[r-t] New method - Auryn Differential Minor

Alexander Holroyd holroyd at math.ubc.ca
Mon Dec 3 20:07:05 UTC 2012

> "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 

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 

> 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.

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