[r-t] Falseness groups

[Simon Humphrey]

Richard:

>    A.  The three-course touch produced by calling three
>    fourths place bobs a course apart in a seconds place
>    method is false if and only if the method has U falseness.
> 
>    B.  A bobs-only composition in which the two tenors ring
>    plain courses throughout is necessarily universally true
>    to abcdefXYZ.
> 
> Do you think that either (or both?) of these statements are
> generally true for irregular palindromic major methods with
> a true seven-lead plain course?

My immediate response is that statement A is false, because in irregular
2nds place methods a 4ths place bob does not necessarily affect 3 contiguous
bells in the coursing order; and for methods where it does not the
composition will include different coursing orders than for methods where it
does. 

A touch of 3 Homes, for instance, could join the 3 coursing orders x5x6x (or
x6x5x) rather than the 3 coursing orders 5xxx6 (or 6xxx5). x5x6x is true for
U falseness, but not H. 5xxx6 is true for H, but not U.  I define U
falseness as being FCOs (relative to abcde) bcade, cabde, adbce, acdbe,
abdec, abecd, eabcd, and bcdea; and H falseness as FCOs cbeda and ebadc.

Statement B might not have an answer in all cases, since a bobs-only
composition with 7-8 unaffected might be difficult (or impossible?) to
achieve for some irregular methods, regardless of the falseness. But if it
was achievable, and not trivially false by repeating whole leads, then yes,
I think the composition would be true. This is because, in my terms, groups
abcdefXYZ have no tenors-together falseness irrespective of whatever the
plain course coursing order is.

SH