[r-t] Double extent of major

Alexander Holroyd holroyd at math.ubc.ca
Tue Dec 4 18:02:32 UTC 2007

It seems to me that there is no such restriction.  Any treble dodging 
method should work.  (I have just checked Cambridge).

Taking rows 1,2,5,6,9,10,13,14 of each half lead gives a plain method 
(with lots of jump changes), so these rows form a true extent.  Then each 
of the other rows can be paired up with one of these, with the treble in 
the same place (row 3 with row 1 etc), and the transposition relating the 
pairs with the treble in a given position is always the same.  Therefore 
they form a true extent too.


> Richard Smith wrote:
> I ought to have added that you are restricted to using
> methods that have sensible parity structures -- i.e. so that
> the three changes when the treble is dodging either have +-+
> or -+- parity.  This is exactly the requirement that is
> needed to make a minor method work too.
> This more or less rules out double changes (e.g. 1258) other
> than at the division ends -- i.e. when the treble moves
> between dodging positions.  (In principle you could still
> have a double change with, say, a 1234.56.1234 block, but I
> doubt many people would choose to.)
> Off the top of my head, the only commonly rung method that
> is affected by this is Cambridge.

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