[r-t] Re: Decisions

[Richard Smith]

Robin Woolley wrote:

> In this paper, I also address Alliance & Little extensions. On the former,
> it is only possible to extend 'ordinary' alliance minor methods with the
> treble dodging in 7-8, whilst 'special' alliance methods can have the treble
> dodging in 3-4, 5-6 and 7-8 or just 5-6 and 7-8. The solution to this is
> trivial.

I hadn't realised this.  Is it really intensional that the
two tables in (G)C.2(b) do not mention GH or EFGH extension?
I had always assumed that their omission was simply because
in most normal methods (i.e. those without penultimate
places made above the treble) GH was the same as FG.

As you say, allowing GH extension above the treble for Major
(or, equivalently, allowing EF extension above the treble
for Minor) would solve the seeming inconsistency between
"Ordinary" Alliance and "Special" Alliance methods.



Regarding extension of Principles, you say in [4.3]:

| This is identical to the 'Little' problem so the arguments
| will not be repeated here.

I do not believe this to be the case.  For Little methods it
is easy to apply the usual rules for extending the treble's
path.  The whole infrastructure for extending
treble-dominated non-Little methods can just be applied
directly.  This is not the case for principles as they are
not "treble-dominated".

It would, I'm sure, be possible to allow the lead length to
increase but you would need to give careful thought as to
how it would be allowed to increase.



Regarding variations of Lincolnshire, all of the variants
other than Gainsborough and Johannesburg (which have a 1236
change) can legitimately be extended in the "obvious way" to
Royal.  For example, Biggal S Royal could be (and probably
should have been) called Vancouver S Royal.  In practice, as
Vancouver S Major has several other indefinite extension
paths available to it, one could argue that one of the
extensions working on 4n bells is the "real" one.

Under the current rules, there is only a problem with the
methods with a 1236 place notation, as these would be
extended to 1258 in the obvious extension.  This splits the
adjacent places in contravention of (G)B.8.  All the others
are perfectly legitimate 5AB/2DE extensions.

Although the similar variations of Superlative do not suffer
this problem as the 1236 place notation in the Major becomes
a 1230 place notation in the Maximus and adjacent places are
thus not split, they don't in general work as the 3-pull
dodge in 1-2 in Maximus is just a copy of part of the 5-pull
dodge.  If the five pull dodge is replaced with an
alternative piece of work, then so must the 3-pull dodge.



Finally, you say,

| Further to my conjection supra, I would like to propose
| the following conjecture:
|
|   'All methods are indefinitely extendible if high enough
|   stages are considered'

This is false.  A counterexample is London S Minor.  It is
possible to prove that this has only four extension mode all
of which work sporadically to Major and at no higher stage.
The proof is too long to include in this email, but it can
be done rigorously, and does prove that no matter how many
stages you examine, the method never becomes indefinitely
extendible.

Richard