COURSING ORDER TRANSPOSITIONS - THE COMPLETE SET

 

In previous sessions we have seen how the coursing order of Minor methods is derived and is affected by all the calls where the Tenor, or observation bell, is unaffected. In this session we will revise these and we will add the remaining transpositions for the calls where the Tenor, or observation bell, is affected. In other words, by the end of this session you will have the information to transpose the coursing order for any call whatever in Minor.

 

Doubles Revisited

 

Very early in the course we dealt with the transposition of bobs at Home and found that 324 was transformed into 243, or that ABC was transformed into BCA. We also saw that this transposition was the basis of all the transpositions for Doubles except that the added complexity of keeping the Tenor at the start of the coursing order imposed a rotation of the coursing order to do just that. The transpositions that we derived were the sum of the basic BCA transposition and the rotation.

 

It will be useful at this stage to revise the transpositions but first we will look at what ABC becoming BCA tells us about what each of the affected bells is doing at the bob. Here is the last lead of a course of Plain Bob Doubles ending with a bob:

 

                        14253

                        41523

                        45132

                        54312

                        53421

                        35241

                        32514

                        23154

                        21345

                        12435

                    -   14235

 

Here we have the coursing order 324 becoming 243. 324 is ABC and 243 is BCA. Notice that bell 3 (bellA) makes the bob, bell 2 (bell B) runs out and bell 4 (bell C) runs in. This is true of Homes in Plain Bob Doubles and Bristol Surprise Maximus.

 

Similarly, at any of the calling positions there will be three bells ABC consecutive in the coursing order which will become BCA where A makes the bob, B runs out and C runs in. Observe a bob at the first lead end of Plain Bob Doubles:

 

            12345

                        21435

                        24153

                        42513

                        45231

                        54321

                        53412

                        35142

                        31524

                        13254

                    -   12354

 

The coursing order is (5)324 where bell 5 (bell A) makes the bob, bell 3 (bell B) runs out and bell 2 (bell C) runs in. If we apply ABC => BCA to the affected bells, 5, 3 and 2, we get 32(5)4. This is what we now rotate to give (5)432 and hence the overall transposition is 324 => 432.

 

If we look at the second and third lead ends we get:

 

                        13524              15432

                        31254              51342

                        32145              53124

                        23415              35214

                        24351              32541

                        42531              23451

                        45213              24315

                        54123              42135

                        51432              41253

                        15342              14523

                    -   13542          -   15423

 

In the left hand column we have the three bells 4, 5 and 3 affected where bell 4 (bell A) makes the bob, bell 5 (bell B) runs out and bell 3 (bell C) runs in. If the coursing order is (5)324 we see that these three bells indeed appear in the coursing order (allowing for "wrapping round") in the order 453 and the same rules about ABC => BCA, including which work each does, are preserved.

 

In the right hand column we have the three bells 2, 4 and 5 affected where bell 2 (bell A) makes the bob, bell 4 (bell B) runs out and bell 5 (bell C) runs in. If the coursing order is (5)324 we see that these three bells indeed appear in the coursing order (allowing for "wrapping round") in the order 245 and the same rules about ABC => BCA, including which work each does, are preserved.

 

The observation that at each calling place there are three bells ABC consecutive in the coursing order which will become BCA and which will, make the bob, run out and run in respectively tells us immediately which of these three bells we are if we are ourselves affected at a bob. We therefore know which other two bells must be affected and what they must be doing:

 

If we make a bob we must be bell A and therefore bells B (running out) and C (running in) must be the two bells in the coursing order immediately following ours.

 

If we run out at a bob we must be bell B and therefore bells A (making the bob) and C (running in) must be the bells on either side of ours in the coursing order.

 

If we run in at a bob we must be bell C and therefore bells A (making the bob) and B (running out) must be the two bells in the coursing order immediately before ours.

 

Although we have used Doubles to illustrate that ABC => BCA at each call and that bell A makes the bob, Bell B runs out and bell C runs in the same is true of any method on any number of bells (where "any methods" excludes methods with funny bobs such as Grandsire and Stedman).

 

Tenor-Affected Calling Places In Minor

 

In previous sessions we have looked very closely at how the transpositions for each calling place could be derived. At this stage such derivation of the remaining ones is left to the interested reader but as such readers are likely to be rare we will not included it here. Instead we will give the transpositions and they can be accepted on trust. We will, however, relate them to the discussion above about bells A, B and C. We should also bear in mind the transposition for a single, ABC => CBA, where bell A makes the bob, bell B makes 2nds (would have run out at a bob) and bell C makes 3rds (would have run in at a bob).

