[r-t] New mirror principles

[Richard Pullin]

On 14 Feb 2021 at 16:53:49, Philip Saddleton wrote:

>I have only just come across this thread - interestingly I had been
>having similar ideas, though from the point of view of getting extents
>of spliced.
>
>Anyone up for a 40,320 of spliced in 105/210 methods, atw and eld for
>all 8 bells?
>

I think a spliced composition would be interesting to pursue for practical
ringing. In terms of pure theoretical interest I prefer the single method
40320 because it is quite satisfying that such a composition is possible
using just one method, compared to other areas of composition where certain
types of extent are only possible by incorporating multiple methods
(bobs-only twin hunt Triples or spliced Little Bob and X Alliance Minor,
for example). The fact that my 40320 is not dependent on multiple methods -
plus the minimalist bobs-only construction of the composition - made it
seem unattractive to introduce course splicers just for the sake of it.

But in terms of producing a spliced 40320 that would be interesting to ring
(see also the July 2012 thread on this topic) then there are lots of
possibilities. Mark's 40320 splices Bob Major with Helixoid methods to
incorporate blocks of stability between the less familiar methods. It would
be harder to do this elegantly in a mirror method peal, the best option
probably being Mirror Bob Major (whose plain course contains only 1/4 of
the mirror rows, thus adding further complications.) Presumably you would
also want to ensure that the treble-dominated methods only ever have the
treble as the hunt bell, for stability reasons. Perhaps 105/210 principles,
atw and eld for all 8 bells is the best answer...but probably a bit too
interesting even for the most adventurous!

>I came up with this:
https://complib.org/method/41162?accessKey=a829c83566f003025dcb638e01a32df35e3064e1
- which I believe is the only possibility for a palindromic >method with
Original lead heads. It has similarities with Quick Six Triples: ring quick
sixes at front and back with double dodging in the middle, then replace 18
with x when it >would come round.
>
>I struggled to think of an elegant way of selecting courses that could be
joined with 3 member Q-sets.
>Would a 5-part or 7-part be possible with more than the minimum linkages?
>

As this principle is palindromic perhaps WHW type q-sets can be used to
produce an exact 5-part or 7-part? Even for the 3-part I found it tricky
working with fluid courses defined by pairings rather than unique course
heads, so I imagine you'd have to plan out the WHW q-sets very carefully,
probably starting with them and building the rest of the peal upwards from
there. (In the 384-row principles you would of course have to use two of
these WHW q-sets to switch back to an odd number of courses!)

Recently I applied this idea to Kidderminster Minor to see if a 5-part 720
were possible. I rotated the method to straighten up the palindromic
symmetry, the call being a 12 single in lieu of X at the lead end.
Compositeur generated some 5-parts, proving that they are possible.

My own principle Double Factorial Major is non-palindromic so a 3-part was
the only option. However, my first idea was to produce a non-group
irregular 7-part where you visit all 15 of the 1,8 pairings in the first
part, and then simply q-set in the remaining six parts arbitrarily.
Unsurprisingly, this proved not to be possible.
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