Grandsire by J. Armiger Trollope

File 01: Preface, Introduction, Pricking Changes, Grandsire Doubles, Grandsire Triples – Pages 1 to 82

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GRANDS IRE

J. ARMIGER TROLLOP£

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\V JIJTr.H l·:A !l ,\: .\I! LL En, I ;rr >. HJ48 By the wune w1lho1·

'l'HE CoUEm YouTHS (1937)

STEDMAN ( 1938)

STANDARD :?\!ETHODS (1940) CONTENTS

PREFACE 5

INTRODUCTION 8

PRICKING CHANGES 9

GRANDSIRE DouBLES 14

GRANDSUI.E TRIPLES: (i) Tim ME.'THOD 20 (ii) CONDUCTING 23 (iii) TOUCHES .. 27 (iv) CALUNG TI!Jo Br-:u.s RouND 42 (v) PEALS 48 (vi) HOLT's 0RICINAL 60 (vii) COMPOSITION 62 (viii) PROOF 76

GRAl'DSlftE C.-\TEHS :

(i) THE METHOD 8~ (ii) DEVELOPMEl':T OF COMPOSITION 87

(iii) AIUtANGEME:-:T OF THE LARGER BELL'; 91 (iv) PRooF 95

(v) TOUCHES AND l'EAl.S 100

GRAXOSIRE C!KQUF:s 114

HISTORY OF THE i\iETJIOD 117

BIBLIOGRAPHY .. 130 PUBLISHER'S PREFACE

T is, I know, with a joyous heart that the Exercise welcomes this new G-rand.d the proof.

MARGT. E. 8:-:0WDO?:\:.

('artmel, 1948. PREFACE

HB .Jasper Snowdon Change-Ringing Series of text-books T have been the standard works on their particular subjects since they were fust published during the closing years of the last centmy. In the preface to Stedman, by .J. Armiger Trollope, were briefly reviewed the achievements of .Jasper Snowdon in commencing the series and of 'William Snowdon in carrying on the work after the death of his bt·other. vVhen, after the lapse of half a century, some books of the series had become out of print and also, to a certain inevitable extent, out of date, a worthy successor was found to carry on the work. Stedman, originally published in l90G, was re-written by J. Armiger Trollope and published in 1938. 81-andard Methods was revised and 1·e-written in 191.0. The first edition of Grandsirc was in manuscript when its author, Jasper Snowdon, died in 1885. The book wa.s, however, published in 1888 by William Snowdon, with t.he help of the Rev. C. D. P. Davies. In 1905 the second edition appeared and with it were incorporated the Thompson papers and diagrams on the Grandsire method. At the request of Miss Margaret E. Snowdon, ?llr. Trollope undertook the work of re-writing Grandsire and preparing it for· a thit·d edition. No one could have been better equipped for this purpose. I [e had, as mentioned, successfully revised two other books of the series, he had an uru·ivalled knowledge of the technical and also the historical sides of his subject, and above a.ll he had the p1·oved abilit.y to write about it in a readable and comprehensible manner. At the time of his death in August, 1947, his manuscript was almost completed, the scope and fm·mat of the book were fixed and there remained to be done only a few chapters, this preface, peal books or boards concerned. These fuller details have now been omitted as they do not contribute greatly to the history of the development of the method and they can always be looked up if required. A comparison between this chaptet· on history and that in the 1905 edition will show slight variations in the dates of cntain peals in the eighteenth century. Often these wet"e due to the change from the .T u.lian to the Gregorian or reformed calendar. This new calendar, although introduced into Catholic countl"ies as early as 1582, was not adopted in England until 1752. At the same time 1st J anu.ary was adopted as the beginning of the legal year (instead of 25th March). It was customary for some time to give two dates for the period intet•vening between lst January and 25th March-that of the old and that of the new year, i.e. January 1752-3. An event occurring in the early part of the yea.r, under the new style, would, however, oft.en be noted as of the year before, under the old style. 6 It has been thought desirable in this edition to pay some attention to Grandsire Caters, which, except for a chapter on their history, were almost ignored in the earlier editions. .Y!r. Trollope had written the chapter to which we have given the title " Development of Composition " and he had been in communication with .Mr. Edgar C. Shepherd of Solihull, Birmingham, on the more technical aspects of Cater ringing. illr. Shepherd has been good enough to send us notes he had produced for Mr. Trollope on the notation and proof of Grandsire Caters and has been so generous as to give us complete liberty to use them as we pleased. We have accordingly tried to amalgamate the work we had from both sources. The chapters on the arrange­ ments of the larger bells and on the proof of Caters are, therefore, almost entirely the work of Mr. Shepherd and we hereby acknow­ ledge our great debt to him. In addition to this editorial work on Caters, we arc responsible for the cha.pters dealing with Holt's Original and with the proof of Grandsire Triples and for the writing of this preface. We are grateful to Miss Snowdon for allomng us to complete t.his work and we are proud to have done so in memory of the author and in the sure knowledge that it is exactly what he would have wished us to do for the use of the :Exercise, to which he gave so much. ERNEST C. 8. TURNER. \VILFRID G. WILSON. January, l 048.

