Universal Surprise Major Compositions
Some years ago I embarked on a project to generate a database of Surprise Major
compositions that are true to large numbers of falseness groups. The initial
aim was to find maximal sets of falseness groups for which a set of courses can
be found that can be linked by Q-sets of bobs. Limiting the problem in this
way, an exhaustive search is possible, and the compositions found can be
adapted to any lead-head order. This initial search took a few months , running
when I wasn't using my Archimedes for anything else. I then set out to improve
the collection.
The criteria for including a composition in the database are that it improves on
the existing collection in some way, ie that no existing composition is true to
the same combination of falseness groups, and has as few leads with the tenors
split. To find a collection that cannot be improved upon is a huge task, and so
I have attempted to limit it, by a series of searches with more constraints.
Q-sets of bobs
The first extension of the original search was to find the "best" composition
for each of the sets of falseness groups already found, ie with fewest split
tenors courses, but still restricted to Q-sets of bobs.
Bobs and singles
Introducing singles increases the search space dramatically, but restricting it
to tenors-together compositions, and whole courses the problem is manageable.
The two searches took about a year to complete, by the end of which I had some
700 "Universal" compositions in whole courses, each of which could be adapted
to any lead-head order. The next stage was to consider whether better
compositions existed using parts of courses, which meant a separate search for
each lead-head group, immediately multiplying the possibilities by a factor of
six (or twelve if fourths-place calls in eighths-place methods are included).
Tenors-together, bobs only
I have completed a search for tenors-together bobs only peals, and believe
these to be the only combinations of falseness groups for which
peal compositions can be found.
Fch grp a b c d e f gx hx jx kx lx mx
BCD K x x x x x x x
BC F x x
BC K * * * * * * x *
BC * * * * * * * * x
B D K * * * * * * x x * x x x
B FG x x
B E x x x x x x x x x x
B L x x x x x x
C E x x
C F K x x
C I x
C L x
C * * * * * * * x * x x
G x x * *
(* => this is included in a larger set of groups)
Nb for 8ths place methods with 6ths place bobs transpose those for groups a-f.
Split-tenors, bobs only
To restrict this search, I imposed a restriction that compositions must be true
to a minimum of twelve groups. I have completed the search for the 2nds place
lead heads. That for 8ths place methods takes longer, as there are no
compositions from the Q-set search in the database, leading to a greater depth
of search.
Tenors together, bobs and singles
I have made a start at this, again requiring a minimum of twelve groups.
Specific methods
I have done a few searches for specific combinations of groups. The time for a
complete search will vary according to the constraints imposed, but typically
takes a few days.
Results
I now have some 6000 compositions in the database, to which I am slowly adding,
and it is impractical to make these available in text form. I have a set of
programs to interrogate the database and would be happy to answer specific
queries. One day I might be able to put a Java applet on this page to enable
visitors to undertake their own queries, but don't hold your breath.
The CC Collection
Many of my compositions appear in the recently published
CC collection. This is naturally biased towards the falseness of rung
methods, but then methods can only be rung if there is a composition available,
so it is a bit of a chicken-and-egg situation. Julian Morgan has done some
analysis of rung methods to determine what proportion are covered by the
collection. I have done some research
into what combinations of falseness groups are most common in all possible
methods.
Because of restrictions on the falseness groups that can occur when the treble
is in 1-2, there are a few of my compositions for which no method can be found.
To check this out I have written a program
to generate methods with falseness restricted to particular groups.
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This page created by Philip Saddleton
Last updated 26 November 2002