[r-t] ringing-theory Digest, Vol 89, Issue 11
Simon J. Gay
Simon.Gay at glasgow.ac.uk
Fri Feb 10 14:49:35 UTC 2012
On 10 Feb 2012, at 14:38, edward martin wrote:
> 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"?
Kelvinbridge Surprise Minor
x 214365 -
36 124635 -
x 216453 +
14 261435 +
x 624153 -
12 621435 -
x 264153 +
1236 264513 -
x 625431 +
1234 624513 -
x 265431 +
36 625341 +
palindromic, lead end 16
All the changes with the treble in 5th place are -, and all the changes with the treble in 6th place are +. So the standard calling doesn't give a true extent. For this reason the method isn't listed in TDMM.
Note that this method is excluded by Philip's conditions for the standard calling to be true.
> 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.
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