7 Introduction " GRANDSlRE is the best and most ingenious Peal that ever was composed to be rang on five bells." So said Hichard Duckworth in the Tintinnalogia, and to-day, nearly three hundred years later, this statement remains fully and litera.lly accurate. It is equally t1·ue when we conside1· the great development in the art and science of change-ringing and the part played in them, then and now, by Grandsire Doubles, by its qirect tl'ansposition the "Standard" extent of Bob Minor, and by all that has come out of them. Ringers and r·inging owe perhaps as much to these things as to· almost all the rest of their art. Yet it is l'Cmarkable with how little regard and esteem the Exercise as a body holds the method to which it owes so much. F'or perhaps the majority it is no more than the earliest and most elementary stage in their training, to be got over as quickly as possible and to be forgotten among the 1·cst of the things whose brief utility has speedily passed. Grandsire Doubles is widel~· used by the men who act as teachers, but most of them are content if their pupils are ablB to hunt tho Treble indifferently and so can go on (as they suppose) to higher and better things. But the system (or want of system) of inst.J·uction gene rail~' used in the Hinging Exercise is thoroughly bad. Instead of the tea.cher trying at the beginning to make his pupil jw.,;t ca.pable of taking part in some simple method, hoping that time and pt·act,ice will eventually make up deficiencif,_., and remove defeets, he should concentrate fi·om the first on those things which are essential to the ringers' art. He should try not so much to teach his pupil Grandsire, ot· Plain Bob, or 'Treble Bob, as to make him an efficient and accomplished ringer·. ~ow to be an accornplished ringer a man must. possess three qualifications. He must be able to handle his bell so that he has full contt·ol of it. 11 e must possess a sense of rhyt.hrn so that he can strike his bell in a way which will satisfy the most sensitive and cl'itical eat·. And he must be able to find his way uneningly along any pat,h which a method may set before him. These things the complete ringer must possess and the essential par·t of all of them must be learnt. in the pr·eliminary stages of his training. \Vhether h(' will be a real success ot· not depends on how he takes the Jirst few steps, and that is why Bob j\linor or Urandsire Doubles can be so impol'tant.. Uell handling shnuld have beAn pract.ically fully H learnt befor~ .s a~·e attempted, but the leaJ·ning of good stdking shouhl hegin anct continue simultaneously with tbe learning of ringing· changes: eat·s and eyes should be trained at the same time. J t cannot b<· insisted on too strongly that to ring changes on five bells. without a cover, as they ca.n and should be rung is a t•belfry. :Hon·c pet·haps ean be learnt of tenor handling at Gt·andsirc Duublcs. o•· Hob .\linur t-han u.t 1-{ajor or HoyaJ, pro­ vided the L"inget· appt••aches the task in the right way.

If it is b·ue that (j mndsu·e has so much to teach the practical dnger it is still h·uer that frll' the conLluctor and the composer it has lessons a!'o i1npu1·tant. and as diflicult as &ny method. The cssenti.a.l fa.cLs of thesP. sides uf ('ha.nge-ringing should he broadly known to all competent. ringel's. They should be able to test and illust.l'at.e on pR.per what they arc told about the changes they ring and they should acquire the ability and habit of doing so from the ear·liest. time they t.uke a.n interest in the art.

We may fairly c·onclude tha,t. ther<> at·e few methods which will in the long •·un be-tter r~>pay a careful and thorough study both in the beihr 11 nd vn P<~J><'l' tha.n Grandsire.

Pricking Changes

P.vF.ItY rin!'-"n' should tr~· lo undcrst.and the a1't of pdckin::,!" changes, and especially su at U1c time when he is just beginning­ to underst.~nd snnwt.hin~ o( t-he J·Hdiments of cha.nge-ringing; for then~ aN· ft'w !hin~s which will help him more to attain pro ficiPncy in the belf1·y t.han a st.utly of methods on paper and by himself; <.ltH.l t.h~'r<' are fe-'1· things which are rnorP. necessary to the COlllpet.ent l'ing-o>t·. ~spe-cially if hfl is a conductor, than to be able to wnrk ot1t tht> e)\ Ret pus it ions of the bells at any givcm point in <\ tnut·h ••r n peal. To prick changes is not merely to copy accm-ately, from are­ liable source, the figures which represent the bells. The art consists in being able to write out correctly and quickly the tigures which represent-. the pla.in course of any method, L'\'en tlw most complex, about which the writer knows a few essrntial fads: and further to be able to write down any changes which ma.y occur at any particular point in a touch ot· a peaL provided he knows, in addition, the calling of the touch OJ' peal in the way that even the least skilful conductor is supposecl to know it. In the ringing in the tower. l•nc change is produced from the preceding one by transposing the positions of one or more pail'S of adjacent bells. That actuaJiy was how changes were first of all consciously produced. The idens in the minds of t.he ringers are not now quite the same: buL so far ns p1·ieking is concerned, the old idea is just as much aJive as ever, and the man who pricks changes to-day is in exact.ly the same position as the man who controlled the ringing in the belfry t hrt>e cC'nturies ago, except that he has a vastly larger !'a.nge of methods to deal with.

All change-ringing is ultimately ba~ed on plain hunting, and the first thing to do is to learn the rulPs for pricking plain hunting bells. W.:: must start with the ii~mes which l'epresent the bP-lls in a definite sequence, and just a.s in the bPlfry we always take rounds as t.he starting row, so when we at·e pl'icking, we usually start wit.h t.he figures in their naturit.l order-I, :!, 3, 4, 5, etc. This is merely a mat.ter of convenience. Any sequence of iigmes representing hells i,:. called a Row, and in theory there is no limit to the numbe1· of figures we may have in om initial row. In the steeple we are. for very practical reasons, limited usually to six or eight bells, ll.ncl we never have more than ten or twelve. \\!hen we are pricking changes on paper we at·e not so rest,·icted and \\'e ea.n. if we like, work with very large numbers; but therP iR seldom any need or reason for doing so. There is, however. one vital clifl'e!·enr.e between the initial rows, whether they are ln.rge or small. Some eonsist of an oven number of figur·es, and the rest. eonsi;:;t of an orld number of figures. The difference between an udd ~Lncl ~tn even numbm·, and its importance, in t.he m·dinary t.hings of E'\'el·yday life a1·e obvious to all. It is not less in1port.ant. in change--ringing, and is far reaching in its effects. JO We set down, first of all, a row consisting of an even number of figures--! 2 3 4 56. This is made up of three pairs of adjacent figures, 1 and 2, 3 ~tnd 4, 5 and o. \Ve transpose the positions of the figures in each of thP.sc pajrs 1 2 3 4 5 6 and we get 2 1 1 3 6 ;), which we write under our :2 1 4 :3 6 5 initial row. We have still ttl!'ee pairs of adjacent figures, but if we were to transpose them, we should come back to our start--1 2 3 4 5 6. So what we do is to reproduce the first, and last figures in the sa.m~e 12:3456 positions, and to t.ra.nspose each of the remaining 21431);) two pairs of fignres-1 >tn

We have now three pairs we can transpose, :2 n,nd 4, l and 6, and 3 and ;), which will give us 4 :2 U 1 ;) :~ : a.ud then once agajn we find we are compeUed to transpose two pahs only. So we go on, first transposing all 123456 three pairs, and then the two middle pairs, until, :2 1 1 :l () 5 when wo have pricke

A set of rows of this kind is called a Hound Block and Hound Blocks play a Ye1·y important pa1·t in the science of vhange- ringing.

