[r-t] ringing-theory Digest, Vol 89, Issue 11

[edward martin]

On 10 February 2012 12:25, Matthew Frye <matthew at frye.org.uk> wrote:
>
>
> There are internal falseness issues with the standard 720 for treble bob methods with single changes in the wrong place.

I'm having difficulty picturing what you mean by  "single changes in
the wrong place"?

I reason that if the full lead block is such that the second half-lead
place notation is the exact mirror image of the first half-lead place
notation and this is brought about by having only one bell make a
place when treble is making 6ths, this bell will retrace its work and
the other bells will each retrace the path of its partner such that
the relationship of any two rows which are equidistant from the half
lead will have treble and pivot bell repeating positions with the
others simply having swapped in pairs; Thus we can adequately express
the whole lead block by merely comparing its lead head and lead end -
whether or not the treble is  plain or treble bob. ( This certainly
does not work in Major, but I don't see how it cannot work in Minor)

> I also might want to take some time to convince myself that it works for *all* lead end orders.
>

Give it a go.
Note that the problem is to join two skeleton courses in which the 1,5
& 6 occuppy every possible positional relationship.
To make it simpler: consider only plain Minor
The plain course (by definition) contains the rows
1 x x x 6 5
1 x x x 5 6
the other rows
1 x x 5 x 6
1 x 5 x x 6
1 5 x x x 6
and their partners with 6 in 5ths are distrbuted with any one of them
to the plain course, the other two to the other course

Robert Roan figured out the solution 400 years ago by applying Reverse
Grandsire Doubles to the 5 working bells.

Eddie