[r-t] New method - Auryn Differential Minor
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? :-)
That's very interesting but on a completely different topic so far as I
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