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Series Six      

 

In July of 2010, I put the finishing touches to my Series 5 "no-duffers" compositions, and created this website to showcase them. In my introduction to that series I wrote, 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. Even as I wrote that, I knew there were indeed further possibilities, and had an idea where to look for them. Curiosity took over as early as the end of July, and so I began the search that led, at the start of 2011, to this, Series Six of my near decade-long exploration of the Bristol Major short-course peal.

What is different this time around? Well, although my previous series featured the occasional singles, they were only allowed in pairs around the course end, in order to prevent negative coursing orders occurring in the middle of the course. But there are plenty of perfectly good negative coursing orders, capable of generating the same back-bell and little-bell music as the positive courses. Unfortunately, allowing these out-of-course blocks into the "no duffers" set nearly doubles the number of courses we can use, and this in turn has an exponential effect on the search time. The search space once again becomes so large that the one-part machine search loses its effectiveness, and so I have returned to the linkage search, combining this technique with the no-duffers search in order to exhaustively mine the new possibilities available.

And what are those new possibilities like? The main benefit you will see realised in these peals is the capability to include all the music annexed by Series Five, but in the space of 20 courses not 19. An extra course may seem like little, but it means the removal of seven course-end calls, and a noticeable improvement in the speed of development of the composition as a consequence. The 5024 arrangements in Series Six have only 17 course-end calls, fewer than one per course on average. With the severely reduced linkage possibilities this entails, I find it nothing short of miraculous that so many music-rich, no-duffers arrangements are possible.

How do the new compositions work? The secret is the increased flexibility and availability of the 5678/8765 rollups. All the arrangements here have a 72 such runs, but whereas with positive, tenors-together courses there are exactly 72 rollups available, no more no less, by including negative courses we have additional possibilities, from which we can pick and choose. Many of these compositions make use of negative coursing orders of the form 56xxx or xxx56, which means we see more 8765s off the back and 5678s off the front, with fewer of the conventional, forwards rollups. Hopefully that should feel a little different to ring.

In terms of little-bell runs, these peals use the same techniques, and achieve similar music counts, as those of Series Five. Generally, positive courses are used to generate the LB music, with the exception of 5152 no.6, where coursing order 64532 gives us eight 4567/7654 rows.

Series Six:
5024 no.572, 18, 136P Jonathan Franklin, April 2011
5024 no.672, 17, 124Stephen J Beckingham, March 2011
5056 no.472, 24, 140Stephen J Bedford, March 2011
5056 no.572, 22, 140Matthew J Edwards, March 2011
5120 no.572, 18, 148James W Holdsworth, July 2011
5120 no.672, 24, 140Thomas J Hinks, January 2012
5152 no.572, 24, 148Stuart C W Hutchieson, April 2011
5152 no.672, 18, 144+10P Jonathan Franklin, March 2012


5024 Bristol Surprise Major (no.5)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  45236      5  -  -
  65432      -  -
  46253      4
  65324   -     2
  43526   -        -
  24536         -
  36452      2
  24653   S        S
  34562   2  -     -
  34625      -     -
  23645         -
  23456      -     -
  ------------------

Contains:
  72 5678/8765 front or back
  18 6578 back
  136 LB4
  37 LB5
  All 7 near-misses

This, the first peal of Series Six, shows off the basic features of all the new arrangements: the full twenty courses, a corresponding brevity and fluidity of construction, and the use of negative 56xxx and xxx56 coursing orders to bring in the complement of 72 back-bell rollups. Here, 56243 is used, giving us more 5678s off the front and 8765s at the back compared to the older peals. As a 5024, this peal must make do with the minimum number of course-end calls, just 17, or an average of 0.85 per course. The usual sets of Befores on the alpha and beta courses helps with this, but is by no means sufficient; instead the length is achieved with a wonderful efficiency of linkage, very often just a single course-end call being used to transition from one no-duffer coursing order to the next.

In comparison with the 20-course peals from earlier series, this 5024 is very musical. For instance, 5026 no.2 from Series Two has just 126 LB4, and 5152 no.3 from Series Five only slightly more, 138, despite the extra length; the latter peal also has substantially fewer 6578. However, compared to the 19-course 5024s in Series Five we are at a slight disadvantage, these peals achieving 140 and 150 LB4. This balance is redressed with a vengeance in the other, longer, peals of Series Six.


5024 Bristol Surprise Major (no.6)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  23564      -     -
  65432   -     -
  46253      4
  52364   -     -
  63425   -     -
  24536   -     -
  36452      2
  56423   S     S
  34625   -        -
  23645         -
  34562      2     -
  56342         -  -
  23456      3
  ------------------

Contains:
  72 5678/8765 front or back
  17 6578 back
  124 LB4
  33 LB5

This arrangement has the property, intriguingly not shared with any of the other short-course peals, of containing no calls at consecutive leads. In all my other peals there is at least one course end with two calls at the same position, but here that remaining static feature of the long-course peal is removed, leaving a wonderfully fluid calling, as smooth as a honey-roasted cello.

Music counts are reduced, for example by comparison with 5024 no.5, but nevertheless this is a musical peal, retaining the "no duffers" property. Structurally the composition is I think very elegant, like my 5056 no.1 making use of calls at W,M to implement a "reverse Before", but this time using this not on the alpha or beta courses, but to replace some of the other 5678 runs generated by the optimal super-efficient block in the earlier compositions.

