The method, Stedman Triples, has been an enigma to many able composers for more than 200 years. The two editions of 'Stedman' make clear its possibilities in one direction - the twin-bob plan - but even the writers of that work have not gone further. As a result, the source of odd-bob, the bob and single peals with few consecutive calls, and others, remain a mystery to most.
Certainly some composers have solved many of the puzzles that the method provides. Unfortunately, those that have passed to their rest have not - so far as the writer knows - left any record of the source of their peals. The writer, feeling that his ability to carry on such work is waning, will endeavour to show how all modern peals have been found. He hopes it will enable anyone, with a knowledge of twin-bob compositions, to put together peals of Stedman Triples as easily as those of Bob Major.
The solution is in the existence of what may be termed Regular Course-end Plans (RCEPs) on six bells. In this connection sixty Course-ends (CEs) are needed, and their relationship must be such that, taking any fifty-nine of them, the relationship of the one left out to the fifty-nine must be the same, whichever one of the sixty it may be. The consequence of such a likeness is that every one of the sixty will give results alike. For instance, all the CEs are followed by sixes which may be numbered 1 to 13. Then the CEs, even if all are transposed in the same way, will give, when followed by a plain, bob or single, a six having the same number. Further, each column of sixty sixes will have the same property. This enables a Table of results to be drawn up, which will be shown later.
Those who intend to follow this treatise seriously will find it useful, if not essential, to write out the whole of the 840 true six-ends. To do this head a column No. 14, and place below it the Hudson CEs. Then thirteen more columns, heading them Nos. 1 to 13. Along each line after each CE, write out the six-ends of the course with the third, fourth, fifth and sixth sixes bobbed. This will give 840 true sixes, and you will actually have, in separate columns, fourteen RCEPs, two of them (the 9th and 14th) with the seventh at home.
As the Hudson courses will stand in this Table of 840 true sixes (to be referred to as Table A), the sixes numbered 1 to 14 will have the letter A added to their number. Further, the three front bells of each six-end may be transposed as 312 is to 123, when B is added to their number. Again they may be transposed as 231 is to 123, in this case C is added. The effect of these transpositions is to treble the number of RCEPs; there are therefore six with the seventh at home.
The position of the row of rounds is changed in the transposed 14s, and it does not appear in the 9s. To avoid confusion the six RCEPs with the conventional row will first be given in skeleton form. Afterwards, with the exception of those from bob blocks, it will be shown how these RCEPs give the basis courses of all peals discovered to date.
1 In mathematical terms, the course-ends form a group (a subgroup of the even permutations on seven bells, A7.
2 The complete set of RCEPs give the cosets of the subgroup in A7. Each row of the table is then a transversal of the subgroup.
This page created by Philip Saddleton
Last updated 16/09/96