[r-t] Falseness groups

[Simon Humphrey]

I said: 
> I thought the mapping of FCHs into groups was invariant, whatever coursing
> order is chosen.  I use Ted Shuttleworth's process (which works with
> coursing orders rather than course heads) for producing the groups, and it
> seems to me to be independent of the plain course coursing order.
> Intuitively, the process should still work if the coursing order was
> written
> in letters "abcdefg".

But what I should have said is, the mapping of false coursing ORDERS into
groups is invariant. Perhaps ambiguities arise with course HEADS: I haven't
looked into this because I invariably work with FCOs.
The number of possible coursing orders for palindromic treble-dominated
major methods is quite limited.
For Plain Bob lead ends it makes no difference to the way the FCO groups are
generated whether we regard the coursing order to be 8753246, 8526734,
8365472, 8274563, 8437625, or 8642357, but for convenience we choose
8753246.  A long time ago I suggested that for irregular methods there
should be a similar arbitrary choice of convenience as to which of the 6
possible expressions of coursing order should be adopted, by defining 87 to
be a coursing pair.  IIRC the coursing order possibilities are then limited
to the following 31, assuming only one working bell lies still at the
half-leads and lead-ends.

2nds place methods:
53246, 54236, 64235, 63245, 35264, 36254, 46253, 45263.

4ths place methods:
53426, 52436, 62435, 63425, 35462, 36452, 26435, 23465.

6ths place methods:
53624, 52634, 42635, 52634, 35642, 34652, 24653, 25643.

8ths place methods:
53246, 52346, 42356, 43256, 35426, 34526, 24536, 25436.

Whichever one of these coursing orders we are working with, the FCOs fall
into exactly the same set of groups with no possibility of ambiguities.  As
an example, representing the plain course coursing order as 87abcde, the
group L tenors-together FCOs will always be +87ceadb, +87becda, +87dcaeb,
-87bdeac, -87dabce, -87adcbe, and -87ecbad.

SH