Cyclic Pangaea: A Dinner-Day Peal | Jan 2014
Or, The Quest for Zero Leads-Without-Music

Every year in December a message arrives in my inbox with a title along the lines of: Dinner Day — got any new methods / compositions? The dinner in question is the Annual Dinner of the OUS, held at the start of February, and the organiser of the St Thomas dinner day peal, and the sender of the email, is Chris Poole. Despite the dangers of Friday-night drinking, over the years the band's ambitions have risen from tenors-together London no.3 to new methods with half-lead calls and cyclic compositions. The band has usually scored and even, I am told, produced first-class performances.

That first email from Chris rapidly develops into a collaboration, with ideas, critiques and compositions thrown back and forth between us. For the 2014 Dinner the thought was to venture some Spliced, so the annealing furnaces were quickly brought up to operating temperature. I have set out the resulting paper-chain of discussions and prototype compositions on this page, because I think it provides an excellent illumination of the composing process, with ideas and requirements introduced and refined, and problems encountered and overcome. The intermediate arrangements are also very good peals, and worth ringing in their own right, even if they didn't meet the final criteria.

Index to compositions:

comp. CJP
Single-method seed
tricky 5-spliced
Bristol, Precambrian, Sgurr, Triton, Yorkshire
low COM
Bristol, Precambrian, Triton, Yorkshire
medium COM
Bristol, Precambrian, Triton, Yorkshire
Pangaea
Bristol, Pangaea, Triton, Yorkshire
Small's Friends
Bristol, Small's Friends, Triton, Yorkshire
stirring it up
Bristol, Pangaea, Triton, Yorkshire
a longer seed
Bristol, Pangaea, Triton, Yorkshire
0 LWM!
Bristol, Pangaea, Triton, Yorkshire
More 0 LWM
Bristol, Pangaea, Triton, Yorkshire
Tittums
Bristol, Pangaea, Triton, Yorkshire
Tittums + 0 LWM
Bristol, Pangaea, Triton, Yorkshire
more music
Bristol, Pangaea, Triton, Yorkshire
a better seed
Bristol, Pangaea, Triton, Yorkshire
seed-squeezing
Bristol, Pangaea, Triton, Yorkshire
a shorter seed
Bristol, Pangaea, Triton, Yorkshire
the solution!
Bristol, Pangaea, Triton, Yorkshire
another gem
Bristol, Pangaea, Triton, Yorkshire

Pangaea is 10th's place Precambrian. Small's Friends is the working name for an unrung Surprise Royal method.

Hey Mark,

Hope you are having a good Christmas! This is my customary annual email on the scrounge for some good methods and compositions. Got anything in the stable? We've not rung spliced for a while - got anything interesting?

Ooh yes, good idea, I'm sure some top-quality spliced would be easily available! Which methods? Precambrian, Bristol, Triton?!

Yes, any of the above would be suitable. Probably no more than two unfamiliar methods unless they are pretty straightforward: Bristol, Triton count as standard; Precambrian, Snow Tiger count as 'unfamiliar'; the likes of Phobos / Sgurr a wotsit probably count as straightforward nowadays... Probably no more than 5 methods to make it gettable (unless they are simple, of course). So I guess minimise the number of methods unless you need a particular group to get music / reduce falseness / quick transition.

The last few years, we've had a composition which looks a bit like tenors together (with / without half lead calls, but quick turnaround of nice coursing orders), tittums, finish with cyclic block. Seems to be a good recipe....

This is the composition rung for the Dinner in 2013; method by MBD, composition by CJP:

5040 Precambrian Surprise Royal (No.1)
Composed by Christopher J Poole

     23456     M  B  W  H
     45236           -  -
     65432        x  -    (8 leads)
     43652           -  - 
     64352              -
     53462           s  s   
     453627089    -     -
     34562              - 
     65432           s  s
     674523908 4 7        (9 leads)
     654320987 x1         (8 leads)
     452390786 x2         (9 leads)
     432098765 x1         (8 leads)
     239078564 x2         (9 leads)
     209876543 x1         (8 leads)
     234567890 1 3        (4 leads)

Calling positions are with respect to the bell in 10th's place at the course end.

