Corrected version of article from the Ringing World August 21, 1992
The "book" beloved of minor enthusiasts is the 1931 Collection of Doubles and Minor Methods, which contains a lead of each of the 141 Treble Dodging methods that have Plain Bob lead-heads and no 5-6 places (except the half-lead) or single changes. A long-standing challenge has been to ring the most methods in seven extents, with the limit now at 79 (page 748). For Surprise the maximum is 37 methods in seven extents, with ten extents needed to ring all 41.
Philip Saddleton's new arrangements make it possible at long last to ring all 41 Surprise in a normal length peal. Although they won't appeal to the six-bell purist who disdains singles and multi-extent blocks, most ringers will welcome them as a lesser evil than half-lead spliced.
The idea behind the callings is so simple that its late discovery is quite surprising. It starts from the observation that every Carlisle-above method has a Cambridge-above analogue. For an extent of any regular method with Carlisle backwork and an out-of-course extent of a regular method with Cambridge backwork, the 5-6 sections of a lead or course can always be exchanged between the extents. Figure 1 shows leads of Beverley and Carlisle from two such extents. If their 56 sections (blocks b and e) are exchanged, Carlisle turns into Chester and Beverley into Cambridge.
A lead-for-lead exchange is only possible here because the b and e blocks end with the same row - this is why Beverley and Cambridge (and Chester and Carlisle) have the same lead-end. If we choose method pairs whose 5-6 sections end in different rows, a substitute block will still link to a 3-4 section from the same course as the one it replaces (since every 56 section must produce a regular method for both backworks); in this case we just exchange all the 5-6 sections of the two courses.
This is a variation of the cross-splice for plain methods. Usually, blocks of rows are exchanged between an in-course 360 of a method and its complementary out-of-course 360. In Philip's splice the starting blocks are mutually false (they contain the same 720 rows); after an exchange they are no longer individually true, but each row is still guaranteed to occur twice.
| Exchanging blocks | b and e in leads of ... | Produces these | leads of ... |
| Carlisle | Beverley | Chester | Cambridge |
125643| 215634| 126543| 216453| 261435|a 624153| 621435| 264153| ______ 624513| 265431| 256413| 524631| 256431|b 524613| 542631| 456213| ______ 546123| 451632| 456123| 541632| 514623|c 154263| 512436| 152463| |
123456| 214365| 124635| 216453| 261435|d 624153| 621435| 264153| ______ 624513| 642531| 465213| 645231| 462531|e 642513| 465231| 456213| ______ 546123| 451632| 456123| 541632| 514623|f 156432| 516342| 153624| |
125643| 215634| 126543| 216453| 261435|a 624153| 621435| 264153| ______ 624513| 642531| 465213| 645231| 462531|e 642513| 465231| 456213| ______ 546123| 451632| 456123| 541632| 514623|c 154263| 512436| 152463| |
123456| 214365| 124635| 216453| 261435|d 624153| 621435| 264153| ______ 624513| 265431| 256413| 524631| 256431|b 524613| 542631| 456213| ______ 546123| 451632| 456123| 541632| 514623|f 156432| 516342| 153624| |
Figure 1
The 1,440 below is based on the exchange of 56 sections from complete courses. The in-course extent contains the six Carlisle-above methods with wrong-place work below the treble. Four of the methods are rung in whole courses; a three-lead splice with 56 fixed is used to add Alnwick and Canterbury. The out-of course extent has the six Cambridge-above methods with right-place work below the treble These are combined using A G Driver's grid with the 5th fixed. All the 5-6 sections are exchanged between the courses 2345 and 5423, 4235 and 5342, and 5243 and 4325.
23456 Sa - 64235 Ct Mo - 26435 Nw Ak Nw Nw Nw - 42635 Nb Cl Cl - 56423 Mu - 56234 Cl Nb - 34256 Mu Mu - 45623 Cl Cl - 52364 Mo - 64352 Wo Wh Wh - 64523 Nb - 42356 Sa Nb Cl - 25634 Mo Mo - 62534 Ch Ch _____ s 32456 Cm | - 25643 Su He He Bv Bv | - 43625 Nf Pr | - 64325 Nf Pr Hu Pr Nf | - 64253 Bk Bk Bk Bk Bk |a - 64532 Bo Ip | - 43256 Du Du Yo Du Du | - 24356 Cm Cm Ip Bo Ip | _____ s 23456
Alnwick (Ak), Berwick (Bk), Beverley (Bv), Bourne (Bo), Cambridge (Cm), Canterbury (Ct), Carlisle (Cl), Chester (Ch), Durham (Du), Hexham (He), Hull (Hu), Ipswich (Ip), Morpeth (Mo), Munden (Mu), Newcastle (Nw), Norfolk (Nf), Northumberland (Nb), Primrose (Pr), Sandiacre (Sa), Surfleet (Su), Whitley (Wh), Wooler (Wo), York (Yo).
The same technique can also be used for splicing the London-above methods with their Norwich-above analogues. The following 2,160 is based on an in-course extent of Norwich-above methods combined using the grid splice of CCC 273 with the 5th fixed. The out-of course extent is London with nine leads of Wells added using three-lead splices with 2,3,4 fixed. An in-course extent of Bamborough is also used. By judicious exchange of the 5-6 sections from individual leads, all the methods except for Annable's London have been arranged into three three-part blocks with standard callings for the bobs.
