[r-t] Double Helix

[Simon Humphrey]

I am amazed to learn that an extent of Double Helix Differential is
possible.
Simon Melen has come up with the composition below.

An exciting development!

Simon Humphrey



40320 Double Helix Differential Major

W         H
------------
-           -
-
-------------  
x 12

With s and * alternately at the end of every 3rd part.

- = 16, s = 1456, * = 123456

The "wrong" is at the end of the 3rd section of the plain course.


To further quote from Simon's emails:

I looked at a half section for the front three bells and realised that they
rang in each of the 56 positions exactly once only.
One thing I'm not sure about even now is whether the method was designed to
have that quality (which would have been very clever - but it's difficult to
imagine you would design that without going the small extra step to realise
you could get the extent), or whether Terry Streeter (who I believe
constructed the method) accidentally stumbled across it in a computer search
as being something which met his criteria and was true to 3 homes.  
Anyway, I think it's remarkable that something so apparently complicated can
lead to something so simple.  
Double Helix was a very well chosen name.

And:

I think the principle I have used could be easily used to get extents on
higher numbers of bells.  
It seems to me that if m and n are coprime and M is an extent on 1+m bells
with a standard treble plain hunting and N is a composition on 1+n bells
likewise, then if you create the right Differential method with
characteristic (m,n) you can come up with MxN, an extent on m+n bells.
 Another possibility is that if, instead of Double Helix, you might be able
to construct another Differential method with twice the section length (224
changes) in which the front 3 bells occupy every position exactly twice,
each pair with different parity.  
If you then stipulate that one of the three bells treble bobs, then in
theory you should be able to get an extent of, at the very least, half lead,
variable treble (regular/irregular) surprise/treble bob/delight major in
maybe 7 methods. 
The other possibility might be to look at characteristic (1,3,4) instead of
(3,5).