CONDUCTING GRANDSIRE TRIPLES
by John Heaton of Derby Cathedral.
Grandsire Triples is a method that causes problems for people. Although it is not difficult to ring, many find it quite hard to call and even more difficult to keep right. Conductors can feel very isolated from the world and as the sweat pours from their brow they long for the time when they can call 'that's all' and finally relax. This article is intended to come to the rescue of those who aspire to call Grandsire Triples and thus capture the admiration of those who gave up long ago. Although some prior knowledge of Grandsire Triples and the conducting of the more regular methods (and the willingness to face the enemy!) is assumed, it is not necessary to be one of those people whose idea of relaxation is to mentally solve the mysteries of the Universe whilst composing a peal at the same time as calling another one and keeping everyone right. The only quality required for the quest ahead is courage.
In order to conquer Grandsire Triples it is necessary to identify exactly what the nature of the enemy is. Once its Achilles Heel has been found we can cut the enemy down to size. To do this we must first look at the problems of calling Grandsire Triples. These are twofold, as in any method. The first problem is how to call the touch or peal in the first place and the second problem is how to keep it right when it falls apart.
The techniques to be described can be adapted for other Triples methods or methods on higher numbers because they apply to the events that occur at a call and do not depend upon the ordinary work of the method.
2. CALLING GRANDSIRE TRIPLES
The calling of Grandsire Triples is not that difficult. The most important point is that most calls come a lead earlier than expected. This is so because calling positions are named, as in other methods, by where the observation bell ends up as a result of the call and not by where it would have been without the call. At a call in Grandsire, most bells end up advanced by one lead and so most of the calls must be anticipated by one lead.
As most people find that they soon 'get the hang' of actually making the calls, no more will be said about it except to say that there is no substitute for practice. What will be described, however, is the naming convention to be used in the rest of this article.
3. NAMING CONVENTION
Unless otherwise stated, the term observation bell will refer to the 7th. Table 1 gives the names of all the calling positions as used in this article. This should be studied at this point because there are other ways of naming calling positions. The first point to notice is that many people refer to the dodge at 4-5 up as a Middle and that at 6-7 down as a Wrong. In one sense this is a consistent way to name these calling positions but in another sense, it makes it harder to relate the calling positions of Grandsire Triples to those in more standard methods. The same arguments apply to other odd-bell methods, to which the same naming convention can be applied.
Call Work At The Call Name Of Call
bob and single double dodge in 6-7 down Middle (M)
bob and single double dodge in 6-7 up Home (H)
bob and single double dodge in 4-5 up Wrong (W)
bob and single double dodge in 4-5 down Out (O)
bob only make thirds and go into the hunt In (I)
bob only make thirds unaffected Before (B)
single only make long thirds Thirds At A Single (Ts)
single only make seconds and go into the hunt In With A Single (Is)Table 1 - the names of the calling positions.
4. CONDUCTING GRANDSIRE TRIPLES - THE TRADITIONAL METHOD
Table 2 gives the figures of the Plain Course of Grandsire Triples. From this it can be seen that in the first lead, after the Treble, all the bells come to lead in the order 234675. In the second lead the bells lead in the order 253467. In the subsequent leads the bells come to lead in the orders: 275346, 267534 and 246753. In order to conduct Grandsire in the old style, the conductor would learn this coursing order. He would notice that at each lead end the last bell in the coursing order must be moved into the second position and that the first bell was always the hunt bell.
Table 2 - the Plain Course of Grandsire Triples1234567 1253746 1275634 1267453 1246375
2135476 2157364 2176543 2164735 2143657
2314567 2513746 2715634 2617453 2416375
3241657 5231476 7251364 6271543 4261735
3426175 5324167 7523146 6725134 4627153
4362715 3542617 5732416 7652314 6472513
4637251 3456271 5374261 7563241 6745231
6473521 4365721 3547621 5736421 7654321
6745312 4637512 3456712 5374612 7563412
7654132 6473152 4365172 3547162 5736142
7561423 6741325 4631527 3451726 5371624
5716243 7614235 6413257 4315276 3517264
5172634 7162453 6142375 4132567 3152746
1527364 1726543 1624735 1423657 1325476
To take this system a bit further it is necessary to see what happens when a bob or single is called. It is easy to write out the first lead of the Plain Course and put a bob at the end and the continue with the second lead. If this is done it can be seen that the coursing order of the second lead is 752346. In other words, at a bob, the conductor simply has to put the last two bells first to obtain the new coursing order from the old. The new hunt bell is the bell that ends up at the start of the new coursing order.