The reverse Before block is coupled closely to two blocks using standard Befores, to generate a simple and graceful shuttling effect at the centre of the peal. Setting WM as B' this can we written as: 4B, M, 2B', W, 2B. If we note that the M and W in this section operate on the little bells, generating back-bell rollups, then the back-and-forth shuttling action on the 5 and 6 becomes even more obvious.


5056 Bristol Surprise Major (no.4)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  64523      3
  23546   -     -  S
  24536         S-
  43652      2     -
  43526      -     -
  26354      2
  26453   2  5     -S
  25463         S-
  34562   -        -
  34625      -     -
  42635         2
  23456      -
  ------------------

Contains:
  72 5678/8765 front or back
  24 6578 back
  140 LB4
  39 LB5
  All 7 near-misses

This is the first Series Six peal to equal or surpass the music counts of Series Five, all within the constraints of twenty courses. Two negative courses are used, on 43256 and 56243, yielding a substantial swing to the 5678 off the front and 8765 off the back, with four 5678s at the back missed. But compared to 5056 no.3, we have the complete set of near-misses, and two more each of 6578 and LB4, all whilst using seven fewer course-end calls. I think that is simply remarkable - once again, I can only say, what a method is Bristol.

It's instructive to see the gradual increase in music counts in the 5056s I have composed since the original no.1 feted by Philip Earis in his "Compositions of the Decade". All of them have contained 72 back-bell rollups, but little-bell counts have slowly but surely risen:

No.1, "The" 5056, Series 2134 LB4, 20 6578 in 19 courses
No.3 from Series Five138 LB4, 22 6578 in 19 courses
No.4 from Series Six140 LB4, 24 6578 in 20 courses

The true splendour of this last composition in the 5056 lineage is that it achieves higher music counts than its forebears, whilst using an average of just 0.9 course-end calls per course, compared to 1.3 in the 19-course peals.


5056 Bristol Surprise Major (no.5)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  45236      5  -  -
  34562      -     2
  34625      -     -
  62345         -  -
  24536   -  5  2
  43652      2     -
  43526      -     -
  26354      2
  24653   -S       S
  23456   2        -
  ------------------

Contains:
  72 5678/8765 front or back
  22 6578 back
  140 LB4
  40 LB5
  All 7 near-misses

Very similar in music content to 5056 no.4, I include this arrangement because it feels to me slightly neater and simpler in layout, if with the slight disadvantage of opening with five Befores.


5120 Bristol Surprise Major (no.5)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  42356            -
  54326         -
  25463      -     2
  34562   -        -
  63542         -
  24536   S     S-
  43265      -
  65432   2     -
  46253      4
  43652   2        -
  43526      -     -
  63254      2     2
  23456   -  5
  ------------------

Contains:
  72 5678/8765 front or back
  18 6578 back
  148 LB4
  43 LB5

Increasing the length of the peal over 5100 changes, with the extra two or three course-end calls that allows, yields substantially more little-bell music. This 20-course arrangement has higher LB4 counts than all but two of my previous 19-course peals.


5120 Bristol Surprise Major (no.6)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  64523      3
  23546   -     -  S
  24536         S-
  43652      2     -
  43526      -     -
  26354      2
  46253   -S    3* -
  25463      5  -  -
  34562   -        -
  34625      -     -
  42635         2
  23456      -
  ------------------
3* = S--

Contains:
  72 5678/8765 front or back
  24 6578 back
  140 LB4
  2 4567/7654
  39 LB5
  All 7 near-misses

An alternative to my 5120 no.5 for those who prefer to ring all the 6578s, whilst maintaining a highly competitive level of little-bell music. See also my 5152 no.5 for a composition including all the 65s of this peal plus the same LB music as the other 5120 - the best of both worlds?


5152 Bristol Surprise Major (no.5)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  64523      3
  23546   -     -  S
  24536         S-
  43652      2     -
  43526      -     -
  26354      2
  26453   2        -S
  25463         S-
  53462   -        2
  65432         -
  24365      3
  34625   -  -     -
  42635         2
  23456      -
  ------------------

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

5152 changes is the maximum peal length I considered for Series Six. This example is absolutely superb, including all twenty-four 6578s as well as extremely high levels of little-bell music, and all the near misses. Indeed, it is probably the highest-scoring of all the Series Six peals. In structure, it is very similar to 5056 no.4 and 5120 no.6, with just the middle section of the peal differing.

Please let me know if you ring it, or any other of these compositions.


5152 Bristol Surprise Major (no.6)

Composed by Mark B Davies

  23456   M  B  W  H
  ------------------
  45236         -  -
  54362      -     S
  56342         S-
  64523      -
  32546   -     -  -
  24536      5  2
  43652      2     -
  43526      -     -
  26354      2
  24653   -S       S
  34562   2  -     -
  34625      -     -
  23645         -
  23456      -     -
  ------------------

Contains:
  72 5678/8765 front or back
  18 6578 back
  144 LB4
  10 4567/7654
  40 LB5

I include this peal because of the very high number of "4-runs" - 226, compared to 220 in 5152 no.5 - achieved partly by use of the interesting negative coursing order, 64532. This provides eight 4567/7654 runs near the start of the peal, a similar effect to that in 5024 no.4 from Series Five. However, that peal had four fewer 4-runs, and only nineteen excursions of the tenors to the front.

 

MBD January 2011