[r-t] Extents of doubles

[Philip Earis]

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:
345.125.145.123.345.123.125.345.123.345.125.345.123.345.145.123.345.125.345.123.345.125.345.123 
= 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 (1.3.1.3.1.5.1.3.1.3.1.125.3.5.3.5.3.1.3.5.3.5.3.145), 
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!