(First published in The Ringing World, 1 April 1921)

STEDMAN TRIPLES BY ODD BOB

A TRIP INTO THE REALM OF FIGURES

Come with me, away from all this jarring tumult. Come into Fairy Land - even into the Fairy Land of Stedman, where the methods cease from troubling and the Lead Ends are at rest.

But I must first warn you that I do not offer to give you a map of that mystic land, but only to act the humble part of a guide and lead you along the trackway that I have followed as a holiday task.

We must start from the 'Brushwood Pile' of solid fact which has been collected in the past; but do not let that damp your ardour. We will visit strange places - aye, and even reach the Lily Lake - the Lily Lake where islands slide, and - who knows? - perhaps also make our way along the 'Thirty mile ride', to its very last milestone, the one on which is inscribed the mystic motto 'This is all.' and where all the peals come round.

But we must come back to the Brushwood Pile, from which we will take all the Plain Courses of Stedman.

Now I know that the experts say that there are no plain courses of Stedman, and, theoretically they are right, maybe. But who cares? This is Stedman Triples we are dealing with. The same old Stedman that we have known and rung and sworn by all our lives, aye, and maybe, sworn at too, when things went awkward in the slow. And we are going to ring it still and ever call it Stedman. So let us get back to our plain courses.

Here they are. Three hundred and sixty in all, and a nice little pile to handle. Fortunately, however, they arrange themselves nicely into six groups with sixty in each, as follows:

I.     1  2  3  4  5  6  3  8  9 10 11  5 13 14
II.   10 11  4  5  7  5  6  8 14 10 11 12 13 14
III.  10 11  5  7 12  7  5 13 14 10  2  3  8 14
IV.    1  2  6  6  6  3 12 13  9  1  2  6 13  9
V.    10  2  7 12  3 12  7  8 14  1  2  7  8  9
VI.    1 11 12  3  4  4  4  8  9  1 11  4  8  9

I. is the skeleton of Hudson's famous sixty courses. Notice the repetition of the 3 and 5 . It is by substituting 7 and 12 in these places respectively that all the twin bob peals have been composed. I call them the Baby Q sets, and they are equally ready to do their work in any other course where a 3 or a 5 appears.

The other five courses are so cross that, as far as I know, no one has yet been able to bring them to reason. But by a judicious use of bobs and singles, other courses have been produced which are available for peal construction.

Of all these the following is the most useful that I have tried:-

1 - 10 2 3 8 - 11 12 3 4 - 5 6 - 13 9 - 14

These I call Mr Carter's courses, as I believe that he was the first to produce them. Incidentally I may mention that I found them quite independently, and had already put them together into my twenty part peal before I learnt that he had been over the same ground before.

 2314567  14
 3426175   1
-3461275  10
 4137652   2
-4176352   7
-1643752   8
-1637452  11
 6715324  12
 6752143   3
 7264531   4
-7245631   5
 2573416   6
-2534716  13
 5421367   9
-5413267   4

Notice the repetition of the 3 . The baby Q sets will therefore work. In the specimen course I have introduced a 7 for a 3 when the seventh bell is in the slow, and by this bobbing we have thirty true touches of two courses each, and all called alike.

Now attention, please, for we are going off the old road. Let us examine the five sixes in which the seventh does her slow work.

You see that they come from two different plain courses, 12 3 4 being in VI, and 5 6 in II. If we call a bob as the seventh comes in we shall have a 4 instead of a 12 , and then leaving out the bob in the middle of the slow work we shall return to our original place as: - 4 5 7 5 6 . There are two 5s here. The Baby Q sets will remove the first, and it now reads: - 4 - 12 - 7 5 6 . Write them side by side and compare them thus:-

 1637452  11   1637452  11
 6715324  12  -6714352   4
 6752143   3  -6743152  12
 7264531   4 -7361452   7
-7245631   5   7315624   5

What do you notice? That all the rows are different! No! no! not that. A boy scout would not have given so soft an answer. Look at 6. She is in the slow with 7 at all the sixes whose characters we have changed.

Hence it follows that if I make this alteration in the calling every time that I find the 6th in the same position (2nd's place) at an 11 all the 4s with the 6th in the slow which were in the third row will move to the first, while all the 12s will drop into the second row.

And what has happened to the third row of the changed part? Instead of a 3 we now have a 7 with the sixth in the slow.

But 3 and 7 are always willing to oblige. The Baby Q sets will change one into another at a moment's notice. We have only to look for 3671452, where the 7th is in quick, and its nine brethren with 6 in the same place, and we shall get rid of the ten 7s that repeat and put back the ten 3s that we have dropped. By this process we change the form and the number of the thirty true round blocks that we had, but the resulting touches are as true as were the original thirty.

