[r-t] Extension of Warkworth and (G)B.8.

[Richard Smith]

In a letter in this week's Ringing World, Robin Woolley
quotes the 3BC/1EF extension of Warkworth that I produced as
a counter example to the conjecture that any method that
extends twice will extend indefinitely.  He then asks
whether this extension contravenes decision (G)B.8, that
"wherever the parent has working bells making adjacent
places, this characteristic must be retained in all
extensions".

The three methods in this extension family are:

  Minor: &-34-4-2-3.4-2.5,1
  Major: &-36-6-256-36.4-2.5.6-4.5,1
  Royal: &-38-8-258-38.4.78.2.58.6-4.7.8-6.7,1

In the Minor, there are three places where working bells
make adjacent places: the 34 change when the treble dodges
1-2, and the two 12 changes when the treble dodges in 3-4
and 5-6.  In the extensions, there are still precisely three
such places.

When the BC section are repeated above the treble, -34-4
becomes -36-6-56-6, which becomes -38-8-58-8-78-8.  That is
to say, in all but one instance, the adjacent places are
split.  Originally, I had read (G)B.8 to mean that all
repeated instances of adjacent places must remain adjacent
in the extension, which would make this extension invalid.
Similarly, I had read (G)B.7 to mean that all repeated
instances of places adjacent to the treble must remain
adjacent to the treble.  This would also make this extension
invalid because the C section has a place adjacent to the
treble in 4ths.  This is not preserved in all repetitions of
the C section.

Back at the end of June, I asked PABS how these two
decisions should be interpreted.  He replied,

> "The characteristic [places adjacent to the treble] has to
> be present, but only once if a section is repeated. There
> are plenty of other examples that would not be permitted
> under your stricter interpretation, e.g.  Bourne, Norwich,
> York. The new (G)B.8 is similarly interpreted.

Assuming this is how the Methods Committee intends the
decision to be interpreted (and I admit it is unclear from
the wording of the decision), the extension is valid.

Richard