But our initia.l row might have contained an odd numbe1· of figures, and that would mean a somewhat different way of working. We begin with (Bhall we say?) 1 2 3 4 ;'J. Now here we hav fl t.wo pairs of adjacent bells, a.nd l :2 :~ .j ,; one extra one>. Obviously wn cannot include all five :2 1 ,j :; G ~in our first transposition. So what we do is to t.ra,ns- pose the figures in the first two pairs, l and :2. 3 and .J, and reproduce the last and odd figure, G, in its origina.l position. \Ve still have two pairs and an odd figure. 1 :2 :: 4 5 -but now we reproduce the leading figure in the same 2 1 ,J :; !i position and t1·anspose the four nthcr figures in pail'S. :2 1- l 5 :3

So we go on-tirst trn.nsposing the lhst four fig\ll·e;o, and then the Ja,st, fow· ligures, until, after· twico as man~; changes as there are figures in our initia,J row, we come bavk to t,hc point from which we sUwted. 11 B 12dL3G 12345

~14:~(iii :2 1 -! 0 :) 2 4 1 (i :1 ,-, :2 -~ l ;) ;l 4 2 (3 ] ;) :l ·1 :2 ;) 1 3 4 (j 2 ;) J ;{ -l G :2 :3 I 04G2:il r, 4 :1 :2 1 li:J4:l:21 :"\ :J

Plain hunting and Ciom·sing Ot·der fon11 t.JH, basis of all change· ringing ; but. so long ·as WI~ keep to plain hunting and the same Cout·sing Ch·der, we do not get very fa1·. \'Vc must vary the plain hunting and change t.he Coursing Ordez·. This VI'C do by va!'ying the pairs of bells we tram;posc an1! t.l1<' z·uks b~· which this vat·ying is June mak<' all the ditl'et·ence bctw,een mdhod. and method.

The t·ule for Plain llob is t.Jaat all tit(' bells plain hunt until the 'L't·cble t·eturns to the fz·ont. Ho far. tlten .. we prick the changes by the rules given above. But. when t.lw Treble strikes the second blow of its whole pull on the front, ins(P-a<.l of transposing 1:2 the remaining bell« in pairs we reproduce the bell in Seconds in the same position, and then transpose the r·emainder in pairs. Instead of-

:1 ~ .) -t (i :) 2 ;) ·i (j we write ~ :1 4 ;) (i :Fi 2 () 4 This gives us a nP-w t·ow and a fresh Cmu·sing Order, which will Sl'rve until the Trebl~ again retm·ns to the lead. vVe should notice that although the Tr<~bl<) now <>ccupies a different position in the Coursing Orde1·, all the other bells retain the same Coursing Order among themselves. The rule of GmnJsire is that all the bells plain hunt until the T!'eble has completed its whole pull on the lead, but at the next change, though we transpose the fii·st pair of figur·es, we reproduce the Lhird figure in the s:tme position, and then h-anspose the rest in pairs. I nsteail of-

1 ;) ~ -~ :; l ;"j :l .j :1 ] ~ ;) :l -t we write~ 1 ~ ;) :J -l ~ I :1 --> -J ~l;).J:~

As with Plain Bub. Wl' get. a i'J-<~sh row and a new Cuur·sing O!'dor. The row J 2 :1 4 .'i rqwesents a change when tho Treble has just completed its whole pull on the front. and therefore the first row pricked hom J·uLmds must be 2 1 :J ii J . \Vhen any b.,JI CCupied in the preceding J·ow, it in saiJace. As we have seen, the plaens made whnn t.he bell is leading or lying behind a.ro a part of plnin lnmting, ;tnd clo not cause an alteration of Coursing- Order·. It is u;;ual, therefore. to confine the tenn ]'lace Jllaking to thus" pia"'"" made in the intetior of the chango, but there is no ueli nit e rule r.n the matt<\!' nur any need for on<>. 1"" ow, just as w., can f1·"ely and easily prick the r·ows of such simple methst. complicated, if we know where the places should collie. \Ve need know nothing whatever about the WOI'k of the metholl. All we need know to \Vrite out Double i\'urwich, for iTL.'Itancc. is t-his-Fourths place in the second change, Thirds a.nd Sixt.hs plac~:s in the fourth chang-e and Fift-hs place 13 in the sixth change. Elsewhere plain huntin,::-, and the second half lead to balance the first half lead.

Grandsire Doubles

1:~34:>) .·\. Hoh ---- Make Thirds !'lace. 1234!) ~135,1[ 231-!.') ~ 1 :; !) 4 3 2 <11 i) ~ :~ I 4 :) 3 4 2 .') 1 :! 2 4 1 ;; 43.G21 :: 4 2 G I 4 :J .'i 2 I 4 5 3 1 2}Dc ass 'I' rebl c .m :1- •I · 54 1 3 2 4 ;) :-11 2 ;)1423 .) 4 1 :3 2 Call Bob. I 5 :2 4 3 i3142:>,)~ k B b 12534) J ,) 4 :J 21 , ta ·c o . ---lDoclge in 4-G down. I 4 52 :1 21543) 2!3134 4I i332 .') 2 3 I 4 4 5 L 2 3 53241 ;) 4 2 l :~ 3 5 ·! 2 1 34i512 .\.Single 4 3 l 52} . ? ,. 1 2 3 4 f) !3 Pass T1·eblc m ~-3. 4 1 3 2 l 4 2 3 G 2 l 3 54 1 2 4 5 3] 2 :n 45 ---.Dodge in 4.-5 up. :12 4 1 i) 21435 :! 4 2;; 1 2 4 1 53 .. :.l 52 1 4 2 .') 1 3 4;; :.l l 2 45231 ;, 4 l :1 2 Call Single. ;)4321 .; l 4 2 :11 53 4 1 2 J G 4 :i 2 3 5 1 4 2}Tr·cblo turns you l ,) 4 2 3 Make Single. 3 I S 2 4 from lead. 13254 ;)14 3 2 I 2 3 4 .'i ;)412:\ 4 ;) :2 l :\ 14 IN' Grandsire on all numbers of bells the Treble has throughout a plain hunting pa.th, and in addition the bell whlch is next after it in Coursing Order (that is the bell which turns it from the ft·•mt and from behind) bas also a plain hunting path from the time one Call* is made until the next. The latter bell (which is the Second in the Plain Course) is termed the Bell-in-the-Hunt. The bells other than these two plain hunt until the Treble has completed its whole pull on the front, then as it strikes in Seconds the bell which it turned from the front makes Thirds Place and t.he other bells above it rlodge in pai.t·s. This place making and d,)dging is at handstroke, and so is all the work, other than plain hunting, on all numbers of bells, except when a Single is made. In the Plain Coru·se of Doubles there are three bells which must pedorm this duty and the ringer has three rules to tell him what t ,l) do. :First, the work comes in regular rotation-make Thirds Pla-ee, then dodge in •1 - 5 down, then dodge in 4-5 up, then again make 'fhirds Pln.ce ; and so on. Sf'-eondly, if he takes notice of whet·e he passes the Treble as he hunts up from front to back t.ltat will tell him what to do and where to do it. Thirdly, by u;;ing his eyes and ears (and ears not less than eyes) he may know when the Treble is leading and the immediate approach of the place-m::Lking and dodging. These rules should all three be used simultaneously, and in their extended forms are applicable to the method on all numbers of bells. The duty of a bell in the PJa,in Course of D oubles can be set down as follows :- !\lake Thirds Place. Pass the Treble in :3 - i up ; Dodge in 4-;) down after lying whole pull behind.

