[r-t] Parity (was: Composing spliced treble-dodging major)

[Michael Schulte]

--- Ben Willetts <ben at benjw.org.uk> wrote:
> Michael Schulte:
> > Parity is quite simply determined by calculating how
> > many transpositions - or called changes if you prefer,
> > so long as each call swaps only one pair of adjacent
> > bells - it would take to get from rounds to the row at
> > which you are looking.
> 
> Actually, the 'calls' don't need to swap adjacent bells. 
> Any two bells will do.

Indeed. My point was simply that it has to be only one pair of bells, not two. I suppose
technically we should say that an odd number of pairs of bells must swap, so swapping three pairs
each time would work. We could also use a four-cycle (change the order from 123456 to 135246, for
example) since a four-cycle is the product of an odd number of transpositions. Or a six-cycle,
eight-cycle, etc.

But swapping only one pair of adjacent bells at a time stays within the confines of 'normal'
ringing behavior as well. If there is such a thing as 'normal' ringing behavior. ;-)

Mike

====
Mike Schulte
Sewanee, Tennessee, USA