[r-t] 40320 Spliced Major (3m)

[Mark Davies]

MF writes,

> Yes. Sounds like we're well into Deep Fundamental Truth territory!
 > (assuming your implementation of the algorithm is sound)

Hah! The audacity of the thought! :-)

> If you go at the algorithm from the other direction. Is it possible
 > to get touches of plain methods with the correct distributions
 > of (123)? (which presumably must be unable to line up with a Helixoid).

Well, I haven't investigated this so thoroughly, and I think I might 
have got some early results without the condition that the three rows 
with a pair-swap from (123) must have opposite sign from the three rows 
with a rotation, which confuses my memory slightly; but I'm pretty sure 
it does works the other way, too.

What we are saying is, if you take the 336 rows with (123) in all 
positions, then insist the sign rule applies to each set of six rows 
with (123) in the same places up to self-permutation, and then enforce a 
pure Plain Hunt path on the treble, it is necessary for the 2 and 3 also 
to follow pure Plain Hunt paths whilst the treble is moving.

Put like that and it sounds more reasonable I suppose. The sign rule 
treats (123) symmetrically, so if we force one bell to do one thing 
(Plain Hunt) then perhaps it is only obvious to expect the other two to 
have to do the same thing. Is that the entire explanation? It sort of 
feels like we need a bit more than that.

MBD