The 5040 calling from last year works really well - stuff like this bubbles up quickly.

Yes, that looks very nice indeed.

Only slight reservation - is it too complicated for dinner day? (What do we get out of the mix for 4 methods, eg. binning Sgurr?) [Or if we reduce the COMs?]

And is this put together by pretending to heat and cool some metal?

The first product of the Furnace. Lots of music, but is it too big a challenge?

5120 Spliced TD Royal (No.1)
Composed by Mark B Davies

5 Methods: 1080 Bristol S, Precambrian S; 1040 Sgurr A'Chaorachain S; 1000 Triton D; 920 Yorkshire S. 97 COM, ATW.

 234567890  B  W  H
 45236         -  -  PY.T.
 64352      x  2  2  PYYTYYPxS.SPTPSB.T.TPTPSBBS.
 53462         S  S  TSTPT'BSB'
 345627089  -     2  PPTT.PPTTSBB.PPSPPT.
 65432         S  S  BSPPTSB'YTSY'
 674523908  5 9      BBSSY.BYBB.YTSB
 870932546  x3       BSYxSB
 534028967  x5       BSPPTxSTT
 576982043  x4       PSBBxTP
 239078564  x6       TPSBBSxY
 209876543  x7       YPYYTYYxBB
 234567890  5 11     SPPTS.BBSSYB.YTYYPYY

Contains:
 320 LB4
 132 LB5
  25 567890/098765

Let's go to the opposite extreme for the moment and consider four methods with changes of methods only at the calls. This looks easier, but the downside is that some potential music is lost. However, we are still competitive with the single-method peal.

In answer to your final question, yes it is basically simulated annealing, but with a tunnelling algorithm applied when either falseness occurs or it looks like we are stuck in a local minimum. Once we've got the criteria sorted, I'll also apply a genetic algorithm - breeding sometimes squeezes a little extra out!

Interesting that the 4-spliced stands up against the single method, pretty much, bar a few LB5 etc. BTW. I don't think the one with many calls is hard per se... more of a challenge on the Saturday morning after the night before...

So I think what we're after is either 4 or 5 spliced (I'll garner some opinion), somewhere between the 21 and 97 COM; interesting to see how much extra is squeezed out by loosening that parameter (up to around 40-50?).

Making it easier — just four methods, with very few changes of method. We're also now counting "Course4" music (any change with the four tenors coursing AxBxCxD) to make the most of the Tittums position.

5080 Spliced TD Royal (No.1)
Composed by Mark B Davies

4 Methods: 1360 Precambrian S; 1320 Triton D; 1200 Bristol S, Yorkshire S. 21 COM, ATW.

 234567890  B  W  H
 45236         -  -  PPPPPPPP.T.
 65432      x  -     BBBBxPPP.YYYY
 64352         -  2  YYYYY.T.BBBBBBBB.
 53462         S  S  YYYYY'T'
 345627089  -     2  TTTT.PPPPP.YYYYYYYYY.
 65432         S  S  BBBBBBBBB'YYYY'
 798204365  4 7 x10  TTTT.TTT.YYYxTT
 452390786  x7       TTTTTTTxBB
 576982043  x7       BBBBBBBxPP
 456789023  x7       PPPPPPPxTT
 354769820  x6       TTTTTTxPP
 234567890  6 8      PPPPPP.TT.P

Contains:
 245 LB4
 109 LB5
  23 567890/098765
 190 Course4

Looking at that now. One problem is that, especially with Sgurr gone, the Triton/Precambrian and Bristol/Yorkshire tend to separate out, so that you have lots of courses with just TP or BY. Looks less elegant.

Here's an example.

I could forcibly remove longer nodes containing TP only to improve this and get a better method mix (with probable loss of some music).

