[r-t] New mirror principles

[Richard Pullin]

On Friday 5th Feb at 13:16, Rob Lee wrote:

>There was some discussion on this list back in November 2012 along similar
lines. I had come up with the following principle:
>36.18-18.36-, 18 (24163857)

>This has a plain course of 96 changes. I didn't realise at the time, but
the plain course together with a partner course (headed 16754238) contains
all the elements of that same >group of order 192, so there will exist 420
courses that together give the extent.

>Probably the best known major principle using those 3 place notations is
Duffield, whose plain course together with, again, its partner course
headed 16754238 gives half of the >same group, and a complementary
principle swapping the place notations (-1-1-36) can be used to obtain the
other half. So, in theory, you should be able to generate an extent
>splicing these two principles in whole courses. I'll leave the composition
as an exercise for the reader...

Interesting, there certainly seem to be elegant possibilities in this
category. I'm glad you pointed out that 2012 thread as I couldn't find much
when I looked in the archives.
Also interesting about the Duffield, which I'd always passed off as
un-extentable due to the uncompleted cycle of the middle 4 bells in each
lead, so the complementary method cancels that problem out presumably.

I forgot to specify that my principle was fairly simple in the way it
produces the full group of 192 rows, whereas shorter principles like
Duffield and Original are obviously quite a lot simpler!
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