Pass- the Treble in ~- :3 up ; Dodge in 1- :> up befot"e lying whole pull behind. The Treble turns you from b ehind and then from the lead : }fake Thirds Place over the Treble and the Bell-in-the-Hunt and lead again. The bell which hunts down in front c,f the Treble and makes Thirds Place is called the Bell Before.

• By a Call i::; me.Jnt Jny Doh, Single or other "Alteration " made at the orde r o f the ("Onductor and not pro\'ided for hy the rules of the Plaiu L o t~r::;e . l i) A Bob is made in the change when the 'Treble is striking the first (handstroke) blow of its whole pull on the lead, and the work of the bells is altered as follows :- 1. The bell which has just passed the Treble in 2-3 up and at. a plain lead end would have dodged in 4-:i up, now makes Thirds Place (handstL"oke), takes the Treble off the lead, and becomes the new Bcll-in-the-Hunt. 2. The bell which has just passed the Tt·cble in :.l-4 up and at a plain lead end would have dodged in J-:> down, now dodges twice in -i-i5 up and at the next lead end will be the Bell Before. 3. The Bell-in-thte-Hunt dodges t·wice in 4 -,) down and at the next lead end if there is no call will dodge in ~-G up. 4. The work of the Bell Before is nut aJlccted by a Bob. /1.t a Single the bells wot·k exactly as at a Bob, except that in the change (backstroke) in which the Tt·eble is completing its whole pull on the ft·ont the two bells in 2-3 lie still. The bell which would have been Before and made 'l'hir·ds Place at a plain or bobbed lead end now makes Seconds Place over the Treble, leads again, and becomes the new Bell-in-the-lJunt.. The bell which has just passed the 'J't·eble in 2-:l up and at a Bob would have made Thirds Place and gune into the TJunt now lies four consecutive blows in 'rhir·ds and takes the position of tbe Bell Befor·e. Ali the extra work at a Dob is in addition to the work at a plain lead, and all the extra. wor·k at a Single is in addition tu the work at a Bob. Bobs and Sinf?;lCs are made at thP clit·edion of the conductor, and his duty is to call clearly ·• Rob" ot· "',Single" at exact.Jy the right moment. That is just as the tt·eble man is beginning to pull his sally in the handstt•oke ehange when he will strike in 'Thirds on his downwat·d path. Jf the eonductur is using his eyes and ears as he should do he will h~tv'" no diAiculty in deciding exa.ctly when to call. A ea.ll too late ur t.oo early is a bad thing and should be avoided.

The extent of Gt·andsire Doubles consists of 1 ~0 changes and by the use of ot·dinary Bobs and Hingles there at·e two W<1ys in which it can be produced. By beginning eit.het· of these com­ positions at different Jead ends they n•ay be ima·en,sed to what for practical purposes may be reckuuetl as ten. Hi ( l) (~) (~) 2 :l 4 :) 2 :l 4 ,; 2 :~ 4 .:;

~ 5 :c3 4 ~ 3 :3 4 2 ;) ~ 4 - 3 't 2 .:; - :l 4 2 5 s ! 3 2 .) ~ f) 4 2 :l ::; 4 2 4 ;) :~ 2 ., ·) - 4 2 ,) ;) ~ i 3 [) - 8 2 -~ .:; t G 2 :3 2 ;) 4 :l ~~ 5 2 4 H ~ •) 4 G - I 3 2 G - 2 ·1 :l ,;

(4) (;)) (()) 2 :l -t G 2 !.l 4 ;:; 2 :l 4 ;)

- 4 !) 2 :l -- 4 ;) ~ 3 I'< 5 4 2 3 -1 3 ;) 2 4 :3 5 2 G 3 •l 2 - ;) 2 4 :l 1:5 2 ·1 3 .. •1 2 5 :3 ;) 3 2 4 2 ":l 5 4 •I :3 2 ;) s 4 2 G :3 t) 4 2 :3 - 2 5 4 3 J 3 2 " :) :l 1 2 2 !l G ·1 Each uf :\' os. l t.o (i to be repeated.

(7) (X) (!J) (10) 2 3 4 ;) ·> :l 1 .) 2 :; t ~) 2 3 4 5 - 4 5 2 3 2 " :l j H !i ·i 2 ::l s 5-1 2 3 1:5 3 2 4 5 s .j :l 2 ;) :i :l ·1 2 -2:354 3 5 2 4 - •) ;) J :) H ~ 1 :i ;) s .!fj 2 3 s 4 2 !3 ;) s :l -1- 2 ;) - ;) ;) 2 4 1 3 52

Jn Nos. l, 2 and :1 t-he Fifth is the Obseevat.ion 13eU, that is the bell whose work serveR as an indication to the conductor as to where to make his calls. \Vhenever the Fifth is Before there iH a plain lead; at the othet· lead ends the Pift.h double uodges in 4.--:) up, the call being a Bob or a Single aH shown. In Nos. 4, :>and() the Third is the Observation Bell, the calling affecting it as it does the J<'ift.h in the first three extents. Jn Nos. 7 and 8 the Fifth is the Observation Bell; at the leau ends when it is Before t.hel'f~ is alternately a Bob and a plain lead end ; at all the other· lead ends there is a Single.

The callings of Nus. !) a.nd l 0 are similar to tha.t of 7 and 8 except that the Third is the Observation Bell. 17 In none of these extents does the Observation Bell go into the Hunt. It has a regular uninterrupted work of Thirds Pl~tce (the Bell Before), and a double dodge in .J-!> up.

