[r-t] What's the meaning of a method having aparticularfalsecoursehead

[Richard Smith]

Leigh Simpson wrote:

> > 1) FCH groups are groups of courses which are false
> > to the plain course.
>
> > 2) FCH groups are groups of courses which are
> > internally false to the plain
> > course (i.e. have the same rows in different
> > positions).
>
> OK, it's clear I don't really know enough to comment
> on much of this, but perhaps someone wouldn't mind
> explaining the difference between internal and
> external falseness, when the whole point of FCH groups
> is to group together courses which are false against
> the plain course. Clearly the plain course is false
> against itself, and it must have a group all to
> itself.

Let's write out the first few rows of Yorkshire:

  12345678
  21436587
  12463857
  21648375

Clearly another course of Yorkshire will be false against
the plain course if it includes any of the same rows.
Consider, for example, the row 21436587.  This can appear as
the 2nd, 4th, 29th or 31st row of a lead (these are
the occasions when the treble is in second's place).

We can write out the relevant bits of method for these four
cases:

  2nd row     4th row

  12345678    12537486
  21436587<   21354768
  12463857    12345678
  21648375    21436587<


  29th row    31st row

  21436587<   21648375
  12345678    12463857
  21354768    21436587<
  12537486    12345678
  --------    --------
  12354768    12436587


We now have four false lead heads:  12345678, 12537486,
12354768, 12436587.  We can transpose these to get false
course heads by repeatedly transposing by the plain lead
head (15738264) until the tenor becomes 8ths place bell.
This gives four FCHs:

  12345678
  13245678
  12354768
  13254768

The first and fourth correspond to A falseness; the second
and third, to B falseness.

Using this mechanism, the first and fourth FCH will always
produce A falseness.  This is because the first lead head is
always rounds, as the row under consideration appears in the
same place in both leads.  The fourth lead head is
also always 13254768 (for regular methods, anyway).  This is
because all you have done is turned the lead updside down
added the lead end change (12), and transposed to the course
head.

Because of this, the first and fourth FCH are sometimes
called the "external" falseness of the method, whereas the
second and third are called the "internal" falseness.

Richard