23456 Bm | - 64235 Bm Ne Bm | - 64352 Lf Lf |b - 23645 Wm Ws Ad Lf | _____ 34256 2b _____ s 24356 Co Li Lo Ke | - 24563 Lo | - 35246 Ke Cu Ke Lo |c - 35462 We | _____ 43256 2c _____ s 23456 No No | - 64235 No | - 26435 No Bc St Bc |d - 63542 Bc Ro Bc | _____ 42356 2d _____ 23456
Allendale (Ad), Bacup (Bc), Bamborough (Bm), Coldstream (Co), Cunecastre (Cu), Kelso (Ke), Lightfoot (Lf), Lincoln (Li), London (Lo), Netherseale (Ne), Norwich (No), Rossendale (Ro), Stamford (St), Wearmouth (Wm), Wells (We), Westminster (Ws).
The final arrangement is for bands who like to get their wrong-place backworks out of the way early on in the peal. The Carlisle-above block has been simplified by plaining the 5-6 Q-set (only bobbed because both the singles in the 1,440 had to be substituted for bobs). The right-place frontworks are now rung in the courses 4235, 3425 and 5432 as the Cambridge-above block starts from the course-head 2435 instead of 3245. The 2,160 is rotated so that the London-above block (now in-course) can follow the Carlisle-above block immediately. Its remaining blocks are now out-of-course, and the Cambridge-above block simply inserted without additional singles.
23456 Mu Mu - 35642 Cl Cl - 54263 Mo - 63254 Wo Wh Wh - 63542 Nb Sa - 63425 Ct Mo - 46325 Nw Ak Nw Nw Nw - 34625 Nb Cl Cl - 56342 Mu - 56423 Cl Nb Sa Nb Cl - 45623 Mo Mo - 64523 Ch Ch _____ - 23456 3c _____ s 24356 a _____ - 24356 3d _____ 24356 3b _____ s 23456
These arrangements fulfil a long-standing need among minor ringers, and should allow half-lead spliced to die a natural death. Not only can the 41 Surprise now be rung in a 5,040 (just add extents of Annable's London and Warkworth), but the callings are significantly simpler than those previously required; the 2,160 has a particularly elegant construction. Definitely best thing since spliced bread!
Old Bailey
From the Ringing World September 18, 1992
Richard Allton notes the possibility of confusion in my article on page 818. This is caused by the omission of a bob from the 3,600 block in 39 methods, the row 24356 at the end of the "a" block being brought up by a bob, and not by a plain lead as shown. This error was introduced by editing the full form of the calling into a more compact one to save some space in the comic for AJB. I'm sure Richard will be pleased to hear that the word-processor has been given a good spanking and sent to bed with no supper. He should find the notation unambiguous once the error is corrected, but the corrected space-filling version below (offered with the usual abject apologies to the editor, AJB and 6-bell ringers everywhere) should remove any lingering doubts.
Old Bailey
23456 Mu Mu - 35642 Cl Cl - 54263 Mo - 63254 Wo Wh Wh - 63542 Nb Sa - 63425 Ct Mo - 46325 Nw Ak Nw Nw Nw - 34625 Nb Cl Cl - 56342 Mu - 56423 Cl Nb Sa Nb Cl - 45623 Mo Mo - 64523 Ch Ch _____ 23456
23456 Co Li Lo Ke - 23564 Lo - 45236 Ke Cu Ke Lo - 45362 We _____ 34256
Repeat twice, adding a single at the end to produce 24356
24356 Cm - 45632 Su He He Bv Bv - 32645 Nf Pr - 63245 Nf Pr Hu Pr Nf - 63452 Bk Bk Bk Bk Bk - 63524 Bo Ip - 32456 Du Du Yo Du Du - 43256 Cm Cm Ip Bo Ip _____ - 24356
24356 No No - 63245 No - 26345 No Bc St Bc - 64532 Bc Ro Bc _____ 32456
Repeat twice producing 24356
24356 Bm - 63245 Bm Ne Bm - 63452 Lf Lf - 24635 Wm Ws Ad Lf _____ 43256
Repeat twice, adding a single at the end to produce 23456
Allendale (Ad), Alnwick (Ak), Bacup (Bc), Bamborough (Bm), Berwick (Bk), Beverley (Bv), Bourne (Bo), Cambridge (Cm), Canterbury (Ct), Carlisle (Cl), Chester (Ch), Coldstream (Co), Cunecastre (Cu), Durham (Du), Hexham (He), Hull (Hu), Ipswich (Ip), Kelso (Ke), Lightfoot (Lf), Lincoln (Li), London (Lo), Morpeth (Mo), Munden (Mu), Netherseale (Ne), Newcastle (Nw), Norfolk (Nf), Northumberland (Nb), Norwich (No), Primrose (Pr), Rossendale (Ro), Sandiacre (Sa), Stamford (St), Surfleet (Su), Wearmouth (Wm), Wells (We), Westminster (Ws), Whitley (Wh), Wooler (Wo), York (Yo).
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