Extents of Doubles Methods

Anthony P. Smith

This article provides an analysis of all possible extents of Doubles methods with one plain hunt bell, produced using just one type of call, made above the treble.

Symmetric calls

Fourteen of the twenty four symmetric calls are identified in the Collection of Doubles Methods, 3rd edition, Part 1, 1980 and Part 2, 1986. The remaining ten calls are as follows.

Figure 1 identifies all extents using these calls.

Methods are grouped together according to their work above the treble. The first row indicates ranges of method numbers from the "Collection" and the first column indicates group letters. The last column identifies which of the compositions, listed in Figure 3, are true.

Where a call is a standard call for a method, the call letter is in brackets.

For example, Stedman Bob is method number 20, group E. From the table we see that calls b or d with compositions 3, 6 or 7 and calls j or k with composition 4 are all true. Calls b,d and j are in brackets and hence produce extents of the method, whereas call k produces a variation (20k).

The 276 variations of methods with places made in 123 or 125 at the treble's lead and four leads in the plain course are listed in the "Collection". However, the table also provides 189 variations of methods with no internal places made at the treble's lead and 188 variations of methods with three leads in the plain course.

There are some combinations of work above the treble and group letter for which there are only methods not conforming with Central Council Decision (E) A.1. Extents for such methods are shown, for completeness, by call letters in italics.

The compositions may, of course, be transposed to start from any lead. However, care must be taken if the composition ends with a call, because this may also affect the start of the extent.

Asymmetric calls

Of the 120 asymmetric calls, 24 are intrinsically false, however 46 of the remainder can produce extents. They are each identified by a pair of letters, the first defining the work before the treble's lead and the second defining the work after the treble's lead.

For example, a Ready Money single is identified by ej, meaning half a Grandsire extreme (e) followed by half a Plain Bob plain lead (j) viz.

   35142 )
   31524 )   first half of a Grandsire extreme
   13542 ) )
   13452 ) ) second half of a Plain Bob plain
   31542   )
   35124   )

Figure 2 identifies all extents using these calls in the same format as Figure 1.

For example, variations of Canterbury Place (method number 18, group C) are obtained by using calls vz or zv with composition 6 and calls uv (New Grandsire plain) or vu (Grandsire plain) with composition 1.

The 96 variations using calls cd (Thurlby single), dc (London single), ej (Ready Money single) or je (Old Hudibras single) are listed in the Collection of Doubles Methods and Variations by M. J. Hiller 1985, with the exception of 53ej and 53je, but note that Medway Valley and Easter Week use a Ready Money single, not a Thurlby single. The remaining 994 variations should satisfy Mr. Alan Pink (RW 1986 p.377), Mr. Andrew Fisk (p.441) and other neonymphiles.

Incidentally, call df is known as a P-single (RW 1968 p.652) and call xu is known as a Hardmead bob (RW 1966 p.125).

The Ringing World, October 10, 1986, page 896