[r-t] Extension question

[Robin Woolley]

Hi All,

Following from my last.

To keep it 'simple'.

Work I did years previously to the Anglia problem showed the following.

In the 1961/75 collection of Minor methods, there were two sorts of 
Alliance methods - ordinary & special. Ordinary had dodging only in 5-6 
and Special had plain sections only in 1-2. I showed from these that 
Alliance methods can only extend from the 'internal sections' so 
Ordinary Alliance extended could *only* have dodging in the last place 
(at all stages) and Special could only have a plain section 1-2.

The reason for this is 'work'. Taking extension above the treble as 
example, if I choose to extend an Special Alliance method by AB-above, 
then I have ABA'B' above in the parent which is plain. However, the work 
below the treble in the second section is dodging since all extension 
paths below must include the C section. (By symmetry, any alliance 
cannot extend by the last sections - FG for Minor).

In summary, an Ordinary Alliance minor method can be denoted as PPT and 
it's extension must be PPPT - in an obvious notation. (We omit the 
treble passing between 1-2 and 3-4 from the notation). A Special 
Alliance is PTT and the extension must be PTTT, etc.

In as few words as possible, the work above and below the treble must be 
of the same 'type'.

Don asks: 'If a hunt path like this does expand, as your answer seems to 
imply, does that mean a major method with the treble dodging in 1-2, 3-4 
and 7-8, when extended to royal, must have the treble dodging in 1-2, 
3-4, 5-6 and 9-10?' Answer - Not exclusively!

(b.t.w., I remember discussing this with RAS when he was devising his 
extension program about 15 years ago.)

To Semi.... We are looking at the work when the treble is in 7-8-9-0.

In Major, the treble work is 5-6-5-6-7-8-7, in Royal 
5-6-5-6-7-8-7-8-9-0-9. It seems intuitive, therefore, that we have a 
perfectly good 1DE extension. We have preserved the 'type' of the 
section(s) when the treble is doing its backwork.

Don's real question seems to be related to the Formula BUT the formula 
quoted in (G)C2 is but one example of many. There are other formulae for 
parental methods on 6 bells, on 7, etc. Here, we have a method which 
does not include position 'I' - position H is the last and we can 
construct a whole set of extensions based on this.

I have concluded that Don's Royal method is a correct extension of the 
major. I base this on the Minor examples above. (Note the definition of 
section H is 'treble in 7-8'. It is section I which says 'treble lying' 
- which it doesn't here.) We have seen that the last section's type has 
to appear once and once only once in the extension and it does so. 
b.t.w., this is not a 'Little' method by definition.

Whether it's the only extension is another matter!

Best wishes
Robin