The situation at a single is similar except that the last two bells are placed first and the swapped over. Thus a single at the first lead end would produce the new coursing order 572346.
Although this system of conducting is very simple on paper, when it comes to mentally manipulating 6-figure numbers at every lead end (360 of them in a peal) whilst ringing, calling and correcting, it becomes very easy to forget to do a transposition from time to time or to forget the coursing order altogether. What is needed is a system that:
1) uses calling position names that correspond to more standard methods,
2) has a coursing order as similar as possible to that of more standard methods,
3) uses familiar transpositions that correspond to those of more standard methods,
4) does not include more bells than necessary in its coursing order,
5) has a coursing order that remains constant throughout a course.
The first point was dealt with in section 3 and the remaining points will be dealt with in the following sections.
5. AN ALTERNATIVE COURSING ORDER
The system to be described satisfies all of the requirements mentioned above. To see what the basic coursing order is, look again at the Plain Course of Grandsire Triples in Table 2. This time, ignore the hunt bell (2nd) and see what is the order of the bells leading on the first lead. This is 34675. In the second lead the bells lead in the order 53467. In the next three leads the orders are 75346, 67534 and 46753. It can be seen that all these rows are rotations of each other and that if the normal practice of rotating the coursing order so that the observation bell comes first is observed, as in other methods, then all leads have the same basic coursing order 75346. The bell that is missing from this coursing order is the 2nd, which is the hunt bell. As will be seen later, the hunt bell is always absent from the coursing order, so it is always easy to determine which bell is in the hunt. Omitting the observation bell from this coursing order as usual gives us the final basic Plain Course coursing order of 5346.
This basic coursing order is only four figures long, strongly resembles that of more standard methods and remains constant throughout a course in the same way as in standard methods. If the hunt bell is ignored, it can be seen that this coursing order can be derived from any lead head of Grandsire Triples by the same process as for more standard methods. In this system, the hunt bell is regarded as being part of the Treble and it is possible to regard Grandsire Triples as Plain Bob Minor with a 'thick Treble'. In conducting the Plain Course, all that is required is to remember that the hunt bell always courses the Treble and its position can therefore always be determined.
5.1 THE EFFECT OF BOBS ON THE COURSING ORDER
Bobs affect this coursing order in a similar way to the effect of bobs at the same calling places on the coursing order of more standard methods. This is a desirable property and greatly simplifies the system.
5.1.1 Bobs At Home
To see the effect of a Bob at Home, the following diagram gives the rows that would be produced by the call.
Table 3 - course end brought up by a bob at Home4315276
The call has produced the row 1342567, which is a course end because the 7th is at Home. Obviously, without the call, the course end 1234567 would have been produced. If the course end 1234567 has the coursing order 5346 then the course end 1342567 must have the coursing order 5426. This is seen by simply taking the bells in the row 1342567 that correspond to the bells in the same position in the row 1234567 and comparing them with the coursing order 5346.
It can be seen that to produce 5426 from 5346, the bells affected are the middle pair. This corresponds to the Home in more standard methods where it is the middle three bells of the coursing order that are affected by the bob. In addition, the affected bells can be imagined to be rotated to the left by one position as in more standard methods, with the old hunt bell appearing at the end of the pair and the first of the pair disappearing.
From Table 3 it can be seen that the bell that disappears is the one that makes the bob and goes into the hunt, the bell that moves one place to the left is the bell that makes 3rds unaffected and the bell that appears is the one that has come out of the hunt. This corresponds closely to the situation in a more standard method where the first bell of the three affected makes the bob and is moved to the end, the middle bell of the three runs out and moves one place to the left and the last bell of the three also moves one place to the left.
In addition to the bells that change places in the coursing order it is also very easy to decide what the remaining bells should do at the bob. The first bell in the coursing order, i.e. the bell immediately to the left of the two affected bells, will be double dodging in 4-5up whilst the bell at the end of the coursing order, i.e. the bell immediately following the two affected bells, will be double dodging 6-7down. The 7th will be double dodging in 6-7up because this is a bob at Home.
