[r-t] Plain Bob lead heads/ends (was ringing-theory Digest, Vol 89, Issue 9)

[edward martin]

In even bell methods, if the lead block is symmetrical about the
treble then the lead heads and lead ends must be in plain bob group
(ie the 2-3-4-5-6 etc will be in a plain hunt relationship because of
the half-lead pivot bell  and its specific conjugate pairs )
On 8 bells these are
2 ; 3x4 5x6 7x8
4 : 2x6 3x8 5x7  etc
Also, given the  same half-lead pivots, an assymetric lead block can
also produce plain bob leads if Court places are made
e.g:
Ring plain bob for half-lead rows
86745231
87654321
then pn x 18 x 38 x 14 x gives
15372846 then either 2nds or 8ths for 15738264 or 13527486

Similarly in twin hunt triples methods the two pivot points are when
1,2 cross in 1-2 and in 6-7
at both these points there will be two rows of plain hunt on the 5
'working bells'
If the lead block is symmetric then the 5 bells will be in the same
coursing order (& give same lead heads as occur in Grandsire, St
Clements  etc

Calgary Bob Triples is assymetric with PN  3 1 7 1 7 1 7 for 6473521
and  6745312
but then 7 3 7 1 5 1 gives 1275634

I suppose that if we must define regular methods then they would have
to have the working bells be in the same coursing order through
lead-end lead-head AND be symmetric about the path of the treble

Eddie