( 11) 240 (12) 240 (13) 2.!0 2 3 4 5 2 :l 4 ,j 2 3 4 5 s 3423 s 54 2 :l - 4 52 :l t; ::l2G! s 3 2 54 S B 2 Li s ,1532 s 4 53 2 ::l 52 4 4 2 5 :l - 3 2 4 5 ~ 4 2 3 G 8 ::lil-!2 s 54 3 2 - 3 54 2 - 4 2 :3 5 s 2 3 G 4. H 2 4::l:; !) 3 4:::! s s'· 4 52;! - :3 52 4 3 2 3 4 4 3 G 2 3 4 52 ~ 4 3 52 Twice repcat.cd. - :; 2 ::l 4 - !) 2 4:3 ;\;foRm,.:',;. :; 4 2 :3 s 3 4 5 ~ s 3 2 id 3 2 4:; 3 1 2 ;) - 4 G 3 2 - 2:; 3 '! s 2 ::l 4 5 - 1 52 3 ;) :l 2 4 4 :l 52 54 3 2 8 '2 G 4 B s 2 3 54 -432i) 2 4 3 G ~ i) 2 4 :l :) 3 2 4 2 54 3 S 4 2 G :l s :~ c~ G - :; 3 '~ 2 - 2 53 -t H 2 4 G ;~ S 1 3 2 G 2 :l 4 :; 4. 53 2 l'!T)f..\N',.:, s 2 :l 4 5

To introduce more vat·iety into th·andsire Doubles ringing some attempts have been made to use blocks of 240 changes, each block containing every Row twice. One way is to begin an extent and then, before it is completed, to ring another extent and after that to finish the first. In No. 13, fot· instance, the Six-scOL'e No. 7 is begun, but after the row 2 4 ::l G an extent called as No. 4 (but with the Fourth as the Observation) is rung and when t-hat is finished the other extent is completed. 18 In M:r. Pitman's c\.t•t·angement (No. 11) two six:-scOt·es called as No. 10 are joined together by substituting a Single for the Boh at the second lead, and the 13th, 11th and 15th lead ends are caUed Bob, Single. Bob instead of Single, Single, Single. In Mr. Morris's Arrangement (:'oro. 12) three consecutive t-iingles and one Bob are followed by t.hree consecutive Singles and one plain lead : and this calling is repeated twice. As with tbe six-scores these Z40s can be varied by beginning at differ­ cut lead ends. · Another, and pel'itaps bet.tct·, plan is to use what in olden times was called Alt<'ration of llunts. In the seventeenth century the belL which had a continuous hunting· path throughout the six-score (as the treble now usually has) was called the Whole Hunt. The bell which had a regular work of Thirds Place and a double dodge in 4- 5 (the one we now tenn the Observation) was called the Half Hunt. Duckworth in Tintinnalogia points out that these works Jllay be perfOJ•med by all the bells ami l:d043 12345 that there are twenty ways in :! 1 { 3 5 21435 which they may be shared. In :24153 2 4 1 53 Bob half of them the leadinJ,.!" on -l2i513 4 2 1 3 5 the front must be at back­ L:i 2 31 4 1 2 53 stroke and handstroke, or else 54 2 1 3 14235 the changes must start at !") 2 4 3 1 12453 backstroke. These would not 2 53 4 1 21543 fit very well into our mude1·n 2 3 G 1 4 25134 Grandsi.re ringing, but th~e :~ 2 1 54 52314 other ten may be useful. :l l 2 4. 5 :)3241 Huppose we make the Fourth 1 3 4 2 5 35421 the Whole Hunt .: we can th•~n 1 4 3 5 2 Bob 8 4 G 1 2 have either the 1-;econd Ot' th11 '11325 43152 Third as th0. Half Hunt anti 4-3152 41325 the changes fl'lllll J·ound>i would begin in each nf t. ht~ 34125 1 4 3 52 two six-scores as follows:- :!1 ± 3 2 1 3 4 2 5 By altering the Hunts and. using the calling of the ten six-scores (Xus. l-10) givena.buve. fifty different extents are made available and thus peals of live thousand changes may be rung without including the same J 20 twice. In reeent years at least two such peals have been J'Ung. 19 Grandsire Triples (i) TilE :\IL;THOD. 12345671 3i)!7ti21 - ----r:\Iake Thirds. 31 :"iu712 2135476 ) J3ti:il72 2 3 I 4 G 6 7 + fi 3 I :i 2 7l Pass Treble 3 2 4 1 G :; 7 1\ -1- 1 3 2 :; 7 f in ::1--L 3 4 2 6 1 7 G fj 1 + 2 3 7 ;) 4362713 J f) 2 1 7 3 .) <1637251 1 :2 fi 7 J G 3) Dodge in 6473521 ·> I f' ·1- 3 !3-7 6 7 4 :; 3 1 2ll>~tss Tt·eble ~ ) - I .)-J' up. 7 6 5 4 1 3 2J in 5-6. :21i17453 7561423 fl :2 7 1 !) -1- 3 5716243 fi/2:)13-J- 5 17263 4 7 fi ,-, 2 3 1 -1 1 527 30 ·1 7 ;) 0 3 :2 -l 1 12 5 37461 . - ,., 7 3 fi + :2 l - .- Dodge 1n 4-:> ;)37~012 2 1 5 7 3 G 4 J down. 3.i47lfl2 2 5 1 J 7 l (i 34:)J72fl 523147(; 1 3 I :--; 2 7 fi\ l'a.ss Treble i)32411i7 -1 1 3 2 ,; 0 7 f in :2-3. 3542fil7 1423():;7 34 5527 1 124fi37 '-' l nd _ . n - ~ e In -13G!'i72J 4637:11:2 ~~~~ :) 7 j -h> up. 6 4 7 3 l 3 2\ Pass 'J:r· eble 211G37;i 6 7 4 1 3 2 ;)j in 4-5. ·I 2 fi 1 7 3 .) 7Gl423ii .J-0271:)3 71(:124;)3 li172Gl3 1726 54 3 li 7 4 .) 2 3 1 1 2 7 5 6 3 7 G :) -1 3 2 1 .J-! Dodge in 6-7 7:)()3-J-12 2 1 7 G ;) J 3 J down. _-, 7 3 (i l -1- 2 27lj(;34 :)37lfi24 72513(-i.J. ] .) 172fi4 7 5 2 3 1 4 fi 3 1 :) 2 7 -J- fl\ TlU'ned from 5732416 1 3 :2 :; - ~ 7 fl/lead by Treble. 5374261 1 2 3 -l :)ll7 20 A Bob A Single