With this transposition it is easy to keep track of the changes in coursing order caused by bobs at Home, and to watch the bells making the bob as it happens.
5.1.2 Bobs At Wrong
If the description of the bob at Home has been understood then the bob at Wrong will not cause any difficulty. In fact, the transposition for the bob at Wrong is the same as for that at Home except that it is the first two bells in the coursing order that are affected along with the old hunt bell. This is in correspondence with the transposition for more standard methods in which a bob at Wrong affects the first three bells in the coursing order. Table 4 gives the lead head produced by a bob at Wrong.
Table 4 - lead head brought up by a bob at Wrong3517264
In this case, the lead head produced by a bob at Wrong is 1532746 whilst the Plain Course produces the lead head 1253746 when the 7th dodges 4-5up. By comparing these rows and seeing how the Plain Course coursing order is derived from the second one, it can be seen that the new coursing order caused by a bob at Wrong is 3246. Once again, the first bell of the affected pair is the one that makes the bob and goes into the hunt, and disappears from the coursing order. The second of the affected pair moves one place to the left and is the bell that makes 3rds unaffected, whilst the old hunt bell becomes the second bell in the coursing order.
The work of the remaining bells follows in the same way as it did for the bob at Home. The 7th is double dodging 4-5up by the definition of the Wrong as given earlier, the bell immediately following the two affected bells is double dodging 6-7down as at the bob at Home, and the bell following that in the coursing order, the last bell, is double dodging 6-7up.
In summary, the affect of a bob at Wrong is the same as that of a bob at Home except that it is the first two bells in the coursing order that are affected instead of the middle two.
5.1.3 Bobs At Middle
In the same way that the bobs at Home and Wrong have been similar to the corresponding calls in more standard methods, so to is the bob at Middle. Once again, it is useful to look at the rows produced in the Plain Course when the 7th double dodges in 6-7down and compare them with the rows produced by a bob at Middle. Table 5 gives the rows.
Table 5 - lead head brought up by a bob at Middle6413257
Table 5 shows that a bob at Middle brings up the lead head 1462375 whereas the lead head that is produced by a plain lead as the 7th dodges in 6-7down is 1246375. Inspection of these two rows shows that the new coursing order after a bob at Middle is 5362, with the 4th in the hunt and therefore absent from the coursing order. The transposition from the old coursing order to the new one is exactly the same as for bobs at Wrong and Home except that the affected bells are now the last pair in the coursing order. Again, this corresponds to the bob at Middle in more standard methods where it is the last three bells in the coursing order that are affected.
Following the usual pattern of which bells are doing which work at the bob, the bell immediately to the left of the affected pair is double dodging in 4-5up, the bell immediately before that is double dodging in 6-7up and the 7th is double dodging in 6-7down. The bell that disappears from the coursing order, the first one of the affected pair, makes 3rds and goes into the hunt, the bell that moves one place to the left makes 3rds unaffected whilst the old hunt bell dodges 4-5down and appears at the end of the coursing order.
5.1.4 Bobs Before
A bob Before is slightly more complex than those so far described. However, as will be seen, there is a strong resemblance between the Before in Grandsire Triples and that in more standard methods. Table 6 shows the rows produced by a bob Before.
Table 6 - lead head brought up by a bob Before7614235
The row brought up by a plain lead when the 7th makes 3rds is 1275634. By comparing this row with the lead head brought up by the bob Before we can see that the new coursing order is 2534. The old hunt bell has appeared at the start of the coursing order and the last bell in the old coursing order has disappeared and gone into the hunt. This transposition bears a strong resemblance to that for the Before in more standard Major methods, in which the last bell disappears from the end and is moved to the front.
The work performed by each bell follows in exactly the same order as for the previous calling places. The bell immediately before the affected bells double dodges in 4-5up. The bell before that one double dodges in 6-7up. The bell before that (the first bell in the original coursing order) double dodges in 6-7down. The old hunt bell double dodges in 4-5down and the 7th makes 3rds unaffected.
5.1.5 Bobs At In
A bob at In does not have an equivalent in the more standard methods, but nevertheless, is reasonably straightforward. Two small compromises to the elegance of this coursing order system have to be made; a bob at In produces a five-figure coursing order and this coursing order changes at each lead end. However, a five-figure coursing order is exactly what more standard methods have and the change that must be made at each lead end is simple.
