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. Some time soon I hope to put a Java applet on this page
to enable visitors to undertake their own queries, but that will probably
have to wait until I update my machine.
The CC Collection
Julian Morgan has taken
over the CC
collection of universal compositions, which should be published soon.
This is naturally biassed towards the falseness of rung methods, but then
methods are generally only rung if there is a composition available, so
it is a bit of a chicken-and-egg situation. Julian 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.
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This page created by Philip Saddleton
Last updated 29 January 2000