[r-t] Multi-cyclic composition

[Simon Gay]

Do you think you could explain what it means to change the cyclic part 
every lead?

Simon


On 28/03/2021 22:19, Jonathan Agg wrote:
> For a while I've been interested in cyclic compositions which mix up the 
> parts, by changing the bells which are pivot bells mid-part. Examples 
> include this one by DJP, which changes twice, once using a link method, 
> and again using mega-tittums: 
> https://bb.ringingworld.co.uk/view.php?id=387809 
> <https://bb.ringingworld.co.uk/view.php?id=387809>. His particles 
> compositions do this too as 12-parts.
> A fairly natural conclusion to this idea is a composition where the 
> cyclic part changes every lead! I set myself the challenge of finding a 
> composition that I thought might be ringable, both in terms of learning, 
> and also importantly enjoyable enough to stand a chance of persuading 
> enough others to try and ring it in the future.
> 
> I started out by looking at the existing link methods, and labelling 
> them, firstly by the standard number of leads of Plain-bob and second by 
> their cyclic jump. For example, Slinky was labelled by (+5, +4) as its 
> lead end (14523ET90786) is the fifth leadend of Plain Bob starting from 
> 167890ET2345, which is "rounds + 4". Other examples include Cyclone, 
> designed to move from 1ET907856342 to 1796E820ET53, which was labelled: 
> (-4, +4). Like other good link methods, these are musical, palindromic 
> and well-structured.
> 
> Restricting the problem to only using palindromic methods and only 
> ringing the 121 leadheads found in the classic cyclic 6 composition, the 
> first step was to find a plan which solved the "11 queens" version of 
> the "8 queens" problem, making sure each part included each plain bob 
> lead end, and each cyclic part once. I tried using the existing methods, 
> but thought there aren't currently enough.
> 
>  From the 121 leadheads, I found the possible leadends by 'undoing' 
> sensible leadend changes from each of them. I then looked for all the 
> possible methods from a leadhead to a leadend which were possible with 
> palindromic symmetry, i.e. requiring pairs swapping, or pivot bells. 
> Interestingly, but after investigation predictably, some of these 
> options corresponded to multiple relevant methods if rung with different 
> leadends (e.g. a method from leadhead 1234567890ET to leadend 
> 12TE09876543 can be rung with a 2nds lead end to give 12ET90785634 and 
> also a 12ths place lead end to give 1T20E8967453).
> 
> This raised my hope of not having to invent 11 methods, with clear 
> associated benefits in reducing the method learning! However, it will 
> still need care to make sure any leads which reuse a method were 
> conducive to music in all of them, probably by requiring the pivot bells 
> to be sensible.
> 
> These candidate methods can be used as edges in a graph with the 
> leadheads as nodes, and this can then be searched. I tried to find 
> frameworks with 6 methods, in the hope the framework would itself be 
> palindromic, but didn't find any. The smallest number of methods used I 
> found was 8, with lots of candidate frameworks. Very fortunately, it 
> felt like the gods were smiling, and I stumbled across frameworks like 
> the one below where the pivot bells in the leads with repeated methods 
> corresponded to the 2 and the tenor for the cyclic part for each of the 
> leadheads. The only issue was the fairly comedic middle method, with 9 
> pivot bells.
> 
> This lists the lead head and the lead ends:
> 
> 11,1 5,11 1,10 4,9 2,8 3,2 8,3 9,4 7,5 10,6 6,7 11,8	(8 methods)
> 1234567890ET
> 1E098765432T
> 10E89674523T (A 1E098765432T,+T, pivot:T)
> 1TE325476980
> 1T3E52749608 (B 1T3E09876542,+2, pivot:3)
> 18694725E30T
> 1684927E503T (C 1T09876543E2,+T, pivot:E)
> 1T0395E72846
> 1T30597E8264 (D 1T0E59876342,+2, pivot:5)
> 108T624E3957
> 1806T423E597 (E 1492E0T83657,+T, pivot:8)
> 1806T324E597
> 108T63425E79 (F 1234587690ET,+6, pivot:lots)
> 19E7254638T0
> 197E5264830T (G 1T0E89756342,+2, pivot:7)
> 1T30584627E9
> 13T504826E79 (D 1T0E59876342,+T, pivot:5)
> 19E728406T53
> 197E8204T635 (H 1T0E87659342,+2, pivot:9)
> 15736T4028E9
> 175634T20E89 (B 1T3E09876542,+T, pivot:3)
> 19E02T436587
> 190ET2345678 (C 1T09876543E2,+2, pivot:E)
> 
> 
> There are thousands more, so there may well be a nicer one hiding in 
> there somewhere, particularly if 11 methods are allowed. This lists the 
> ones using up to 9 methods: 
> https://drive.google.com/drive/folders/134is8T8uoWd54U8xWtjXJ__f5Oi8p4hd 
> <https://drive.google.com/drive/folders/134is8T8uoWd54U8xWtjXJ__f5Oi8p4hd>
> 
> Coming up with methods was a challenge given the opposite pairs are 
> unfamiliar, and there's also no possibility of rollups at the half lead. 
> I had various goes at this, and eventually came up with these ones which 
> I'm broadly happy with, though can certainly be refined further:
> https://complib.org/composition/76082 
> <https://complib.org/composition/76082>
> 
> My favourite one is the first method, which gets to megatittums over the 
> half lead with lots of plain hunting, with the tenor being pivot, then 
> 2,E, 3,0, 4,9, 5,8, 6,7 being opposites. Normally a method which is a 
> cyclic shunt of 1 is less popular as it's not as disruptive music-wise 
> as shifting by a larger amount, but in this composition this concern 
> goes away!
> 
> The issue with the middle method can be reduced by ringing a silly 
> Bastow-style method with places which fairly naturally has the desired 
> effect in a very short space of time.
> 
> If anyone has ideas for how to improve any of these methods, all 
> feedback is gratefully received.
> 
> Overall, I'm pretty happy with what I've managed to come up, especially 
> in structure, though some of the methods are a bit too fiddly in places. 
> Learning these unfamiliar methods would be tricky, but I think possible. 
> Perhaps in another year's time...
> 
> Jonathan
> 
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> 

-- 
***************************************
Professor Simon Gay

Head of the School of Computing Science
University of Glasgow

www.dcs.gla.ac.uk/~simon
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