Increasing the COM to a "medium" level:

5160 Spliced TD Royal (No.1)
Composed by Mark B Davies

4 Methods: 1360 Precambrian S; 1280 Triton D, Yorkshire S; 1240 Bristol S. 74 COM, ATW.

 234567890  B  W  H
 45236         -  -  PTTPTTTP.T.
 43652      x  2  -  BBBYxPPT.YPP.BBBYBB.
 64352            -  YYTYYTYYP.
 53462         S  S  TY'BBBYBB'
 345627089  -     2  PPPT.BBB.TYT.
 65432         S  S  TTPPPTTP'BBBYBB'
 890234567  7.11     TYYTYYP.BYBB.BY
 654320987  x2       BBxY
 452390786  x8       TYYPYYPYxY
 576982043  x7       YPYYPYYxTP
 456789023  x7       PTTTPPTxTP
 354769820  x6       PTTPPTxTP
 234567890  6.11     PPTTPP.BBYBB.P

Contains:
 275 LB4
 122 LB5
  26 567890/098765
 197 Course4

OK, on reflection I think the inelegant thing is having two methods with the same LH order. With 4-spliced it would be better to have a nice balance with two each 2nd's and 10th's LHs, and four different LH orders. Four different backworks would be good too, assuming the difficulty isn't made much higher. Agree with those criteria?

If so then I think the ideal method list would be: Bristol, Triton, Yorkshire, and the 10th's place version of Precambrian (working title Pangaea!). An alternative would be to use another unrung Jennie method such as Small's Friends Surprise -5-4.5-2.3-3478-58-6-7.6-8.9 lh 10 (k1), which would give another naming opportunity without raising the difficulty index.

Here are examples with each of those methods. The methods are clumping together still, but this seems less ugly given they are now all different LH orders. I suspect I can stir them up a bit more with further searches.

Personally, I don't have a strong opinion about the 10ths and 2nds place lead ends... but yes, those criteria look good, and 4 different backworks also good.

New method also good, as it'll give us something to talk sh!te about in the KA for an hour or two. Looking at the lines, could go with either of Pangaea or Small's Friends, so whichever is easier I guess and gives the most music.

Changing the method selection to improve the balance of the composition. Precambrian out, Pangaea in.

5080 Spliced TD Royal (No.2)
Composed by Mark B Davies

4 Methods: 1360 Triton D; 1280 Bristol S; 1240 Yorkshire S; 1200 Pangaea S. 38 COM, ATW.

 234567890  B  W  H
 45236         -  -  TTTPTTT.T.
 43652      x  2  -  PPTTTTPPPxPT.PPPTTT.T.
 64352            -  TTPPPT.
 53462         S  S  TTTPTTT'P'
 345627089  -     2  PTT.BBB.YYYYYYYYY.
 65432         S  S  BBBBBBBBB'YYYY'
 890234567  6.10     TYBYYP.YBBY.YTY
 654320987  x3       YTYxBB
 678902345  x6       BBBBBBxP
 432098765  x4       PTPPxY
 239078564  x8       YYYYYYYYxBB
 354769820  x7       BBBBBBBxP
 234567890  8.10     PPPPPPPP.TT.T

Contains:
 280 LB4
 129 LB5
  20 567890/098765
 172 Course4

5120 Spliced TD Royal (No.1)
Composed by Mark B Davies

4 Methods: 1320 Small's Friends S, Triton D; 1280 Yorkshire S; 1200 Bristol S. 40 COM, ATW.

 234567890  B  W  H
 45236         -  -  YYYYY.T.
 65432      x  -     YYYYYYYxTTT.T
 64352         -  -  TTSTT.T.BBBBBBBB.
 53462         S  S  TSTTT'BSB'
 345627089  -     2  TTTT.BSSB.TYT.
 65432         S  S  SSSSSSSSS'YYYY'
 890234567  8.11     SSSSSSSS.YST.YTY
 798204365  x3       YTYxTT
 452390786  x7       TTTTTTTxBB
 658709324  x7       BBBBBBBxSSS
 239078564  x4       SSSSxBB
(354769820) x7       BBBBBBBx
 234567890  5.10     SSYSY.YYTYY.YYYY

Contains:
 277 LB4
 123 LB5
  17 567890/098765
 183 Course4

Ah yes, here you go - slight loss of music but methods much better distributed (this uses Pangaea). Feels less like two different compositions of 2-spliced patched together! I like the solid sections of Yorkshire, Bristol and Pangaea in the cyclic section, with the Triton to finish. Also all four methods rung in the first course.

