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 there 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 &36-3.4-22.214.171.124-126.96.36.199.2.5,2 &36-3.4-188.8.131.52-184.108.40.206.2.5,1
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
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