[r-t] New method - Auryn Differential Minor

[Alexander Holroyd]

> "I'd like to understand better how this works"
>
> Thanks for this, Ander. I understand Auryn has been generated from 
> "first principles", but aren't you just tweaking around with Morning 
> Star TB variants?  Morning Star is the only one of the "standard" 147 TD 
> minor methods that has the tenor path mirroring the treble, something I 
> like a lot (and mention every time during a handbell peal where Morning 
> Star appears). An 720 is of course trivially obtainable.

No, there's nothing particularly surprising about the fact that the 6 
treble bobs.  The surprising thing about Auryn (when viewed as a treble 
bob method) is that the standard calling works in spite of the two 
normally fatal obstacles (either one generally fatal on its own) - 
asymmetry and the -25- section.

Again, for anyone who doesn't find it surprising, can you find any other 
example?

Alternatively, can you find any other method for which the standard 
calling works but which does not admit 6 mutually true courses?  (My 
reaction would have been that this was impossible).

> The 2-lead-unit of Auryn seems to effectively be two of these half-lead 
> spliced together (the -25- when the treble/tenor is in 3-4 isn't a 
> problem as you have the same pairs of bells, 2-3 & 4-5, together in the 
> first and second half-lead). Or am I missing something here?

I don't know why that would be relevant (indeed that is a requirement if 
the treble is dodging in 34).  The problem with -25- is that the parity of 
the rows for the section are +-+-, so the two rows with the treble in 3rds 
are the same parity.  The proof I know that the standard calling works 
requires paity structure +--+ or ++-- in each section.

Similarly, symmetry is crucial for the usual proof, because the standard 
calling involves ringing part of one course backwards.  There are a few 
rung asymmetric TD methods, but I think all the others can have the rows 
of the lead rearranged into something symmetric.  Auryn does not have this 
property.

> Alternatively, Mike Ovenden's December 2005 message to this list might be phrased in language you're more at home with? :-)
> http://www.bellringers.net/pipermail/ringing-theory_bellringers.net/2005-December/001221.html

That's very interesting but on a completely different topic so far as I 
can see.