Falsest Method

What is the falsest TD Major method?

Stephen Penney asked (a paraphrase of) this question in April 2005. Richard Smith provided the answer.

Most False Course-Heads (FCHs)

Ignoring Double Darrowby (which has ABCDEFKLMPTUabcd falseness, but also has a course six times as long as a standard Surprise Major method), a Treble Dodging Major method 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 two 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. In practice you can only get three of these simultaneously with T and U, and there are 17 such methods. The best you can then do is E and L, giving AELMNRTU falseness, and 33 FCHs (not including 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, but Don Morrison has produced a composition for the second of them:

 5,088 'Unnamed' Surprise Major
 by Donald F Morrison 
 234567   M  T  V  W  M  B  H
 ----------------------------
 35246    s  s  s           -
 54623       s  s           -
(724653)     s     s  -  -
 642753            s        s
 632457         -
 34526       s  s           -
 42653       s  s           -
 523746      s  -           s
 625437         -        -
 42356       s  s           s
 ----------------------------
 Repeat twice. Fourths-place calls.
 Contains no backstroke 87s, and is all the work.
 'Unnamed' (36x3.4x5.2.36x4x345.6x36.5  lh k  fch AELMNRTU)

True Composition to some of the Falsest Methods

The most in-course, tenors-together FCHs for which a universal peal composition (with common bobs only) is listed on Philip Saddleton's universal peal compositions website, http://www.saddleton.freeuk.com/comps/universe.htm, is six (groups ABCDK). There are 38,074 methods with just this falseness, and compositions exist for any of them with a seconds-place lead-end.

A J Cox has produced a universal composition for groups ABDEGINORTbfXYZ (29 in-course, tenors-together FCHs), but this does not use common bobs or singles:

 5376 true to ABDEGINORTbfXYZ
 by Anthony J Cox

 2345678  2  3  4  5  7
 ----------------------
 8675423           s
 6587234     s           \}a
 5768234       9a
 4238657           s
 4236857              s
 3427865   s    s        \}b
 3428765              s  \}
 2345678      10b
 ----------------------
 s=1256.

The falsest method that can be rung to the above composition is the unnamed

 &3-36.4-5.2.3.2-4.3.4.36.2.3

with 27 in-course, tenors-together FCHs (falseness groups ABDEGNORT), found by Philip Saddleton.

Falsest method yet rung

Again ignoring Double Darrowby, the rung method with the most in-course tenors-together FCHs is Wollaton Surprise with ABDEKNTac falseness (19 FCHs, not including rounds). The top 14 are:

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

Rung Treble Bob methods are way down the list. The falsest are Noxious (ABDKPa) and Jupiter (ABFKNad), both with 9 FCHs. Methods