Even better stuff may percolate up - I'll keep you posted.

By the way, an x to finish does work, but then the possibilities for the first and last nodes are dramatically reduced. It may be better to look at a longer seed composition, with more calls in the tenors home and Tittums sections, which would then reduce down nicely in the spliced. If you can come up with something I'll stick it in the furnace!

I'll try to put together a slightly longer comp tonight. What do you reckon in order to give more flexibility - another couple of courses? I might engineer out the singles if there's more space too, which'll keep Dr B happy.

How easy is it to get to 0 leads without music? ;-)

Trying to distribute the methods more evenly through the peal.

5120 Spliced TD Royal (No.2)
Composed by Mark B Davies

4 Methods: 1360 Pangaea S; 1280 Yorkshire S; 1240 Bristol S, Triton D. 45 COM, ATW.

 234567890  B  W  H
 45236         -  -  PTPPP.BBBYBB.
 43652      x  2  -  PPPTTPPPxPT.PPPTTP.T.
 64352            -  TTTPTPP.
 53462         S  S  TPPPP'BBBYBB'
 345627089  -     2  PTT.BBB.YYYYYYYYY.
 65432         S  S  PPPTP'BBBBBBB'
 870932546  7.11.x14 YYYYYYY.YBBY.YYYxTP
 678902345  x6       TTTTTTxTT
 432098765  x5       PTTTPxY
 239078564  x8       YYYYYYYYxBB
 354769820  x7       BBBBBBBxP
 234567890  4.6      PTPP.TT.T

Contains:
 255 LB4
 122 LB5
  23 567890/098765
 181 Course4

This, I think, adds in another course in the Tittums and hits different LB5 COs (more little-bell Tittums, which seems more apt), and removes the singles. Not sure if will be any better or not, but feel free to put in the furnace...

WH xBW WxH HH BMW MH H MxH [then cyclic section as per other composition]

V. good, new comp works, gives more music. Here's an example. How is that looking for you, especially in terms of COM/ringability?

Not sure 0 Leads-Without-Music is likely, unless we add more music definitions!

A new seed calling is tried.

5120 Spliced TD Royal (No.3)
Composed by Mark B Davies

4 Methods: 1360 Pangaea S; 1320 Triton D; 1240 Bristol S; 1200 Yorkshire S. 45 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  YP.T.
 43265      x     2  x  BBBYxTTT.PPPPP.Tx
 32465               2  TYT.PTTTTTTT.
(645237089) -  -  -     BBBB.BY.Y.
 35426         -     -  YTPT.TTPTPP.
 43526               -  YYYYYYYYY.
 65432         -     x  T.BBBBBBBBBx
 890234567  7.12        PPPPPPT.YTPTT.BBB
 798204365  x2          BBxP
 678902345  x6          TTTTPPxP
 432098765  x4          PTPPxY
 239078564  x8          YYYYYYYYxBB
 354769820  x7          BBBBBBBxP
 234567890  4.10        PTPP.PPPPPT.YYTYYTY

Contains:
 280 LB4
 131 LB5
  16 567890/098765
 213 Course4

Ah! This is easy to achieve in fact. It was a bit daft running the searches with music defs that would not pick up cyclic runs like xxxxx56789 etc. Not only was no music was being counted for some of the cyclic leads, but the music wasn't being optimised in these sections, either. So I've changed the music defs to count up the following:

  • 567890 runs - front and back, both directions
  • 4-runs
  • 5-runs
  • 6-runs
  • 4-course - includes tittums+tenors home with back 4 in AxBxCxD
  • 657890 rollups - back ascending only

Here are two examples where every lead contains at least one of those types of music, i.e. LWM=0. Should be able to improve on those with a bit more work. Like the idea though?

I was thinking in the shower this morning that it was slightly suspicious that all the cyclic parts were just one method...

I like these, very much, thanks. Slight preference for the 5000, just because of the length (but that's all...).

