< Home     Series Four   New: Spliced Series Six >

Series Five      

 

My classic 5056 no.1 from Series 2, composed using the combination of human skill and computer power made possible by SMC32's linkage search, accidently achieved the goal of "no duffers" - that is, no undesirable coursing orders in the middle of the course. The fact that I had found one composition with this property belatedly led me to wonder whether there were others, and how to find them.

In Series Four I experimented with a pure "no-duffers" search, for the small tenors-together blocks needed to complete my cyclic peals. This worked so well that, tentatively, I applied it to the full peal length. There are two conflicting lines of thought here: on the one hand, one-part machine searches in an astronomically large space like Bristol are normally so far into the impossible that it is not even worth thinking about them; and on the other, the decimation of linkage possibilities caused by the restriction of the search to a small set of musical coursing orders is so harsh that you may reasonably expect no results at all of any significant length.

But once again Bristol came up trumps. A one-part no-duffers search completes in respectable time, and generates millions of interesting compositions; so many, in fact, that selection becomes a challenge in its own right. The compositions in Series 5 are a result of a thorough analysis of the results of several types of no-duffers searches, with varying numbers of singles and other basic parameters. And there are some absolute crackers, compositions which pack in more music than the best of any of the previous Series; see in particular the 5024 no.4, and the phenomenal 5088 no.7, which is a sort of reworking of 5056 no.1 with a staggeringly impressive increase in music counts.

The question is of course raised, if all these compositions have "no duffers" throughout, how can one be more musical than the other? The answer is that some no-duffers courses and half-courses have more musical rows than others. In particular, and as explained further in the notes below, the Series 5 compositions major on repeating leads of little-bell music: shifts of the 2 or the 6 at a Before, which repeat runs of the remaining little bells at the back. This, and the corresponding increase in the number of calls at Before, is a characteristic of all of the new peals.

So is this the end of the line, or are there more wonders lurking in the universe of compositional possibilities that is Bristol? Time will tell.

Series Five:
5024 no.372, 14, 150Benjamin Constant, September 2010
5024 no.472, 24, 140+10David Pipe, December 2010
5056 no.372, 22, 138Thomas J Hinks, July 2020
5088 no.772, 24, 148David Pipe, July 2010
5120 no.472, 23, 140Thomas J Hinks, December 2020
5152 no.372, 13, 138Jonathan Agg, April 2012
5152 no.472, 22, 152Thomas J Hinks, December 2010


5024 Bristol Surprise Major (no.3)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  52364      -     2
  26354   -  -
  62453   2        2
  34256   -        -
  45236         2
  65432      -  -
  24365      3
  63425   -  -     2
  24536   -     -
  43652      2     -
  54326      -     2
  25463      -     2
  23456   2  4
  ------------------

Contains:
  72 5678/8765 front or back
  14 6578 back
  150 LB4
  42 LB5

When I first turned my attention seriously to Bristol Major, in early 2004, I had some new ideas for the method, but also doubts that there would be any unmined territory left in the field of straightforward, tenors-together peal compositions. It turned out there was: in fact, the virgin resources of entire new continents were waiting to be plundered. It is now 2010 and I have revisited my original endeavours three times, and each time I have found, to my surprise, that Bristol has vast new hinterlands to explore.

The pinnacle of my second series of Bristol Major peals is the 5056 no.1 composed in 2007 (also available on this site). It has 19 courses elegantly threaded together into a near-palindromic construction in order to deliver the maximum number of 5678/8765 runs front and back (72) and to fill the rest of the peal with little-bell music, together with most of the 6578s and all the near-misses. But the magical property of the 5056 is its achievement of 'no duffers' - by which I mean no undesirable coursing orders outside the course end leads.

I had thought that the 5056 couldn't be bettered. However, returning to the field in 2010 I discovered that many other - possibly millions of other - compositions share the 'no duffers' property, and the blocks I had thought optimal to bring in the 5678/8765 music (the five Befores and my 'optimal super-efficient block' of BMHBHWH from co 62345) are not the only way of putting together a peal on this plan.

So here's the first one of the new series. It has 19 courses in minimum length, so contains just 24 course-end calls. It has all the 5678/8765 runs, slightly fewer 6578s, but a greatly increased little-bell count compared to 5056 no.1: 150 4-bell runs versus 134. The structure is more fine-grained than the arrangements from earlier series, with greater use of Befores to split coursing orders up and to shunt the bells around. We still have the seamless 'no duffers' transitions of one desirable course straight into another, but now we are shifting gear more often, and the arrival and interplay of music is perhaps less predictable.

Interestingly, these Befores are often used almost like course-end calls, to prolong a series of runs with a repeating lead. For instance, this 5024 contains the coursing order transitions 35426->63542, 64352->26435, 53462->25346 and 24536->62453, as well as four similar transitions in the normal 'Five Befores' rotations. These have the effect of repeating the position of the little bells, to generate two consecutive leads around the Before, each with four LB4 runs each off the back. Of course, despite the repetition, this is achieved without increasing the length of the course, since the tenors keep moving. In effect, the composition is using these Befores to cherry-pick the best leads from the little-bell coursing orders, and it is this which generates the high number of LB4 runs.

