[r-t] Major methods where anything goes

[Philip Earis]

Just to bring together a few strands that have surfaced on the Ringing 
Methods facebook group and elsewhere in recent days...

John Bissell got in touch about the double method Megan Delight major (e 
&x36x1x5x36x4x1x36x7, 12  EL falseness), in which the first peal was 
recently rung (http://bb.ringingworld.co.uk/view.php?id=447009).

Megan is the 7ths/2nds counterpart to Cambridge Blue Delight Major,which was 
first rung in a peal containing the only 4 regular double treble-dodging 
major methods with no adjacent places at all in the notation 
(http://www.cantabgold.net/users/pje24/nonadj.html). Cambridge Blue is an 
extremely fluid method, with much complete plain hunting from front to back 
(and of course from back to front).

One of the properties John liked about Megan is that a peal composition is 
very easy to achieve...indeed any composition that leaves bells 6,7,8 
unaffected will be true. A simple 24-course block arrangement was used for 
his peal:

===
5376 (5152) Megan Delight Major
2345  W  H
-----------
3542  2  ss
4235  -  -
-----------
Six part : single for bob at halfway and end. For 5152 omit one ss
===

Whilst the falseness groups that are often seen in rung methods, like B and 
D, have courses with the 6 in 6ths that are false against the plain course 
(as indeed do the a and c fchs present in “clean” methods like Bristol and 
Cray), in a method like Megan where any "6,7,8 unaffected" composition can 
be called you still have CEGHILMNORSbef at your disposal.

To test how common this property is, I did a  quick search of all 
treble-dodging major methods with fairly constrained properties to keep the 
search space small (treble does one dodge in each position, conventional 
palindromic symmetry, regular leadheads, no bell makes more than 2 
consecutive blows, no more than 2 places made in any change, no places in 
7ths except at the healflead, and all sections symmetrical)

The results indicate that just 608 (0.93%) of the 62627 methods generated 
have this property, and the only rung (named) methods are Megan and 
Cambridge Blue Delight. There are some structurally interesting methods 
produced, like the double &36x36.4x5x1x4x5.36x36.7, 12, but I won’t be 
rushing out to ring this soon...

On a slightly related point, Stephen Beckingham has posed the question if 
there are any nicer treble-dodging major methods than the mx Muppet Show 
(http://ringing.org/main/pages/method?match=muppet&name-query=Search), which 
has a rather fabulous mega-tittums course.

(As a reminder, Stephen has produced the interesting website 
http://bex280.x10.mx/ to generate the most musical quarter peals in any 
treble-dodging major method).

Rob Lee replied, pointing out Hat & Feathers Surprise (and indeed 
Superlative) also have extremely nice mega-tittums courses, as has been 
pointed out on here repeatedly. Rob flags up,

“I have had a look at other methods that generate as much music as Hat & 
Feathers in the mega tittums course, if we relax the criteria of regular 
lead ends. One possibility is the right place -36-4-2-1-7-5-36-3 (le 16), 
but this is still a bit static. Far better is 36-5.4.5.2-36-7.4.5.4-36 (le 
18). The 'effective' course end for these methods is 62534 and 54362 
respectively"