Other question - what's the cost in terms of the rest of the music of getting full Tittums in there? (In 62345 in the Bristol, assuming my memory serves me correctly...?)

Belated realisation that a cyclic composition needs 4-runs to be counted... and the consequent achievement of Zero LWM.

5000 Spliced TD Royal (No.1)
Composed by Mark B Davies

4 Methods: 1440 Triton D; 1360 Bristol S; 1280 Pangaea S; 920 Yorkshire S. 48 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  PTPTTT.P.
(65432)     x     -     BYYxYTPTT.
 43265            -  x  PPPPP.BBBBBBBx
 32465               2  PY.PTTPTTP.
(645237089) -  -  -     BBBB.BY.Y.
 35426         -     -  YTPP.BBBBBBBBB.
 43526               -  YYYYYYYYY.
 65432         -     x  T.TPPPPx
 890234567  4.9         BBBY.YTPTT.YTY
 798204365  x3          YTYxTT
 452390786  x6          TTTPTTxBB
(432098765) x7          BBBBBBBx
 456789023  x3          TYTxP
 354769820  x8          PPPPPPPPxTT
 234567890  5.7         TTTPP.TT.T

Contains:
 453 4-runs
 189 5-runs
  66 6-runs
  15 567890/098765
 181 Course4
Zero leads without music

5120 Spliced TD Royal (No.4)
Composed by Mark B Davies

4 Methods: 1360 Bristol S; 1320 Triton D; 1240 Pangaea S; 1200 Yorkshire S. 48 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  PTPPT.YBBYB.
(65432)     x     -     TYYTYYPxYYY.
 43265            -  x  PY.YTPPYx
 24365               -  BBBBBBBB.
 32465               -  PTTTTTTP.
(645237089) -  -  -     PTT.BB.Y.
 35426         -     -  PPPPPT.TTTPPP.
 43526               -  BBBBBBBB.
 65432         -     x  T.YYYYYx
(890234567) 7.12        PPPPPPT.BBBBB.
 798204365  x3          YYYxTT
(678902345) x6          TTTTPTx
 432098765  x2          TYxBB
 456789023  x6          BBBBBBxP
 436587092  x5          TTTPTxTP
 234567890  3.1         PPP.YYYYYYYY.T

Contains:
 408 4-runs
 173 5-runs
  64 6-runs
  22 567890/098765
 184 Course4
Zero leads without music

OK, here's an early arrangement with Tittums. Note LWM=1 is the lowest discovered so far, but hopefully 0 will be available given more cooling time.

Looks like Tittums appears in the Yorkshire after the Before - occurs at handstroke full lead for any PB method with co 623450987.

Yep, thought Tittums was in the 62345 tittums course. Good that that's in...

Got LWM=0 yet? How long does the algorithm take to run, out of interest?

Hmm, something's wrong. Can't seem to get lower than LWM=1 if Tittums is included. Searches are finding LWM=0 but only if Tittums not present. I can't immediately understand why. Any ideas?

Algorithm can be told to stop whenever you want. Runs are generally around 15 mins - 4 hours with current criteria, although I can see the best comp found so far as it runs. The main tunnelling algorithm I'm using starts off using very fast cooling schedules, basically equivalent to a greedy random walk, to explore the local area. Once it stops finding improved compositions (i.e. is likely stuck in a local minimum) it gradually increases the length of the cooling schedule up to the total time (# steps) you've specified for a full annealing run.

This seems to work well, delivering good results very rapidly, but squeezing more out if you let it run longer - it generally does better than a single annealing run from scratch. Also I am able to time-limit it, pulling the plug after a given number of seconds for example, which is useful when going through the libraries to find the best method for the next spliced stage.

Need to work out what's blocking LWM=0 for Tittums!

Tittums change included - but there is a Lead-Without-Music!

