[r-t] Extents of doubles
pje24 at cantab.net
Fri Aug 4 11:27:14 UTC 2006
Here are some words you don't often hear: Barry Peachey has written an
article in this week's RW with some interesting bits in it. Amongst the
usual bluster, misplaced grandiosity and misguided sentiments he talks a bit
about Crambo doubles, which was apparently 'first published in Fabian
Stedman's Campanalogia in 1677'.
Crambo is a doubles principle with 24 changes per lead; ie the plain course
generates the extent. There is no RW reference next to it on the Methods
Committee website (http://www.methods.org.uk/online/prin5.htm#76),
suggesting that it hasn't been rung in recent years.
The noation for Crambo is:
= 45123 (you can even call it cyclic!)
As Barry points out, it would be a serious challenge to ring Crambo. It
puzzles me a bit that many ringers assume you have to go to higher numbers
of bells for complexity: a peal of 42 different doubles principles whose
plain course generates the extent would absolutely blow something like a
peal of ORABS, or Double Helix etc. out of the water in terms of complexity.
There are other interesting methods on the same webpage, from the familiar
Orpheus, to Mermaid (126.96.36.199.188.8.131.52.184.108.40.206.220.127.116.11.18.104.22.168.22.214.171.124),
which has some beautiful symmetry.
Can anyone generate an exhaustive list of all 24 change-per-lead doubles
principles whose plain course generates the extent? Or at least estimate a
lower bound for the number that exist? I'm curious.
It sounds like the kind of thing RAS might have done before, but I can't
find the relevant email if he has!
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