L:iu14~~~ 7 3 G 1 J 2 :~ ;; 1 I ti ::l 4 :3 Call Bob. ;) 7 l G 2 4 :1 Call Single. ;)]7~1)34 G 1 7 ~ n 3 4 J;)76243 ];)76213 I 7 ,:; :2 1\ :~ 4 1 G 7 2 6 :3 4

7 I :') () :3 4 :1 :)176243 7 .) 1 2 (i : ~ 4 :; 7 1 2 () :~ 4 ;) 7 2 1 :! (l J 1 !) 2 1 3 f) 4

Except for the two extra bells and the two e xtra dodging positions Urandsire Triples is similar to Grandsi.re Doubles . The 'l't·eble has throughout a plain hunting path and the b ell which i~ next after it in Coursing Order is the Bell-in-the-llunt and ha.s· also a plain hunting path from the time that one Bob or Single is made until the next. The duty of each of the other flvc 'Vorking Bells.aftcr making Thirds Place is as follows:-

1. Pa,ss the Treble in G--6 on your way up. Dodge in 4-:l down after· lying whole p111l behind.

2. l'a.ss the Tr<,ble in •!-;) up. Dodge in G-7 down after lying whole pull behind,

:~. Pass the Tr·eble in :~-t up. Dodge in 6-7 up before lying whole pull behind.

J. PM;s the Treble in :2-:l up. Dodge in 4-5 up.

;). Treble turns you from the back and then from the fr·ont.. :'lla.k(' Thirds Pla<'c over Treble and B ell-in-the-Hunt and go to lead again. This is the Bell Rcfore.

The work occurs in regular cyclical rotation, and in addition the ringer who uses his eyes and ca.rs as he should do can tell when the Treble is leading and so when the place making and dodging must be made.

The following table sets out the alterations caused by a Bob to the work of each bell : 21 . ·- --- · - · ·------··-·--··--- - : Work at following Work of Bell at Work at a Bob. I Lead End, if no further Plain Lead. ; ('(l/l is· made.

1. In the Hunt. JDbl. Dodge in 4-G down. I Dodge in 6-7 down. 1 3. Dodge in 4-5 down .. 0-7 6--7 up. 3. .. 6--· ,. G-7 up. .. l-5 4. 6-7 up. .. -1-.:i " Make Thirds Place (the Bell Before). il~ .. .j,<) :Make Thirds Place, takej Remain iu the Hunt.: Treble off the Leadi and become the Bell: I in the Hunt. I

G. Thirds Place I Unaffected. Dodge 1n -t-5 down. 11' (the Bell Before). I

At a Single t-lw work of ~til the bells is Lhe same as at a Bob except that :- ]. The Hell Before mitkes l:ieconds Place at backstroke ove1· the Treble. lPa.ds n.gain. :md becomes the new Bell-in-the-Il unt.. 3. The bell which at a llob would have made Thir·ds l'la.ce and gone into the Uunt now strikes four consecutive blows in Thirds Place. 1 t t.akes the position of the Bell Before and at the next lead <'nu (if there is then no call) will dodg·t' in 4-5 down.

The general I·ule is that at. a Call a bell double dodges in the position next before the one in which it would have made a single dodge had there been no Call; in 6-7 down instead of t--5 down: in 6-7 up instead of o-7 down; and in 4-5 up instead of li-7 up.

All the work at a Bob is in addition to what would have been done at a plain lead, and and all the work at a Single is in addition to whnt would have been done at a Bob. 22 Scales for Pricking Lead Ends

Plll.in Bobbed Po;;it.ion of 1 ,eMi Ends Lead Ends 8even1h----t.ho from :2~4Gf$7 234567 Observation.

Fir·st :2 5 3 7 4 (i 7 ;)2634 In kecond :27?>6B4 () 7 2 4 :') 3 Befor-e Thin! ~ 6 7 -1 :'i H j fi 2 8 7 .) Wronp: Fom·th :2 4 (i 3 7 :i 3•125[)7 Ri~ht Fifth :2345()7 .)32741) :\Liddle For singlNl lead ends transpose t-he Hrst two figures of each of the rows in the column of bobbed lead ends.

In an

Holt's Bob Singles :! 2 1 :; 4 7 6 321 L iG7 :! 1 :2 4 5 (i 7 :~125 •171> J:3:2!i •171) l :l 2 4 G 6 7 123:>476 1234367 :21:~1:)()7 :21:3547!3 ~ :! 1 :; 4 7 6 2314:)tj7

Grandsire Triples

(ii) CO!'DUCT!NG

A CONl>Ul'Ton's job is a threefold one. He has by his Calls to let the rest. of the band know at the correct moment when the necessary Bobs a.nd Singles must be made. This is the most essential par·t of his task, and in an ideal band, when every member did his work without fault, it would be the only part of the t.-1.sk t-h11.t could be noticed by anyone except t.h(•. man hims\,lf. In the best ringing-, b eyond the calling of the Bobs, no 2::1 word should be said by anyone. But ideal bands hardly exist. There is always the possibility that something may g" Wl'Ong with the ringing and that either the membet·s of the band or the conducto1· himself have made some mistake. To check this tendenc~· the conductor 1nust be aware, if not throughout the l'inging. at. least ttt fairly frequent inteJ·vals, if the prnper changes are being rung, nnd this knowledge is, in addition, :tn immense help to him in his job of calling the needed Ht>bs. Finally. there is often the necessity for corr-ecting an e1·ring l'in~er and for telling him what he ought to do. The gift of being aD!e to correct faults in ringing promptly :tnd effectively cannot be imparted by inst.ruction, least of all by \V:l'itten instruction. Nor is the faculty of knowing and undet·­ standing hOW the changeS in a touch Ol' pea) i1l'e pl'O~l'eSSing a matter of Learning certain definite rules. 1 t comes to the ma.n who studies, on paper and in the belft·y, and mot·e Ol' less undet·­ stands all there is to know about a nwthod, its construction. its wm·k. its touches, its peals. and its c<>mpositiun. There aJ'l' not. many things in a tBxt-book like this present one which dn not. in some way. ltwge m· small, help a conductor to understand thP touch ot· pt'al he is conducting.