5040 Spliced TD Royal (No.1)
Composed by Mark B Davies

4 Methods: 1320 Bristol S; 1280 Yorkshire S; 1240 Pangaea S; 1200 Triton D. 45 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  PTPPP.YBBYB.
(65432)     x     -     TYYTYYPxBBBBB.
 43265            -  x  PPPTTP.Px
 32465               2  PY.PTTTTTTT.
(645237089) -  -  -     BBBB.YYYYYY.Y.
 35426         -     -  YBYY.PPTTTT.
 43526               -  TTTPPTT.
 65432         -     x  T.BBBBBBBBBx
 890234567  3.8         BYY.YTPTP.YB
 654320987  x2          BYxY
(452390786) x8          YYYYYYYYx
 432098765  x6          TPTTPPxBB
 456789023  x6          BBBBBBxP
 234567890  x8.10.11    PPPPPPPPxYP.TT.T

Contains:
 437 4-runs
 189 5-runs
  64 6-runs
  21 567890/098765
 178 Course4
   1 lead without music
     Tittums

Can you see where the LWM(=1) is? Is it in the 62345 course somewhere, which would suggest that any of the leads coming out of the Tittums lead (or ways into it) [given the method constraints / falseness of what's already gone] are duffers?

Don't have that output at the moment, but I've just listed all the splices from the node head 1908574632 and it turns out only one of them includes Tittums whilst keeping all leads within music: YTPTPTT. So that is almost certainly doing the damage - the searches simply aren't managing to find or link that one splice (out of 31 possible) into the composition.

So I've put in place a filter which allows only that choice for the critical node. Searches are now proceeding happily, so there is no reason why we can't have a composition on that plan, although it does push COM up slightly, and maximum music may be reduced. The best results are already looking respectable though - how about this?

COM not a problem - could increase further if you think it'll squeeze goodness out.

What's the iteration process? Throw a few GAs at it, or will it normally settle in the same minimum?

OK, excellent. This is looking like a deep minimum at the moment - not getting anything else close to it, and it is competitive with the best results without Tittums and with LWM>0.

However I will try a few more runs allowing higher COM, and will also run some breeding programmes using the best results from a number of searches as the gene pool. It is also sometimes helpful running a strong greedy search around the locality of the lowest minimum - occasionally finds a nearby candidate which for whatever random reason the annealing process has missed.

I'll let you know if any improvements come out, otherwise I think you are good to go. What's your chances of scoring?!

Solved! Forcing the one splice that includes Tittums with 0 LWM.

5080 Spliced TD Royal (No.3)
Composed by Mark B Davies

4 Methods: 1320 Pangaea S, Yorkshire S; 1280 Triton D; 1160 Bristol S. 46 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  YYYYY.YTYBYY.
(65432)     x     -     PPTTPPPPxBBBBB.
 43265            -  x  PPPTTP.Px
 32465               2  PY.BBBBBBBB.
(645237089) -  -  -     BYB.YTPTPTT.TTTTTTT.
 43526         -     2  YBYY.YYYYY.PPPPT.
 65432         -     x  T.YYYYYx
 798204365  4.6.x9      BBBB.PT.YYYxTT
 678902345  x6          TTTTPPxP
 432098765  x4          PTPPxBB
 354769820  x6.x8       BBBBBBxYPxP
 234567890  5.12        PTTTP.PTPTPPT.YYYY

Contains:
 440 4-runs
 180 5-runs
  44 6-runs
  16 567890/098765
 202 Course4
Zero leads without music
     Tittums

Chances of scoring - reasonable. Same band as the Precambrian, without that Dr Byrne (Yeo instead).

BTW how do you like this one over the original? It has slightly higher music counts, although the increase in 4-runs is at the expense of fewer 5-runs. Also I suppose it's a long way until you get to any serious amount of Pangaea.

Second comp seems to advocate ringing most of the 63425 course in Bristol. Presumably that's just firing on tenors together music? I half wonder if sticking in an extra course somewhere would give it more freedom to reduce down... can't see anywhere obvious to put in a WHWH or similar though...

I'll stick with the first, unless you can see an obvious place to squeeze in an extra course to see what it does...

A bit more music squeezed out... but a new question raised.

