[r-t] Re: Extension (Again)

[Richard Smith]

Sorry for not replying to this sooner.  It got lost 
somewhere in my "todo" list.

Robin Woolley wrote:

> Is it possible to extend Roker via the paths of either of 
> the royal extensions to higher stages?
>
> Roker S8: x3x4x2x3.4x4.3x456x7; 2nds
>
> 'royal #1':  1BC/NHI x3x4x25x36.4x4.3x456x7x456x7 (N = number of bells at
> current stage)
> 'royal #2': 1CD/1FG x3x4x2x36.4x4.3.6x6.5x678x9

Neither of these extend beyond Royal.

(Incidentally, there is no need to introduce the notation 
"NHI" with N being the number of bells -- as subsequent 
extensions can never introduce places between 1st place and 
(N-7)ths place (exclusive), this can simply be called a 7HI 
extension.)

> If there are no extensions further down these paths, are there any 'quantum'
> (i.e., modal) extensions?

Yes.  There is an extension that work on 4n bells -- it is 
4FG/7HI.  The extension to Maximus has the place notation

   &-3-4-2-3.4-4.3-456-7-456-7-456-7,2

This is the only indefinite extension.

Richard