindromes (singles at both apices)

As well as versions of the two different palindromic peals already produced by the two part search, six more palindromes of 5,120 were produced:
       No. 1                   No. 2                   No. 3

 B   H   2 3 4 5 6       B   H   2 3 4 5 6       B   H   2 3 4 5 6
 -----------------       -----------------       -----------------
 x       3 5 2 6 4 **    x   -   2 3 5 6 4       x   -   2 3 5 6 4
 x   -   3 5 6 4 2       x       3 6 2 4 5 **    x       3 6 2 4 5 **
 x       5 4 3 2 6       x       6 4 3 5 2       x       6 4 3 5 2
 x   -   5 4 2 6 3       x       4 5 6 2 3       x       4 5 6 2 3
 x       4 6 5 3 2       x       5 2 4 3 6       x       5 2 4 3 6
 x       6 3 4 2 5       x   -   5 2 3 6 4       x   -   5 2 3 6 4
 x   -   6 3 2 5 4       x   S   2 5 6 4 3       x   S   2 5 6 4 3
 x   S   3 6 5 4 2       x       5 4 2 3 6 **    x   -   2 5 4 3 6
 x       6 4 3 2 5       x   -   5 4 3 6 2       x       5 3 2 6 4 **
 x   -   6 4 2 5 3 **    x       4 6 5 2 3       x       3 6 5 4 2
 x       4 5 6 3 2       x   -   4 6 2 3 5       x   S   6 3 4 2 5
 x       5 3 4 2 6       x       6 3 4 5 2       x   -   6 3 2 5 4
 x       3 2 5 6 4       x       3 5 6 2 4       x       3 5 6 4 2
 x       2 6 3 4 5       x   -   3 5 2 4 6       x       5 4 3 2 6
 x   S   6 2 4 5 3       x   S   5 3 4 6 2       x   -   5 4 2 6 3
 x   S   2 6 5 3 4       x       3 6 5 2 4       x       4 6 5 3 2
 x   S   6 2 3 4 5       x       6 2 3 4 5       x   S   6 4 3 2 5
 x       2 4 6 5 3       x       2 4 6 5 3       x       4 2 6 5 3
 x   S   4 2 5 3 6       x   S   4 2 5 3 6       x   -   4 2 5 3 6
 x   S   2 4 3 6 5       x   S   2 4 3 6 5       x   S   2 4 3 6 5
 x   S   4 2 6 5 3       x   S   4 2 6 5 3       x   -   2 4 6 5 3
 x       2 5 4 3 6       x       2 5 4 3 6       x       4 5 2 3 6 **
 x   S   5 2 3 6 4       x       5 3 2 6 4 **    x   S   5 4 3 6 2
 x   S   2 5 6 4 3       x       3 6 5 4 2       x       4 6 5 2 3
 x   S   5 2 4 3 6       x   S   6 3 4 2 5       x   -   4 6 2 3 5
 x       2 3 5 6 4       x   -   6 3 2 5 4       x       6 3 4 5 2
 x       3 6 2 4 5 **    x       3 5 6 4 2       x       3 5 6 2 4
 x       6 4 3 5 2       x       5 4 3 2 6       x   -   3 5 2 4 6
 x       4 5 6 2 3       x   -   5 4 2 6 3       x   S   5 3 4 6 2
 x   -   4 5 2 3 6 **    x       4 6 5 3 2       x       3 6 5 2 4
 x       5 3 4 6 2       x   -   4 6 3 2 5       x       6 2 3 4 5
 x   S   3 5 6 2 4       x       6 2 4 5 3       x   -   6 2 4 5 3
 x   -   3 5 2 4 6       x   S   2 6 5 3 4       x   S   2 6 5 3 4
 x       5 4 3 6 2       x   -   2 6 3 4 5       x   -   2 6 3 4 5
 x       4 6 5 2 3       x       6 4 2 5 3 **    x       6 4 2 5 3 **
 x   -   4 6 2 3 5       x       4 5 6 3 2       x       4 5 6 3 2
 x       6 3 4 5 2       x       5 3 4 2 6       x       5 3 4 2 6
 x   -   6 3 5 2 4       x       3 2 5 6 4       x       3 2 5 6 4
 x       3 2 6 4 5       x   -   3 2 6 4 5       x   -   3 2 6 4 5
 x   S   2 3 4 5 6       x   S   2 3 4 5 6       x   S   2 3 4 5 6
 -----------------       -----------------       -----------------

