[r-t] Candidate definition #10

Richard Smith richard at ex-parrot.com
Tue Aug 12 17:04:26 UTC 2008

Don Morrison wrote:

> In this definition we do have to give up those invariants that my
> intuition cries out for.

Yes, I noticed that too.  To recap: your first invariant was 
that if a peal is true, then any rotation of that peal 
should also be true.  This is a special case of your second 
invariant, which was that if a peal is true, then any other 
composition containing precisely the same rows is also be a 
true peal.

While I would have liked the more general second invariant 
to have been true, I won't lose too much sleep over it.  But 
this definition also loses the first invariant, and that I'm 
not happy about.

If I ring a 60 of Grandsire Doubles: pbpbpb, followed by 
seven extents of Plain Bob Minor (WHW x6, s half-way and 
end) but replacing the final single with a bob to bring up 
132456, followed by 60 changes of Grandsire Doubles: pbpbps. 
This is not true, per your new definition, because you have 
two incomplete blocks of doubles.  But if I rotate it so 
that all of the Grandsire is together, it is now true.

And I'm not happy with that!


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