View source for Coursing Order in Stedman Triples

===by Derek Butterworth (transcribed from The Ringing World 1966 page 227)===

Many ringers believe that Stedman Triples is one of the easiest standard  methods to ring but one of the most difficult to conduct. Unfortunately, Stedman Triples has the peculiarity that even so-called experts tend to be easily displaced in the method when a trip occurs, particularly in the slow work. This has meant that many peals have been lost because the conductor has been unable to correct mistakes when they have occurred. Thus only those conductors who have exceptional memories, or exceptional bands, have been able to cope with this method. The following description of a “coursing order” technique should open the held of conducting Stedman Triples to many conductors who would normally avoid this method because of its lack of coursing order.

==Derivation and use of the Coursing Order==

The principle of Stedman is the combined effect of ringing alternate quick and slow three-bell sixes with the remaining bells dodging above thirds place. This results in the breaking up of the natural coursing order within each course. Nevertheless, a cyclic order exists in which the bells follow each other into the quick  or the slow work. This order, which I have called “the coursing order for Stedman Triples” is 7165234, using the 7th as the starting point in the cycle in the plain course.

'''Examples:'''

 (a) If 6 goes in quick, 5 is the next quick bell
 (b) If 4 goes in slow, 7 is the next slow bell

If a fixed bell is now chosen (I have chosen the 7th as this is usually the fixed bell in compositions of the method) and the coursing order written without it, then the following may be derived from the plain course and extended to apply to any course. The coursing order with the 7th as fixed bell is 165234. Let these six numbers be divided into three pairs and name them ''First'' pair, ''Quick'' pair and ''Last'' pair  respectively, viz:

  16     52     34
 ''First''  ''Quick''  ''Last''

Now in any course of Stedman Triples, without calls, the following facts apply. In each case given below, the bells which refer to the plain course are given in parentheses I suggest that a copy of the plain course is used to help comprehension.

1. Order of Dodging

The 7th dodges with the other bells in the order: ''First'', ''Quick'' after quick work (1652); and ''Quick'', ''Last'' after slow work (5234).

2. Order of Passing Bells

The 7th passes the other bells (i.e. 3-4 up, 5-6 up, 5-6 down, 3-4 down) in  the  order: ''Last'', ''First'' (3416).

3. Quick Work

When the 7th goes in quick, the two bells in the slow work are the ''Quick'' pair (52).

4. Slow Work

When the 7th goes in slow, the slow bells on the front are the ''Last'' pair (34). The quick bells which enter during the 7th’s slow work are the ''Quick'' pair (52), and the slow bells which enter are the ''First'' pair (16). 

From the above it will be realised that a ringer who knows the coursing order of any particular course of Stedman Triples which is being rung is potentially capable of checking the ringing and correcting, if necessary, any trips that may occur. This is of course assuming the ringer is capable of applying the information given. It now remains to describe how transposition of the coursing order may be carried out when bobs or singles are used.

==Transposition of Coursing Order==
The greatest difficulties associated with the transposition of coursing orders in Stedman are that the factors are complicated and two different types are required (one for quick and one for slow sixes). If one limits the compositions used to those which work on a twin bob plan, then each pair of bobs may be transposed together, resulting in easy transposition factors. A table of factors for twin bob peals is given below. It will be noticed that once the four bells which are affected at a twin bob have been isolated the transposition function is always the same (1234 becomes 2143).
                        transpose by
 Bobs at        3.4 (S)    214356
                5.6 (H)    132546
                7.8 (L)    124365
              12.13 (Q)    213465
 Singles at 9 or 14 (V)    612345
            2 or 11 (VI)   234561 

Using this table, the coursing order of any twin bob peal of Stedman Triples may be followed throughout. The amount of mental effort required in transposition may be reduced by limiting the type of composition used to one which is based on a three-course block plan. By the use of these compositions only five numbers need be transposed and the number of transpositions may be reduced by transposing adjacent twin bob pairs together. As an illustration of the above, a Thurstans' block is given showing firstly how only five bells need be transposed, and secondly how twin bob pairs are transposed together.

== Transposition of Thurstans' Block==
Let the coursing order of a course, before calling Thurstans' block, be 162345; then transposition of this block is as follows:

       162345
       ------
 3.4   613245
 7.8   612354
 3.4   163254
 5.6   136524
 12.13 316542
 5.6   361452

Note the path of the 6th through the coursing orders. If this is committed to memory then the following transposition factors may be used.
                    transpose by
 Bobs at 3.4 (S)       13245
         5.6 (H)       12435
         7.8 (L)       13254
       12.13 (Q)       21354
 Singles at 2 or 11    23451
            9 or 14    51234

Note the effect of a single on the position of the 6th as given in the full peal composition given later. 

If adjacent twin bobs are transposed together, then:
                    transpose by  
 3.4 and 5.6           13425
 3.4 and 7.8           12354

If these are used care must be taken between calling positions not to apply the wrong coursing order. For compositions such as Thurstans’ reversed or Brooks' variations, then the five-figure transposition factors will have to be determined for these compositions. The factors given are suitable for the following compositions: Thurstans’, Dexter’s No. 1 and No. 2, variations of Thurstans' and Washbrook's variation (this is not the usual composition associated with Washbrook). 

An example of how the coursing orders are transposed throughout a peal is given below. If 5-number transpositions are used, then ignore the 6th, and if adjacent twin bob pairs are transposed together, ignore the coursing orders which are in black type figures.

Once the basis of this coursing order technique has been mastered, extensions of its usefulness may be developed. As in standard Major methods the coursing order may be utilised to predict those bells which will be affected at the calls and to facilitate the actual calling of the bobs and singles, so too the coursing order in Stedman may likewise be used. These will however, become evident to those who require them by the use of pencil and paper and clarification is not necessary therefore. 

The great advantage of using the coursing technique outlined is that the progress of the ringing may be checked constantly throughout with about the same amount of mental effort required to conduct a peal of Surprise.

== Dexter's No. 1 Variation of Thurstans' 4-Part==
                                    Course end                      Coursing orders                 at course end            
 2   3.4   5.6   7.8  12.13  14       231456       2       3.4      5.6      7.8     12.13      14     165234 
 ------------------------------       ------     ------------------------------------------------------------
      x           x             |     246351              612534            615243
      x     x           x       |     432561              162543   126453            216435
            x                s  | A  (135462)                      261345                     526134  
            x                   |     315426                       562314
 ------------------------------       ------     ------------------------------------------------------------
              2A                      523416                                                           361524
 ------------------------------       ------     ------------------------------------------------------------
      x           x             |     546213              635124            631542
      x     x           x       | B   425163              365124   356412            536421
            x                   |     245136                       563241
 ------------------------------       ------     ------------------------------------------------------------
              3B                      351246                                                           164352
 ------------------------------       ------     ------------------------------------------------------------
      x           x             |     326541              613452            614325 
      x     x           x       | C   253461              163425   136245            316254
 s                              |     541326     162543    
 ------------------------------       ------     ------------------------------------------------------------
       3B, C, 3B, C, 4B               231456                                                           165234
 ------------------------------       ------     ------------------------------------------------------------

==References==
* ''The Ringing World'', No 2868, 7 Apr 1966, pg 227.