[r-t] Composing spliced treble-dodging major

Ben Willetts ben at benjw.org.uk
Mon Aug 8 23:37:31 UTC 2005

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.  Example:

Swapping adjacent pairs:
321654 ... 312654 ... 132654 ... 123654 ... 123564 ... 123546 ... 123456
Six swaps, therefore even parity.

Swapping any old pairs:
321654 ... 123654 ... 123456
Two swaps, therefore even parity.

Another way of looking at it is imagining a method which only gives you
even-parity rows.  To get odd ones, you need to use a single.  It doesn't
matter where you call the single, i.e. which two bells it swaps, it still
changes the parity.


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