5080 Spliced TD Royal (No.4)
Composed by Mark B Davies

4 Methods: 1360 Triton D; 1320 Bristol S; 1240 Pangaea S; 1160 Yorkshire S. 59 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  YYYYY.YTYBYY.
 43265      x     2  x  YBBxBBYB.PTTTTTTP.Px
 32465               2  BBBBBBBB.YYTYYTYYP.
(645237089) -  -  -     BBBB.YTPTPTT.TTTPTT.
 43526         -     2  BBBYB.PPTPP.PPPPP.
 65432         -     x  T.TTPPTTx
 890234567  3.5         BYY.PT.YB
 870932546  x2          BYxTP
 678902345  x5          TTTPPxP
 432098765  x4          PTPPxBB
 35426      x6.x8.10    BBBBBBxYTxYP.PT
 234567890  5           PTPPT.YYYY

Contains:
 453 4-runs
 167 5-runs
  52 6-runs
  16 567890/098765
 217 Course4
Zero leads without music
     Tittums

Looking at the PC of Bristol Royal it appears there is a 7890 or 0987 rollup in every lead, which is presumably why "0 LWM" is reasonably easily achieved! It's also why the course from 63425 is OK in Bristol. That course won't score highly compared to others though, so I guess it's only coming up because shorter splices are either (a) false, (b) missed, or (c) have LWM>0.

We could go into 64235 from 26435 instead - would get some more 3456/6543s then. The (longer) calling WH xB W WH H WxBH MWH does the trick. Here's an early example of this. Starting to get higher method-changing complexity in the cyclic section, and there are of course more bobs to call. Fewer 56 rollups too.

Belated realisation that LWM=0 doesn't mean much for tenors-together Bristol Royal. We try another seed calling, to further improve the tenors-together section.

5040 Spliced TD Royal (No.2)
Composed by Mark B Davies

4 Methods: 1320 Pangaea S; 1280 Bristol S, Triton D; 1160 Yorkshire S. 59 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  YYYYY.P.
 43652      x     2  -  BBBBxTTT.YTP.T.
 64352               -  TPPTPP.
(56342)           -     YYYYY.
 56423      x        -  BBBxPPPTTPPP.
 32465         -  -  -  P.B.YBBYB.
(645237089) -  -  -     BBBB.YTPTPTT.Y.
 43526         -     2  YTPP.PPTPP.YBBYBB.
 65432         -     x  T.TTTPPPx
 890234567  3.5         BYY.PT.YB
 798204365  x2          BYxTT
(678902345) x6          TTTTPTx
 432098765  x6          TPTTPPxY
 436587092  x5.x7       BBYBBxYTxTP
 234567890  3.9         PPP.BBBBBB.YYYY

Contains:
 487 4-runs
 181 5-runs
  54 6-runs
  13 567890/098765
 208 Course4
Zero leads without music
     Tittums

Here's another possibility with the longer calling.

Also there is another shorter calling, MWH H W xB WH, which avoids the 64235 course and achieves fairly good results. May be more by the morning - must to bed now!

I was about to go to bed, but now have some emails to read ;-)

More work on the seed callings.

5080 Spliced TD Royal (No.5)
Composed by Mark B Davies

4 Methods: 1360 Pangaea S; 1320 Bristol S; 1240 Triton D; 1160 Yorkshire S. 60 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  YYYYY.P.
 43652      x     2  -  BBBBxTTT.YTP.P.
 64352               -  BBBBBBBB.
(56342)           -     TY.
 56423      x        -  BBBxPPPTTPPP.
 32465         -  -  -  P.TYYT.YBBYB.
(645237089) -  -  -     BBBB.YTPTPTT.B.
 43526         -     2  YTPP.PPTPP.TYT.
 65432         -     x  T.TPPPPx
 890234567  3.5         BYY.PT.YTY
 798204365  x2          BYxTT
 452390786  x6          TTTTPTxY
 432098765  x4          YYYYxBB
 456789023  x6          BBBBBBxP
 354267890  x4.6        PTPPxYP.PT
 23456      5           PTPPP.YYYY

Contains:
 479 4-runs
 186 5-runs
  62 6-runs
  16 567890/098765
 213 Course4
Zero leads without music
     Tittums

