Mention has just been made of seven-bell RCEPs, and these chapters on Stedman Triples would not be complete unless readers are given the opportunity of posessing them.
Investigation will show that there are 720 rows having a seven-part relationship to 1234567. They may be found by placing the seventh in first place and finding all possible rows with it in that position. There are 120 of these, showing that there are that number of different seven-part blocks of seven rows each. Eight of them are involved as factors in every RCEP and none can be used in more than one plan. It follows then that there are fifteen plans involving 2,520 sixes, which of course cannot be set down here.
1234567 1325467 1452367 1543267 3126457 3214657 3641257 3462157 2563147 2651347 2315647 2136547 6254317 6523417 6432517 6345217 5146237 5412637 5621437 5264137 4513627 4156327 4365127 4631527 7162453 3751246 6347125 5623714 4516372 2475631 |
Fortunately, with the aid of the column of 24 rows given in the margin and
six heads of other columns, they are not difficult to complete. This is best
done in seven columns, the one shown being the first. Place the other six rows
at the head of the remaining six, and prick 23 rows below each with the same
relationship as those in the firs t column have to the head. The result will be
one RCEP of 168 six-heads, with the quality that what one will do all will do. To write out four more, prick half a B block from each of the 168 six-ends. That is, from the first RCEP prick bobbed slow sixws, preferably placing them in the same order. From the second plan prick bobbed quick sixes. Again from this bobbed slow sixes, and for the last, quick sixes from the fourth. Readers who take this trouble will be well rewarded, for they will have five RCEPs of inestimable value, with the 840 true sixes in an order in which they have never before been placed before the exercise. Furthermore, by transposing the three front bells, as in the case of the Hudson Courses, in all five plans, they will be able to tabulate the results from all fifteen plans. |
Those who have been able to follow what has already been said will no doubt be able to make a table similar to table B. If the first five plans are marked 1A, 2A, 3A, 4A and 5A, in the order they are described above, then the transposed plans will be marked B and C as before. The first column will then contain 1A, 1B, 1C, 2A, 2B, 2C, etc., fifteen in all, and the results will follow on the same line. In Stedman Triples a slow six always comes after a quick, aand vice versa, so that some modification is necessary in the new table for mixed sixes. This is so because every six is marked by its end row. When reversed this row is at the head, and slow and quick sixes give different results. This can be overcome if reversed slow sixes are arranged to conform to the first column, and a final column put in with the lettering altered to give the results from a reversed quick six. This merely means that, whereas in the first column the letters are in the order A, B and C, in the last it will be B, C and A.
Words can hardly express what these plans mean to an enthusiast, so the writer will give a few illustrations of what they will do. When the new table is completed it will show the following blocks:-
Stedman Stedman Plain Course of Erin
10 S2415367=2A 1234567=1A 4315267=5A
1 -4523167 3C -2415367 2A 3546172 5A
2 -4531267 4C -2453167 3A 5637421 5A
3 5146327 1C 4326571 4C 6752314 5A
4 5167423 5C 4367215 7261543 5A
5 -1754623 2B Six times repeated 2174635 5A
6 S1746532 5C 1423756 5A
7 7613425 1C Stedman and Erin 4315267
8 7632154 4C -3124567=1B
9 -6271354 3C 1436275 2A
S6213745 -1462375 3A
4217653 4C
-2746153
Six times repeated
The calling of the first course of ten sixes forms a block of three courses. The numbers show that there is repetition, but the finding of the false course-ends is simplified by the plans, for where repetition can occur is clearly seen. It is enough to say now that many variations of 84 true courses are possible, and all the seven-part peals published by the writer were found by means of these plans.
The second block of Stedman is the familiar bob two and miss two, giving 28 sixes, and all the 1As will give 24 true blocks. These do not include the No. 5 Plan, and from all the 5As twenty-four plain courses of Erin are obtained as shown. As the Erin may be incorporated into the longer blocks, and the latter into the Erin, innumerable extents of spliced Stedman and Erin are possible by these means alone. Exactly the same applies to the mixed Stedman and Erin block, in its relation to the plain courses of Erin.
These extents possess the much-desired property of triple changes throughout. Further, if the blocks of mixed Stedman and Erin are used the bobs are all isolated, and when the Stedman blocks are used there are never more than two bobs together.
Note. - The 2,520 rows will give a second set of fifteen plans, but as they are the exact reverse of those described they are not given.
This page created by Philip Saddleton
Last updated 01/09/96