[r-t] multi-peal extent of major

[Philip Saddleton]

I recall an article in the RW a few years ago discussing a set of eight 
peals of PB Major which between them contained all the rows, with only 
the plain course repeated. I can't remember whether these had been rung, 
or if it was merely a theoretical exercise.

There are certainly enough ways to get in and out of rounds without 
repetition. Here's a plan:

Consider pairs of changes which, combined, are equivalent to place 
notation 'x'. There are seven of these, i.e. place notations

1234 5678
1256 3478
1278 3456
12 345678
34 125678
56 123478
78 123456

Given a right-place plain method, take any one of these pairs, and find 
the lead containing the two rows given by rounds transposed by these 
PNs, e.g.

12435687
12345678 1256
21346578 3478

This gives a way of smuggling rounds into a different lead in each case, 
providing it is not a second's place or group M method (take Double 
Norwich, for instance). Along with the lead starting from rounds this 
gives eight separate leads. Then find a way of partitioning the extent 
into mutually true blocks each containing one of these leads. Eight 
5040s, seven of which have an extra row inserted so that you can start 
and finish with rounds.

-- 
Regards
Philip

Frederick Karl Kepner DuPuy said  on 07/12/2009 19:49:
> I'm probably not the first one to think about all this, though. What
> conclusions have been reached on the question before? Has it ever
> actually been done?