5120 Spliced TD Royal (No.5)
Composed by Mark B Davies

4 Methods: 1400 Triton D; 1320 Bristol S; 1200 Pangaea S, Yorkshire S. 58 COM, ATW.

 234567890  B  M  W  H
 46532         -  -  2  P.TYYP.T.BBBBBBBB.
 34562            -     YT.T
 32465      x     -  -  TTTPxYYTYYT.BBBYBB.
(645237089) -  -  -     BYB.YTPTPTT.TTPPT.
 35426         -     -  YTYYTYYP.BBBBBBBBB.
 43526               -  YYYYYYYYY.
 65432         -     x  T.TPPPTx
 798204365  3.5.x8      BYY.PT.YYYxP
 678902345  x6          TTTTPTxP
 432098765  x4          PTPPxBB
 354769820  x6.x8       BBBBBBxYTxP
 234567890  8.10        PPPPPPPP.TT.PTTPTTP

Contains:
 451 4-runs
 176 5-runs
  69 6-runs
  21 567890/098765
 215 Course4
Zero leads without music
     Tittums

Overnight realised two things:

  1. My algorithm has gone slow since LWM included in the score - about 1/4 the speed it should be! Now rectified - LWM calc done efficiently.
  2. Wondered whether restricting the search space to include ONLY nodes with LWM=0 would be helpful. Smaller search spaces usually good, but with SA not if the landscape has more barriers. Trying it this morning to see.

The best run from last night was this (with the longer calling).

Code optimisations... and the perfect solution?

5000 Spliced TD Royal (No.2)
Composed by Mark B Davies

4 Methods: 1400 Triton D; 1200 Bristol S, Pangaea S, Yorkshire S. 58 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  PTPPP.P.
 43652      x     2  -  TYYTYYPxBBYB.YTP.T.
 64352               -  TTTTPPP.
(56342)           -     YYYYY.
 56423      x        -  BBBxTPP.
 32465         -  -  -  T.TTPPT.YTPPY.
 645237089  -  -  -     BBBB.YTPTPTT.B.YYYY
 43526         -     2  YYYY.TY.YTT.
 65432         -     x  T.TPPPTx
 654320987  4.9.x12     BBBY.YTPTP.YYYxBB
(452390786) x6          BBBBBBx
 432098765  x6          TPTTPPxBB
 436587092  x6.x8       BBBBBBxYTxTP
 234567890  3.5         PPP.TT.T

Contains:
 465 4-runs
 188 5-runs
  62 6-runs
  23 567890/098765
 208 Course4
Zero leads without music
     Tittums

Here's one with the same longer calling, giving comparable music with lower COM. Not sure how much losing 10 com helps? But quite a nice arrangement.

I think I'll suggest the 5000 to Mounsey - always the risk of Henry barfing in the last few leads!

Wise!

OK, good luck...

 

Update, February, 2014:
Sadly, the peal was lost... maybe next year!

Another excellent variation, but Chris goes for the shorter length. And we're done.

5080 Spliced TD Royal (No.6)
Composed by Mark B Davies

4 Methods: 1320 Bristol S, Triton D; 1280 Yorkshire S; 1160 Pangaea S. 50 COM, ATW.

 234567890  B  M  W  H
 45236            -  -  PTPTTT.T.
(65432)     x     -     PPTTTTPPPxBBBBB.
 43652            -  -  YTT.T.
 64352               -  TTTTPPP.
(56342)           -     YYYYY.
 56423      x        -  BBBxYYYYYYY.
 32465         -  -  -  P.B.YTPPY.
(645237089) -  -  -     BBBB.YTPTPTT.Y.
 43526         -     2  YTYBYYP.YYYYY.YTT.
 65432         -     x  T.TPPPTx
 654320987  4.6.x9      BBBY.PP.YYYxBB
 678902345  x6          BBBBBBxP
 432098765  x4          PTPPxBB
 436587092  x6.x8       BBBBBBxYTxTP
 234567890  3.5         PPP.TT.T

Contains:
 465 4-runs
 185 5-runs
  63 6-runs
  23 567890/098765
 213 Course4
Zero leads without music
     Tittums