This use of Befores with more rapid changes of direction is a theme that repeats in all the new, series 5 compositions, and I think it should make these peals exciting to ring, if slightly more busy than their forebears. See the 5024 no.4, 5056 no.3, 5088 no.7, 5120 no.4, and 5152s no.3 and 4, also available on this site. Please let me know if you ring one of them.


5024 Bristol Surprise Major (no.4)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  42356            -
  54326         -
  54263      -     -
  26543         -  -
  45236   -  3  -  -
  65432      -  -
  46253      4
  43652   2        -
  43526      -     -
  24536         -
  32465      -     S-S
  63254      -     2
  64352   -  2  2
  23456   -        -
  ------------------

Contains:
  72 5678/8765 front or back
  24 6578 back
  140 LB4
  10 4567/7654
  42 LB5
  All 7 near-misses

This Series 5 peal seeks to bring in 4567/7654 runs in addition to the littler-bell music and traditional back-bell rollups; in terms of '4-runs' it is therefore more complete. The peal contains 10 such runs, two from the expected 54632 coursing order present at the penultimate course end, and a further eight from the more unusual 64523 coursing order used from the Home to the Wrong of the third course.

Compared to 5024 no.3, it has the same number of 4-runs, but also brings in the 7th near-miss (12354678) and the complete set of 6578 rollups (albeit at the expense of a block of three Homes). The final addition to the Series 5 canon, I think it is the equal of any of the other compositions.


5056 Bristol Surprise Major (no.3)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  62345      4  2  -
  62453   -  2     2
  34256   -        -
  45236         2
  34562      -     2
  54632         2  -
  43652   2  2     -
  43526      -     -
  26354      2
  52436   2  3  2  -
  23456   -  -
  ------------------

Contains:
  72 5678/8765 front or back
  22 6578 back
  138 LB4
  40 LB5

This was the first series 5 peal to stand direct comparison with 5056 no.1, bettering it in all music counts - 22 vs 20 6578s, and 138 vs 134 LB4 runs - with the one omission being the 54 near miss.

Even more so than in 5024 no.3, the 5678/8765 runs are absolutely splintered through the peal; there seem to be no blocks threading them together, but nevertheless appear they do, every single one. The 8765s off the back are mostly divorced from the 5678s on the front, appearing in separate parts of the peal: the former brought in by pairs of course-end calls between changes 4000 and 4764, and the latter appearing in six different courses between changes 1132 and 3912.

I think this is an interesting composition, but it is bettered again by 5088 no.7 (also available on this site) at the cost of one extra course-end call and a pair of singles.


5088 Bristol Surprise Major (no.7)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  42356            -
  54326         -
  54263      -     -
  46253   -  -
  43652   2        -
  43526      -     -
  24536         -
  34265      -     S-
  56342   -S    -  -
  45236      3  -  -
  65432      -  -
  32465      3     -
  63254      -     2
  64352   -  2  2
  23456   -        -
  ------------------

Contains:
  72 5678/8765 front or back
  24 6578 back
  148 LB4
  43 LB5
  7 near misses

This is the One. Compared to 5056 no.1, it looks busy, there is no immediately clear structure, and the course-end bobs cluster in pairs more often. However, it squeezes out more music from the method than I dreamed possible from this plan. It outdoes the Series 2 peal by some margin, containing all the 6578s instead of just 20, 14 more LB4 runs, 3 more LB5 runs, and retaining all seven near-misses. And in fact, as I describe below, it is really just 5056 no.1 broken into pieces and reassembled into a new, more efficient form.

How is this possible? If all these compositions are built from 'no-duffer' courses, how can this 5088 jam in more music than the others? The key is partly that pair of singles, which efficiently sweep up the 6578s without requiring 6-5 coursing orders to be maintained too far past the course end. With the 65s dealt with more ably, there is space in the remaining structure to add further little-bell music. Compared to 5056 no.3, also from Series 5, this 5088 manages to fit in extra half courses of the LB4-generators 24536 and 62453 in addition to the same back-bell fare.

In common with the other Series 5 peals, heavy use of Befores splits courses up frequently in this composition, with half of the 'big six' Bristol coursing orders (53246, 64235 and 46532) appearing in separated half-courses. The fact that the plain course appears towards, but not at, the end of the peal is reminiscent of 5056 no.1, as is the Home start and finish; but the separation of the plain course into two segments is a distinguishing feature of the new arrangement. As in several other Series 5 peals, the calls at Before are also used as repeating-lead generators for the little-bell coursing orders, with transitions such as the aforementioned 24536->62453 efficiently gathering up the best leads from both courses in the minimum amount of time. There is a great density of little-bell music throughout.

