[r-t] Falseness Groups

[Glenn Taylor]

Matthew:
> I'm certain someone else will provide more detail, but falseness groups
> don't usually cover tenors parted (or out of course?) so presumably the
> problem leads come between the pairs of singles.

Alan:
> Well they do really it's just they have more courses associated to them.
> The problem may well be between the singles (I haven't checked) but it
> could also be elsewhere like in my Pudsey / Dorchester example.

Like Alan I haven't checked the specifics here, but in general there is
always the possibility that the lead(s) between s3rds and s5ths can run
false with leads that have tenors together. Additionally, in some methods it
is possible for leads between these calls to run false with ss3/v called
from another course (even if they are clean with tenors together sections).
Exactly the same problem can occur with ss5/4 or bobs In/V. The fewer the
number of leads between the pair of calls means that the possibility is
minimised, and it turns out that ss3/v and bobs In/V are "benign" in some
methods (e.g. Rutland S Major) in the sense that they don't introduce
difficulties of this nature. One always has to check this situation when
composing for an unfamiliar method.

The gist of internal falseness is to ask the question 'If this row were to
appear in a different lead, then what would be the lead head in which it
happens', and such a lead head may be from a course with a course head that
has tenors parted. As soon as one false course head (FCH) arises it is
always the case that a fixed set of other FCHs also arises when the
equivalent rows in the remaining leads of the plain course are similarly
investigated. These sets of FCHs are what we know as the falseness groups.
Some of these groups appear to have more members than others, but this is
simply because the "missing" ones are course heads with parted tenors. Each
of the 360 possible in-course course heads belongs to one of the falseness
groups and there are three groups, X Y Z (or X, gamma, delta in old money),
that only contain parted tenor FCHs. Pudsey S Major has one of
these...delta, I think.

Somewhere or other I have all 360 tabulated on a scrappy piece of paper but
I think that I have seen them in print.


Glenn