Table 7 gives the figures produced by a bob at In and also for the whole of the succeeding lead.
Table 7 - lead brought up by a bob at In5716243
Table 7 shows that the 7th has gone into the hunt. This means that all the other bells must be included in the coursing order. The coursing order for this lead is 52346 because that is the order in which all the bells lead after the 7th has lead.
The original coursing order was 5346 and after a bob at In, the next lead has the coursing order 52346. Therefore the transposition required at the time the call is made is simply to add the old hunt bell into the coursing order in second position. Following the usual pattern, the bell following this in the coursing order is the one that double dodges in 6-7down, the next double dodges in 6-7up, and the last double dodges in 4-5up. The 7th is the bell that makes 3rds and goes into the hunt and the first bell in the coursing order makes 3rds unaffected.
The lead head brought up by the bob at In was 1752634 which gave a coursing order of 52346. The next lead head to be produced is 1765423, which by analogy to the previous lead head, must correspond to a coursing order of 65234. As a result, it is necessary when the 7th is in the hunt to rotate the coursing order at each lead end. If the lead starting from 1765423 is written out it will be seen that the bells do indeed come to lead in the order 65234.
This rotation must be done at each lead end at which the 7th remains in the hunt. When the time comes to call the 7th out of the hunt the rotation is not performed at that lead end because the transposition to be given next for this call takes into this account.
5.1.6 Bobs At Out
Table 8 gives the rows produced by calling the 7th out of the hunt at the lead end following its being called In from the Plain Course.
Table 8 - lead head brought up by a bob at Out from the position in table 76413725
Table 8 shows that when the 7th is called out of the hunt when the coursing order is 52346, this becomes 5236 with the 4th in the hunt. This can be seen to be so by comparing the row 1467352, brought up by the bob at Out, with the row 1267453, which is the Plain Course lead head that occurs as the 7th dodges 4-5down.
The transposition at a bob Out is therefore to drop the 4th bell in the coursing order, and this bell is the one that becomes the new hunt bell by making 3rds. The first bell in the coursing order double dodges in 6-7down, the second double dodges in 6-7up, the third double dodges in 4-5up and the final bell makes 3rds unaffected.
5.1.7 Summary Of Transpositions For Bobs
Table 9 gives a symbolic summary of all the transpositions developed so far. In this table, the letters represent arbitrary coursing orders and the letter in brackets represents the hunt bell.
Position From abcd (e) Example
Home aced (b) 5346 (2) to 5426 (3)
Wrong becd (a) 5346 (2) to 3246 (5)
Middle abde (c) 5346 (2) to 5362 (4)
Before eabc (d) 5346 (2) to 2534 (6)
In aebcd (7) 5346 (2) to 52346 (7)
Out abcde (7) to abce (d) 52346 (7) to 5236 (4)
Table 9 - summary of transpositions for bobs
5.2 THE EFFECT OF SINGLES ON THE OURSING ORDER
Rather than go through a procedure of describing in detail the effect of singles at each calling position, this section will only present a table summarising the transpositions for singles. It will use the more symbolic form used in table 9.
Position From abcd (e) Example
This table should be self explanatory, but it is recommended that the reader write out the rows produced by a call at each calling position and prove to himself that these transpositions are correct.Home abed (c) 5346 (2) to 5326 (4)
Wrong aecd (b) 5346 (2) to 5246 (3)
Middle abce (d) 5346 (2) to 5342 (6)
Long Thirds ebcd (a) 5346 (2) to 2346 (5)
Seconds deabc (7) 5346 (2) to 62534 (7)
Out abcde (7) to abcd (e) 52346 (7) to 5234 (6)
Table 10 - summary of transpositions for singles
In general, the transposition at a single affects the same pair of bells as at a bob, but all that needs to be done is to swap the second bell of the pair with the old hunt bell. The bell that is swapped is the bell that makes seconds and goes into the hunt. The old hunt bell double dodges in 4-5down. The bell that immediately follows the bell that makes seconds in the coursing order is the bell that double dodges in 6-7down. The next bell is the bell that double dodges in 6-7up. The next bell is the bell that double dodges in 4-5up. The next bell, which is the bell immediately to the left of the bell that makes seconds, makes long thirds.