Looking at the structure in more detail, we can see that it does in fact bear resemblance to 5056 no.1. The heart of it is still the two blocks of five Befores, one from the plain course (which I'll call Alpha) and one from the reverse coursing order, 64235 (which I'll term Beta). However the two blocks are both split in half and linked across each other in an interesting way.

Anatomy of the peal:

  1. The start of the Beta block is brought up in the third course using the same initial calling as 5056 no.1.
  2. But, after just one Before, the 5088 transitions away into a truncated version of the 'optimal super-efficient' block, which usually gathers up all of the 5678/8765 not included in the Beta block, but here misses one half-course.
  3. This truncated block ends, rather than starts, in 62345, and this enables a cluster of course-end calls (sH,H,M,sM) to wrap up the more awkward 6578s by using negative coursing orders.
  4. We now enter the middle of the Alpha block, starting at 46532 and proceeding for three Befores until the plain course is reached.
  5. A bob Wrong transitions out of 53246 after just half a course, pulls in the 54 near miss, and, via a Home and Before with extra little-bell music (see further discussion below), arrives back into the Beta block.
  6. Three courses of the Beta block are rung, almost completing all five courses. (Crucially, two short segments of the block around the fifth Before are missed, and this enables courses with superior music to be added elsewhere in the composition.)
  7. Another short transition sweeps up the 5678/8765 off the front missed by the truncation of the optimal super-efficient block at the start of the peal, and adds an in-course 65 course end...
  8. Before depositing us back into the Alpha block at the start of the plain course.
  9. The peal now ends in a very similar fashion to 5056 no.1, going forward through the Alpha block (instead of backward, using the M/W calls of the older peal) until 46532 is reached, whereupon the same calling brings the peal round with the last 5678 rollups from the 54326 coursing order.

The result of all this chopping and changing is that the same coursing orders of 5056 no.1 are pulled in to the 5088, with just the loss of the odd half-course here and there where the musical content is less worthwhile despite the non-dufferdom of the coursing order. This enables the new arrangement to add five leads of the little-bell generator 64352, which acts as the exit course from the singled-in 6578s described in section 3 above, and brings in extra 3456/6543s and an LB5 run (76543 off the back). In addition to this entire new LB course, the use of a Before to link 35426 and 63542 in section 5, rather than ringing uninterrupted central leads of the latter as in the older peal, also increases the 2345/5432 counts.

This type of subtle change is sufficient to increase the final score dramatically, as the old peal is reassembled into a magical new form.


5120 Bristol Surprise Major (no.4)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  63425      4  -  -
  54326   -        -
  42563      -
  32654   2  -     -
  34256   2        -
  45236         2
  65432      -  -
  43265      3     2
  34265         -S
  46253   S- -
  43652   2        -
  54632         -
  52436   2        -
  23456   -  -
  ------------------

Contains:
  72 5678/8765 front or back
  23 6578 back
  140 LB4
  42 LB5

My 5056 no.1 has a cousin in Series 2 - 5120 no.2 - which adds three more 6578s at the expense of two extra leads. This is a direct competitor in length, and like all of Series 5 packs in more little-bell runs, giving 6 more than the original peal. It is of course not as music-rich as the new 5088, but I think it has merit in its own right.


5152 Bristol Surprise Major (no.3)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  26354      -  -  -
  65324         2
  54326   -        2
  42563      -
  63425   2     -
  24536   -     -
  36452      2
  62453   -  5     2
  34256   -        -
  45236         2
  45362      -     -
  23456   -  4
  ------------------

Contains:
  72 5678/8765 front or back
  13 6578 back
  138 LB4
  38 LB5

The original Series 1 peals had 20 courses, whereas Series 2 generally slipped to 19, the demands of greater linkage winning out. Series 5 is largely the same, with the exception of this peal, which delivers a no-duffers arrangement in 20 courses. With just 21 course-end calls, so an average of just 1.05 per course, it seems impossible that the parade of no-duffer coursing orders can be maintained - but this I think unique arrangement achieves just that goal.

Use of fewer calls gives this 5152 a simpler, neater appearance than the other Series 5 arrangements. However, although it contains all the 5678/8765, the little-bell and 6578 counts are reduced. Compared to peals from earlier series, it is still superb though, with more little-bell music than anything in Series 1 or 2.


5152 Bristol Surprise Major (no.4)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  62345      4  2  -
  24365   -  -
  63425   -  -     2
  43265   -  -     -
  43652      -     -
  54326      -     2
  42563      -
  26354   2  -
  62453   2        2
  34256   -        -
  45236         2
  65432      -  -
  24536      2  2
  42635      -  -  2
  23456      -
  ------------------

Contains:
  72 5678/8765 front or back
  22 6578 back
  152 LB4
  42 LB5

The penultimate Series 5 peal (5024 no.4 composed after the others). This has probably the highest combined music score of all the new compositions, with two fewer 65s than 5088 no.7, but four more LB4. With the longer length and a Before in all but three courses, it has more calls and a busier look to it, but should still be very rewarding to ring. Please let me know if you ring it (or any other of the Series 5 compositions).

 

MBD July 2010