[r-t] Designed for falseness

[Richard Smith]

Stephen Penney wrote:

> What is the most false method treble dodging major method that can be
> produced (with a true plain course)?

What do you mean by "most false"?  The most different
falseness groups?  (And if so, are you just counting
tenors-together falseness groups, or perhaps just in-course
tenors-together falseness groups.)  Or the most false course
heads?  (Again, what are you counting?)  Or something else?

For the sake of argument, let's assume you mean the most
in-course tenors-together FCHs.  I'm also going to answer
about surprise not treble dodging in general.  I'll reply
later about treble dodging, but you've caught me in the
middle of regenerating my database of treble dodging major.

You can have up to eight falseness groups.  Having both T
and U (the only groups with eight in-course tenors-together
FCHs) is necessary to be maximally false.  Of the 11,115,834
surprise methods with vaguely sensible properties (regular,
no sevenths above the treble, no single changes, no more
than 2 consecutive blows in one place, and a true plain
course), 25,549 have both T and U falseness.

There are six further groups (M,N,O,P,R,S) with four
in-course tenors-together FCHs.  Obviously it would be nice
if there were a method out there with PMRSNOTU falseness
which would have 40 FCHs (or 41 if you choose to include
rounds, the identity falseness).  In practice you can only
get three of there simultaneously with T and U, and there
are 17 such methods.  The best you can then do is E and L
giving AELMNRTU or 33 FCHs (34 if you include rounds from
the A falseness).  There are four such methods:

  &36-3.4-5.2.36-4-345.6-36.5,2
  &36-3.4-5.2.36-4-345.6-36.5,1
  &36-3.4-5.2.36.4-234.5.4.36.2.5,2
  &36-3.4-5.2.36.4-234.5.4.36.2.5,1

Unsurprisingly, they've never been rung.


> What is the most false method that can be used to get a peal length?

If your definition of "most false" means most FCHs or
falsenes groups, I'm assuming you mean a peal in whole
courses, i.e. a "universal" peal composition.

If so, PABS' web page,

  http://www.saddleton.freeuk.com/comps/universe.htm

lists the maximal sets of falseness groups for which
bobs-only "universal" peal compositions exist.  The largest
set (in terms of number of in-course tenors-together FCHs)
is BCDK (6 FCHs) for which compositions exist for any
seconds place method.  There are plenty of methods with just
these falsenesses (38,074 to be precise).

> What is the most false method yet rung?

Assuming we ignore Double Darrowby (which has
ABCDEFKLMPTUabcd falseness, but also has a course six times
as long as a standard surprise major method), the method
with the most in-course tenors-together FCHs is Wollaton
with ABDEKNTac falseness (i.e. 19 FCHs or 20 including
rounds).  The list continues:

19      Wollaton                ABDEKNTac
18      Jesus College           ABDLOUcd
18      Enderby                 ADNOT
18      Corpus Christi College  ADFKMT
17      Coney Street            ABEGOTac
17      Bendigo                 ABDEGINO
16      Pall Mall               ADFGHTb
16      Kings Cross             ADEMORa
15      Romsey                  ABDNUe
15      Revelstoke              ABDPU
15      Ranmore                 ABENTd
15      Peterhouse              ADELMNe
15      Antigua                 ABENTc

I can understand why Derek had problems finding a
composition for Jesus College!

Richard