 

The calling positions we must deal with are calls at 4ths (bob and single), bobs before and calls at in (bobs) and 3rds (singles).

 

Bobs At 4ths

 

If the Tenor makes 4ths at a bob it must be bell A. Therefore, given the coursing order (6)5324, bells A, B and C must be bells 6, 5 and 3. When the transposition is done (6)53 becomes 53(6) and so the complete coursing order is now 53(6)24. This is rotated to get the 6th back to the start to give (6)2453.

 

Thus the overall transposition for a bob at 4ths is to put the first two bells last. 5324 => 2453. One could put the last two first but if one thinks of it as putting the first two last then this applies to all numbers of bells.

 

Singles At 4ths

 

If the Tenor makes 4ths at a single it must be bell A. Therefore, given the coursing order (6)5324, bells A, B and C must be bells 6, 5 and 3. When the transposition is done (6)53 becomes 35(6) and so the complete coursing order is now 35(6)24. This is rotated to get the 6th back to the start to give (6)2435.

 

Thus the overall transposition for a single at 4ths is to put the first two bells last and swap them. 5324 => 2435. One could swap the first two and then put the last two first but if one thinks of it as putting the first two last and swapping them then this applies to all numbers of bells.

 

Bobs Before

 

If the Tenor runs out at a bob it must be bell B. Therefore, given the coursing order (6)5324, bells A, B and C must be bells 4, 6 and 5. If we rewrite the coursing order to make things easier by putting the three affected bells together we might write it as, say, 24(6)53. When the transposition is done 4(6)5 becomes (6)54 and so the complete coursing order is now 2(6)543. This is rotated to get the 6th back to the start to give (6)5432.

 

The overall transposition is to put the last bell second. 5324 => 5432. One could put the middle two bells last but if one thinks of it as putting the last one second then this applies to all numbers of bells.

 

Bobs At In

 

If the Tenor runs in at a bob it must be bell C. Therefore, given the coursing order (6)5324, bells A, B and C must be bells 2, 4 and 6. If we rewrite the coursing order to make things easier by putting the three affected bells together we might write it as, say, 24(6)53. When the transposition is done 24(6) becomes 4(6)2 and so the complete coursing order is now 4(6)253. This is rotated to get the 6th back to the start to give (6)2534.

 

The overall transposition is to put the next to the last bell first. 5324 => 2534. One could put the first two bells into the middle but if one thinks of it as putting the next to the last one first then this applies to all numbers of bells.

 

Singles At 3rds

 

If the Tenor makes 3rds at a single it must be bell C. Therefore, given the coursing order (6)5324, bells A, B and C must be bells 2, 4 and 6. If we rewrite the coursing order to make things easier by putting the three affected bells together we might write it as, say, 5324(6). When the transposition is done 24(6) becomes (6)42 and so the complete coursing order is now 53(6)42. This is rotated to get the 6th back to the start to give (6)4253.

 

Thus the overall transposition for a single at 3rds is to put the last two bells first and swap them. 5324 => 4253. One could swap the last two and then put the first two first but if one thinks of it as putting the last two first and swapping them then this applies to all numbers of bells.

 

Summary Of All Calling Places Of Doubles And Minor

 

We have now covered bobs and singles at every calling place in Doubles and Minor. There are four in Doubles and, including bobs and singles, ten in Minor. There is little choice but to learn them and the best way to do this is to call touches that use calls at just a couple of calling places and practice just those transpositions. In time they become familiar.

 

The job of remembering the transpositions can be made easier if the ways of looking at them as described above are observed. The summary below reiterates these.