Tlw eol'l·ect calling of Bobs and Sing-los is :1 mat.tet· of definitt· rule which should be carefully studied and nndet·stood. The verbal call should be made quite clearly and just at the mmnent the 'l'l·eble man begins to pull his sally wh1~n hP ic; about to strike in Thit·ds on llis way 1lown to t.he ft·ont. The man who calls ad entls which separat.e t.h"se at which c:dls must bt.· 24 made. Touch Xo. G (page 33) could be called by the man who knows that it consists of alternately a plain lead end and a. bobbed lead <>nd until the. bdl,:; come round. Or touch No. 1 :; (page :)4) by ornitt.ing at. two successive lead ends and callin~ at two until I'o\mds tm·ns up. The same plan will serve fm· a numbet· of t.hc simplet· touclws. but it is not one to be recom­ mended fm· serious US<) as it is littlt' more than a ma,keshift and will give tlw novice in condnding little experience which will be of any t·eal ntlue to hilll.

Calling from an Observation Bell is the best plan when thm·c is one bell wltich repeats its work at stated intervaJs throughout the touch 01' peal. It is also best when the touch can be con­ ,-enient.ly divided into Coueses which consist of the changes which are rung fL·om t.he t.ime the Tr·eble and the Observation occupy in the same changt.> at ba-ckstroke their home positions until tho ll<)xt. tim., they nccup~- t.he same relative positions. This will bl'· made rtuit.e dPar ]flt.c·r·.

Any bell ma~- serve as an Obs('l'nI' impossible for a man himself to L·ing so heavy a bell, touche'> and peal>< in which nthel" bells (as light perh' will natut·ally ring the bell he is using as his Ohsl't·,·ation a.nu "Ollie ptef0r· to do so at any time, but. a skilful nnd J)l'adisocl man can if he wishes use any bell jn t.he tt>wet· II>' hi:< Obs<'t'\'i\.t.ion though he himself is ringin~ nnothf'P.

The position" in( u whi('h t lw ( lbservation bell may fall at a Bob or· 1:-'ingl<- HJ'P ;Hi follow>':-

1. Into the lltm! with a Hob (I n).-'l'he bdl has dodged in o-7 up at thC' pt••vious lead <'tHl ancl would at 11 plain lead end ading. 2. Into the llunt with a Singll'.---This is when at a plain m· bobbed Jcau •·nu thP hell \\'Olllcl haYe been Before. Call when about t.o sh-ik•· thl' fit·st bluw of the \dwlc pull on the lead. 3. Out of the Hunt (Out).-Call when about to strike tl1e handstroke blow in Fifths on t,J1e way down after turning the Treble from behind. A bell is said. to be called " ln and Out., when the two Calls are at successive lead ends. ln and Out. at~ mea.ns that the llob which brings the bell out of the Hunt is at two leads distance from the one which put it, in, there being one plain lead end between them. In and Out at 8 means that the bell must be called out at the third lead end after bein~ cnJicd in. And so on. 4. Before (B).-CaU when about. to st1·ike t.he first blow of the who! e pull on the front before being turned by the Treble. 5. Before with a Single (Long 'J'l1irds).-The bell l1as dodged in 6-7 up at the previous lead end ,.nd would at a plain lead end dodge in 4-5 up. Instead it makes four blows in Thirds. Place and returns to the lead after the Bell in the Hunt. 6. :'lliddle (M).-Call when about to strike m·er the Treble in l<'ourths when hunting up after having liodgecl in 6-7 down. 7. Wrong (W).-Call when about. to shiko the second blow of the whole pull behind after hm:ing nHHk Thirds Place.

8. Hight (R.).-Call when about to st-rike in ~ixt.hs (huntin!; up) a.fter having dodged in .J-.'l down. The term lfome is some~ times used for this Call but it is inaclvisahlc ("XCi>pt perhaps in the case of the Seventh. When a Bob in any position is follm.\'e " wit.h a Double." Thus an alternative way nf saying Before and \Vrong is Before with a Double, or of saying Wrong a.nd ::VIiildle is V\'rong with a Double. '.rhis expi"ession is mostly used when the calling is by the Bobs BP.forc. In this tho conclnctor first lea.1·ns tho order in which the hells at·e Before at all the Bobs t.hnHlghont the touch or peal. lT e then watches each of them in its t.urn until he meets it immediately before t.he Treble in Coursing Order. and a.s it begins to make its wbole pull on the !f•ad he cnlls t.he Bob. This wa.y of conducting, which is a,lmost peculiar to Urandsire Triples, has the advantage that t.he conductor r-a.n 11se it equally well whatevet· bell he is ringing. n.n caused by John Holt's two pel1ls. the Original a.nd t.he Ten Part,, both of which lfmd themselves admir11bly t.o its use. Circum­ stances have made t-he Ten Pf1t't almost obsokte. but, the Original is still frequently nmp; ~~nd is gener<1lly eallt~rl by the bells Before ; and so arc 11ny other similar one-part. peals. l3ut for the most popul:u of mDllern peals -.T. J. Parke1··s T'wclve Pm·t­ as well a..:; fm· the great majority of touches rung, calling from an Obset·vation ),; nsu;tl nowadays and is the best plan. Dy whatevet· plan a comluctot· calls he should fh·st study his tou('h or peaT on pa.pet· and tJ·y to unde1·stand how the b(,Jls wnrk together·. ]Je shou]{] not rely on any ruJ.e-nr-thnm b directiL>nS giv~>n him by another ver·baJly, h•)Wcver tJseful they ma.y bt~ in addition. Grandsire Triples