       No. 4                   No. 5                   No. 6

 B   H   2 3 4 5 6       B   H   2 3 4 5 6       B   H   2 3 4 5 6
 -----------------       -----------------       -----------------
 x   -   2 3 5 6 4       x   -   2 3 5 6 4       x   S   3 2 5 6 4
 x       3 6 2 4 5 **    x       3 6 2 4 5 **    x       2 6 3 4 5
 x       6 4 3 5 2       x       6 4 3 5 2       x       6 4 2 5 3 **
 x       4 5 6 2 3       x   S   4 6 5 2 3       x       4 5 6 3 2
 x       5 2 4 3 6       x   -   4 6 2 3 5       x       5 3 4 2 6
 x   -   5 2 3 6 4       x       6 3 4 5 2       x   -   5 3 2 6 4 **
 x   S   2 5 6 4 3       x       3 5 6 2 4       x       3 6 5 4 2
 x   -   2 5 4 3 6       x   -   3 5 2 4 6       x   S   6 3 4 2 5
 x       5 3 2 6 4 **    x   S   5 3 4 6 2       x   -   6 3 2 5 4
 x   S   3 5 6 4 2       x       3 6 5 2 4       x       3 5 6 4 2
 x       5 4 3 2 6       x       6 2 3 4 5       x       5 4 3 2 6
 x   -   5 4 2 6 3       x   -   6 2 4 5 3       x   -   5 4 2 6 3
 x       4 6 5 3 2       x   S   2 6 5 3 4       x       4 6 5 3 2
 x       6 3 4 2 5       x   -   2 6 3 4 5       x   -   4 6 3 2 5
 x   -   6 3 2 5 4       x       6 4 2 5 3 **    x       6 2 4 5 3
 x   S   3 6 5 4 2       x   S   4 6 5 3 2       x   S   2 6 5 3 4
 x       6 4 3 2 5       x   S   6 4 3 2 5       x   S   6 2 3 4 5
 x       4 2 6 5 3       x       4 2 6 5 3       x       2 4 6 5 3
 x   -   4 2 5 3 6       x   -   4 2 5 3 6       x   S   4 2 5 3 6
 x   S   2 4 3 6 5       x   S   2 4 3 6 5       x   S   2 4 3 6 5
 x   -   2 4 6 5 3       x   -   2 4 6 3 5       x   S   4 2 6 5 3
 x       4 5 2 3 6 **    x       4 5 2 3 6 **    x       2 5 4 3 6
 x       5 3 4 6 2       x   S   5 4 3 6 2       x   S   5 2 3 6 4
 x   S   3 5 6 2 4       x   S   4 5 6 2 3       x   S   2 5 6 4 3
 x   -   3 5 2 4 6       x       5 2 4 3 6       x       5 4 2 3 6 **
 x       5 4 3 6 2       x   -   5 2 3 6 4       x   -   5 4 3 6 2
 x       4 6 5 2 3       x   S   2 5 6 4 3       x       4 6 5 2 3
 x   -   4 6 2 3 5       x   -   2 5 4 3 6       x   -   4 6 2 3 5
 x       6 3 4 5 2       x       5 3 2 6 4 **    x       6 3 4 5 2
 x   S   3 6 5 2 4       x       3 6 5 4 2       x       3 5 6 2 4
 x       6 2 3 4 5       x   S   6 3 4 2 5       x   -   3 5 2 4 6
 x   -   6 2 4 5 3       x   -   6 3 2 5 4       x   S   5 3 4 6 2
 x   S   2 6 5 3 4       x       3 5 6 4 2       x       3 6 5 2 4
 x   -   2 6 3 4 5       x       5 4 3 2 6       x   -   3 6 2 4 5 **
 x       6 4 2 5 3 **    x   -   5 4 2 6 3       x       6 4 3 5 2
 x       4 5 6 3 2       x   S   4 5 6 3 2       x       4 5 6 2 3
 x       5 3 4 2 6       x       5 3 4 2 6       x       5 2 4 3 6
 x       3 2 5 6 4       x       3 2 5 6 4       x       2 3 5 6 4
 x   -   3 2 6 4 5       x   -   3 2 6 4 5       x   S   3 2 6 4 5
 x   S   2 3 4 5 6       x   S   2 3 4 5 6       x   S   2 3 4 5 6
 -----------------       -----------------       -----------------
Nos. 1, 2 and 6 have no variations, the available P/S Q-sets being abortive, and these three are independent compositions, though there is a curious correspondence between the first 17 courses of No.1 and the reverse of courses Nos. 39-16 in No.6. Nos.3, 4 and 5 are all related, and to No.2 of the 2-part palindromes, by altering P/S Q-sets. Removal of the four singles in No.3 which have not got bobs at home on both sides causes the peal to break up into a 4-part palindrome and two short 2-part palindromes, from which the other peals, and further variations, may be constructed.

A curious feature of No.5 are strings of 13 and 19 courses which form open-ended palindromes.


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