This I call a Giant Q set, and it deserves its name, for it alters 20 courses instead of 4 as the Baby Q sets do.

There are six Giant Q sets in all - one for each of the working bells. Let us use the one that we have already examined, with the sixth in the slow.

Oh here we are, I told you so. Here we are at the Lily Lakes, where the Islands slide. Four and twenty Islands! Four and twenty round blocks, all ready to slide, and the Baby Q sets still ready to push them about.

Let us try how we can push them into one long line to form the thirty mile ride - the peal that we are seeking to put together.

    A         B         C         D         E         F  
 2314567   4263157   6412357   3214657   3126457   4621357  
 3426175   2345671   4265173   2435176   1635274   6145273  
-3461275  -2356471  -4251673  -2451376  -1652374  -6152473  
 4137652   3627514   2147536   4127563   6217543   1267534  
-4176352P  3671245  -2175436  -4175263P -6275143  -1275634  
-1643752P  6134752  -1524736  -1542763P -2561743  -2516734  
-1637452  -6147352  -1547236  -1527463  -2517643  -2567134  
-6714352   1765423   5713462B  5716234   5724136B  5723641  
-6743152   1752634   5736124B  5763142   5743261B  5734216  
-7361452   7213546   7652341   7354621   7356412   7451362  
 7315624  -7235146  -7623541  -7346521  -7364512  -7413562  
 3572146   2574361   6374215   3672415   3471625   4376125  
-3521746  -2543761  -6342715  -3624715  -3416725  -4361725  
 5134267   5326417   3261457   6431257   4632157   3142657  
-5142367  -5364217  -3214657  -6412357  -4621357  -3126457  

But first let us notice their nature. A and B are five-part touches and have been so shaped by the Giant Q set. There are two other five-part touches like them, which can be produced by transposing 2 with 3 and 4 with 1 at the course end.

This gives us four round blocks containing twenty courses. C, D, E and F are as they were and all the other courses can be had by transposing them from the course ends of A. So we have four five-course touches and twenty two-part touches.

Now set the Baby Q sets to work and all will soon be done. First of all I notice a bad blot in A. There is a six bob set. However, the Baby Q sets can soon deal with that; we will leave out the first two of the set. This allows the sixth to go on up behind, and we find ourselves in column D, and by leaving out the two corresponding bobs there we shall be able to return again. The two places are marked P in the courses. We have now introduced two 5s instead of two 7s; these must be found and bobbed out. They come up in C and E, and I have marked them B to show that two bobs must be introduced at these two rows.

Making these alterations every time that we come into these positions we find that the whole twenty-two round blocks affected become gather themselves together and become two long five-part round blocks each called alike.

    231456  2  4  5  6  7  8  9 10 12 14
a.  641235  -        -           -  -  -
d.  312645  -  -  -  -     -  -  -  -  -
b.  462135  -  -  -  -           -  -  -
d.  321465  -  -  -  -     -  -  -  -  -
e.  514236  -        -  -  -  -     -  -

And the whole peal is now in four round blocks: these two five-parts, and the two shown in B. Remains to put them together.

Turning to B, we find that of the two 3s in each course only one can be replaced by a 7. The other is involved in the Giant Q set and must not be changed.

Alter, then, the calling of the following Baby Q sets.

 3417526o  4713526e
 3467251o  4763251e

The extras will join one of the two Bs on to one of the long parts and the omits will join the two long parts together. Thus the peal is in two parts, and an obliging S at 11 in the first course will join the two together. Let me give a table of course ends of the callings used, and by lettering them we shall save much space in writing it out.

   231456  2  4  5  6  7  8  9 10 12 14
a  641235  -        -           -  -  -
b  541326  -  -  -  -           -  -  -
c  614325  -        -     -  -  -  -  -
d  514236  -  -  -  -     -  -  -  -  -
e  614325  -        -  -  -  -     -  -
f  612435  -  -     -           -     -

THE PEAL

231456
251643 S
145632 4f
641235 S
426315 2d
316254 4a
462135 c
321465 d
514236 e
624513 a |
145623 d |
265413 b | A
154263 d |
342516 e |
652431 a
123564 c
435216 e
213546 4A
653214 a
132654 d
562314 b
423651 c
563241 b
432561 d
125346 e
231456 2A

The first of the two courses marked S is produced by

2  6  10  (11S)  13  17

and the second by

2  4  6  (8S)  9  11

There is 'The thirty mile ride'. What do you think of it? May you reach the last milestone as safely in the tower as I have done on paper. And so the schoolmaster bids you all adieu, and returns to his boys.

E. B. J.


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Last updated 29/08/96