[r-t] Multi-cyclic composition

[Adam Brady]

In the classic 11-part structure a cyclic "shunt" happens only once per
part in the link method (the first method in the classic palindromic
11-part) and the rest of the methods have plain bob lead heads, so you get
11 lead heads in a row which all belong to the same "cyclic part", one set
of these lead heads being all the plain bob lead heads and rounds (the
final part in the classic palindromic 11-part).

I'm not sure if this is an absolute definition, but that is my
understanding of it.

In Jonathan's structure, you get 11 lead heads in a row which all come from
different cyclic parts as we would describe them above.


On Wed, 31 Mar 2021, 14:07 Simon Gay, <Simon.Gay at glasgow.ac.uk> wrote:

> 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
> >
> > _______________________________________________
> > ringing-theory mailing list
> > ringing-theory at bellringers.org
> > https://bellringers.org/listinfo/ringing-theory
> >
>
> --
> ***************************************
> Professor Simon Gay
>
> Head of the School of Computing Science
> University of Glasgow
>
> www.dcs.gla.ac.uk/~simon
> ***************************************
>
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