 

Bobs In Doubles

 

Basic transposition ABC => BCA

 

Call                 Comments                                                                              Example

 

4ths:                 Tenor is bell A. Put first two last                                                324 => 432

B:                     Tenor is bell B. Put last one second (swap last two)                   324 => 342

I:                      Tenor is bell C. Put next to last one first (swap first two)            324 => 234

H:                     Tenor is unaffected. Basic transposition                                     324 => 243

 

 

Bobs In Minor

 

Basic transposition ABC => BCA

 

Call                 Comments                                                                              Example

 

W:                    Tenor is unaffected. Basic transposition on first three                 5324 => 3254

4ths:                 Tenor is bell A. Put first two last                                                5324 => 2453

B:                     Tenor is bell B. Put last one second                                           5324 => 5432

I:                      Tenor is bell C. Put next to last one first                                     5324 => 2534

H:                     Tenor is unaffected. Basic transposition on last three                  5324 => 5243

 

 

Singles In Minor

 

Basic transposition ABC => CBA

 

Call                 Comments                                                                              Example

 

W:                    Tenor is unaffected. Basic transposition on first three                 5324 => 2354

4ths:                 Tenor is bell A. Put first two last and swap them                        5324 => 2435

B:                     Tenor is bell B. Swap the bells at each end                                5324 => 4325

3rds:                 Tenor is bell C. Put last two first and swap them                        5324 => 4253

H:                     Tenor is unaffected. Basic transposition on last three                  5324 => 5423

 

 

Some Useful Touches

 

Touches of Plain Bob Doubles are completely covered in the notes for Session 4. The same touches can be used or adapted for other Doubles methods such as St. Simon's and St. Martin's, or indeed any Doubles method with one hunt bell and a bell making 2nds as the Treble leads.

 

The touches of Plain Bob Minor so far given should be revisited so that practice is gained in the Tenor unaffected calling places. Below is a selection of touches that together include all calling places:

 

 

72                                72                                72                                168

W I      23456              4th       23456              B H      23456              B I       23456

 -  -       23456              -          54326              -   -      23456              -  -       45236

 -          23456                                                  -  -      23456

 

The touches of 72 are interesting because they show that the transpositions for certain pairs of calls cancel each other. That for in I is the reverse of that for a W, that for a 4ths is the reverse of itself and that for a B is the reverse of that for a H.

 

 

120                                                      120

W 4th B I H     23456                          4th I H             23456

      -                 54326                                2                52436

 -        -  -  -     23456                          -       -             23456

 

The first 120 is actually a bob every other lead and it uses all five calling places so is good practice for conductors. Not only that but every bell does everything at a bob and so is a good exercise for learners. The second 120 has the 5th unaffected all the way through and is the basis of a 720 built to the same plan as the standard 720 W H W. The 2 in the I column simply means that two bobs at I must be called which, for Plain Bob, are at consecutive lead ends.

 

 

240                                                      360/720

W 4th B I H     23456                          4th I H             23456

 -            2        35426                                2                52436

 -   2          -     42356                          -                      34256

            2    -     23456                          Repeat twice. For 720

                                                            call S H at the end of

                                                            the 3rd part and repeat

the whole.

 

The 240 is similar to the first 120 in that all calling places are used and every bell does everything. It is really a 5-part touch, B P P B five times. The 360/720 is the standard calling.

 

 

120                              120                                          120                              120                                          120

W        23456              4th 3rd             23456              B          23456              4th 3rd             23456              H         23456

S          53426              S                      34526              S          23546                    S                52346              S          24356

S          23456                    S                23456              S          23456              S                      23456              S          23456

 

These 120s allow practice at transposing singles at just one or two calling places and show that singles can be called in pairs to cancel each other. Longer touches can be built by including any of these touches inside another one.

 

 

72                                            120                              240

W 4th H           23456              W H     23456              W 4th B 3rd H             23456

 S   S   S          32456              S  S     54326              S             S                  25346

 S   S   S          23456              S  S     23456                          S                      25436

                                                                                     S  SS           S             43256

                                                                                                S  S  S             23456

 

The 72 is a single at each lead end and the 120 is just like the W H W H touch with bobs but with singles instead. The 240 is like the bobs only 240 above but with singles called instead of bobs. It is a 5-part touch, S P P S five times. Each bell does everything and is an excellent touch for learners to practice their singles.

 

As a point of interest, in Plain Bob any two consecutive bobs can be replaced with two consecutive singles and two consecutive singles can be replaced with two consecutive bobs. Thus the standard touch can be varied as follows:

 

120                              120                              120                              120

W H     23456              W H     23456              W H     23456              W H     23456

 -   -     45236              -   S    54236              S  -     45326              S  S     54326

 -   -     23456              S   -    23456              -   S    23456              S  S     23456

 

Summary

 

In this session we have learned how to know what each of the bells A, B and C affected at a bob are doing. We have dealt with all the calling places where the Tenor or observation bell is affected and we have looked at a selection of touches that use these new calling places along with the Tenor-unaffected ones.