[r-t] 56 singles, (was Diamond Delight Major)

[Don Morrison]

On Wed, May 26, 2010 at 4:08 PM, Mark Davies <mark at snowtiger.net> wrote:
> So this is interesting, anyway. In PB methods, under what conditions of
> falseness are 56 singles likely to be useful?

I have no idea what the answer from theory is.

Empirically I've often found them useful

- when there is no a or C falseness, for obvious reasons. Though, of
   course, even if such falseness is present 56 singles aren't
   completely contra-indicated, just as 34 singles aren't necessarily
   useless in methods with D falseness, depending upon where it
   occurs. But lacking a and C falseness certainly makes it more
   likely 56 singles will be a boon.

- They seem particularly likely to be useful when there's also D (+
    possibly B) falseness present since they give a way to stitch the
    65 courses and their ilk in in whole courses, without having to
    carefully use bits and pieces of courses false with 34 singles.

- They also seem particularly likely to be useful when c falseness is
    not present. Undoubtedly there are other FCH groups it is
    similarly useful to have absent, but c is so common it sticks out.
    If it's not present, than 56 singles can be handy for easily
    sticking in the courses with 56 coursing together at the front or
    back of the course order in, which are frequently attractive. For
    example, some entertaining, tidy compositions of Superlative are
    easily assembled using 56 singles.

- And empirically it seems 56 singles are often useful when trying to
   get a composition, any composition, of methods with intractable
   falseness. There is likely a theoretical basis for when this will
   be useful or not, but my experience is just trial and error, and
   shows it to be frequently useful.

I believe several folks, at least including Tony Cox and Simon
Humphrey, have put together a variety of clever ensembles of courses
using 56 singles that are true to a wide variety of FCH groups.
There's one in particular by Tony Cox that uses just 56 singles with
no bobs to stitch together a peal's worth of courses, many of them
tenors parted, true to all of BDEGINORTbfXYZ.

They can be used to good effect in Cambridge Major, too, allowing you
to get all the 56s and 65s into a relatively simple, tenors together
composition:

   <http://ringing.org/main/pages/dfm/major/single-surprise/cambridge#4161>

It is entertaining to note that using 456 singles to combine the three
in course 56 courses with the three out of course 65 courses gives you
an exceedingly simple and tidy quarter true to all of the standard 8 +
Glasgow and Belfast, except Rutland. Or, obviously, true to any method
lacking a, U and C falseness, a being the only one that comes up in
methods commonly rung.



-- 
Don Morrison <dfm at ringing.org>
"If a man extols his own faith and disparages another because
of devotion to his own and because he wants to glorify it, he
seriously injures his own faith."
      -- Ashoka, _The Edicts of Ashoka_, tr N A Nikam & R McKeon