[r-t] Extents of minor

Richard Smith richard at ex-parrot.com
Wed Aug 18 12:40:02 UTC 2004

Stephen Penney wrote:
> ROH: "I think there are only 11 place notations"
> I make it 12:

Percy is quite correct if the null change is excluded.  In
general, the number of changes on N bells, (including the
null change) is the Nth term of the Fibonacci series
(defined with F_0 = F_1 = 1).

Why is this?  On n bells, changes fall into one of two
classes -- those in which a place is made in n-ths place,
and those in which the bells in (n-1),n swap.  The number of
n-bell changes with a place in n-ths is just the total
number of (n-1)-bell changes; similarly, the number of
n-bell changes with a swap in (n-1),n is the total number of
(n-2)  bell changes.  This gives the familiar Fibonacci

  F_n = F_{n-1} + F_{n-2}.


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