(iii) TOUCHES

( t "\..) (l B) (1 C) lGR lHB IHS ::! :~ 4 ;) u 7 2 :l I :) I) 7 2~\IGilH \V

2.J:37Jij ii 7 2 4 !) :t 2 :l ;) .J 2 6 - -()7~4;):~ :l ·J f\ G 7 2 I ;; 2 ·i ;~ fl -::!4(}()72 (\ 7 :t .j 2 ;; :1 ~Ji.'jrJ- 35·12G7 i)~IH27Jl :~ 2 :; 7 ·1 fi H 7 ,-, 1 :{ 2 :t 67342;} 2 4 13 :: 7:; 1 .'j 4- () 2 7 3 .1' L 2 :3 .j :; tl 7 1 5243()7 53274ti (\ 7 54 :l 2 - 24ti37;) 2 3 4 5 f3 7 There are three genct•td wa.y.; in which a. tuueh of Grandsi1·e Tt·iplcs can be set down un p;1pep, Jn one evet·y ba.cksLruke r0w of the Treble's whnle pulls on the front is written tluwn. EveJ·y row whieh is proi!uccu by a Bub has the mark - put in f!'Ont of it.; •~very one pr()(]uced by a. Hingle has thn letter :-; in front of it: plain lead ends m·c not mnt·kcd. 27 c In the second way only the rows produced by Calls are written; bobbed lead ends are not marked, but lead ends pro­ duced by Singles have the letter S on the left hand side of them. If rounds turn up at a plain lead it has then the letters PL along­ side of it. After each row is a figm·e showing its distance in number of leads from the pl'(Wious lead end. The third way is by ·the Course Ends. The ~eventh is usually the Observation and the l'OWS shown on paper are the back­ stroke rows when the Treble is leading and the Seventh is dodging in 6-7 up. The figure 7 is usually omitted. After each Course End is shown the calling by which it has been produced. Each of these three ways has its advantages. The first tel.lli the condud!W what eve1·y hell is doing throughout. the touch and he can select any one of the six to be his Observation ; but to write out every lead end in a touch of any length, and especially in a peal, wouJd be a very long and tedious job and it is only in the shol'test of touches that this way is used. The second way is the une which best serves must pm·poses and from it the plain lead ends can easily be written out if they are needed by means of the t.ables given on page 23. It some­ times happens that a touch comes home at handstroke. Rounds is nut then a lead end and in that case the lead end 3 2 5 4 7 u (which would have followed it had the ringing gone on) is shown : but. as it does not actually appea1·. it is put in brackets and is called a Natural Lead End (see touches .:'IOos. :i, 7, H, etc.). The Cmn·se End way of setting down touches is the most concise and. if it were not for its limitations in Grandsire Triples, would be the one generally used as it is in p1·actically eyer~· 1\lajor method. But in Grandsire Triples only a part of the touches and very few of the peals can be divided into courses, a.nd for those that can, theJ•e is no simple system such as is avail­ able fot• Bob Major, Treble Bob. Cambridge Surprise and the like. There' are SfWet·al ways of nsing the Course End plan in Urandsite Tt·iples, due to the peeuliat· circumstances of the various compnsitiuns. That shown in touch l\"o. 1 C (page 27) is the commonest and t.he others explain themselves 1•eadily enough when they a1·e examined. Most toueht's of any length and seveml peals arc divided into Pat·ts. In t.helll a certain sequence in the order of the Bobs and 2~ Singles occurs two, or three, or five, or six times over, and the figw·es of the first part only are as a rule written out, though in. special circumstances the whole of vet·y short touches may be given, as has been d•me with the example above which is a three­ part touch. The Row which finishes the part is called the Part End. It may be a plain lead end. or a bobbed or singled lead end, or a course end ; but it is always shown. In it the observa­ tion bell or bells, and perhaps one o·r two others are usually in theit· home positions; but some instances occur where a.ll the si-x working bells are displaced at the part end. (2) (3) (4) 210 210 210

~:34;iu7 2:~45()7 2345()7

~ ;)72634 l 752634 1 672453 :! ~ -!3!i2(l7 ~ H 43726G 2 536247 2 3542(J7 4 s Gn4723 2 72543(1 1 673425 2 (i 4 5 7 2 :~ 4 G37264 3 .34G273 236574 2 425637 1 1)75432 :; 452730 s 734562 ~ 2 4 0 :l 7 5 1 2 :l 4 5 () 7 :-l H 2 6 7 4 5 :~ 2 PL 23-!.5u7 PL 234567 2 Every touch which comes -round at. backstroke is a Round Block • and Variations of it can be ha.d by beginning the com­ position a.t any lea.d end and making Calls at the same intervals as in the original. For instance, 6 7 5 4 :3 2 is the thirteenth lead end of touch No. :! above, and ft·om it the Call making intervals al'e 1, 2, 2, -4, 2, 1, 3. We treat rounds as an ordinary row and after we haNe t•eached the bottom of t.he original figw·es we carry on from the beginning until we have gone from (J 7 ii 4 3 2 to it. again. As rounds comes at a plain lead end we add the bottom right hand ftgure to the top one to get the interval the Single comes from the preceding Bob. Using these call intervals a.nd starting ft·om rounds we produce touch No. 0.

Or again, 4 7 2 H 3 i) is the fifth lead end of the original and is a plain lead end between the Single 4 3 5 2 G 7 and the Bob

• See pages II and 70. 29 3 5 4 2 6 7. Our first call interval will be 2, and following that we J·ead 2, l, :3, J, 2. 2, 2; which gives us touch No. 4. In a. similar fashion we could start from any lend end of touch Ko. 2.

The variations we produce by this means are all the same composit.ion as the original, and the call intervals are the same :. but for practical purposes they differ a lot and in no case are the changes rung the same. This gives an excellent way of altering and varying the Observation. In No. 2 it is the Seventh and the ca,Jiing is Before (Long Thirds) and Hight (both with Singles); Right at a Bob; and Before and Wrong twice. In touch :Xo. 3 the Third becomes the Observation. The lit·st Bob is the second of the two ·wrongs and from it the Callinp; from the Third is exactly the same as the calling in the OJ'iginal is from the Seventh. The new Observation can be found by noticing what posit.ion the old Observation occupies in the lead end of the original selected as the start of the vat·iation. The compusition of touch No. a stru·ts ft·om 6 7 i'i 1 :3 2 in touch ~o. 2; the Seventh is in Thirds and so the Third is the new Observation.

This varying of the Obser-vation can now and then be a help to a conductor ; for it may enable him to call a touch he knows when he is not ringing the bell be uses as the Observation. He may be a visitor in a strange belft·y and when rounds is being rung is invited to call. Suppose he is ringing the Fifth and is accustomed to call in his own tower from the Seventh. Possibly he is a. rather nervous and diffident person who mistrusts his ability to call from a non-observat.ion bell, a.nd so he declines the invitation. But he need not. The touch we have just been rliscussing may have been a favourite one of his and he could have called it from the Fifth in a similar way to that he was accustomed to from t.he Seventh. Only there are some points he must watch. He cannot begin by calling himself Before with a Single for at the st.a.rt he is already past the posit.ion which would enable him to do that. But he can begin his touch at a later lead end. He can call himseli Before and Wrong twice and then go on to the Singles and the Bob Hight. At the finish he would probably be surprised to find what a good touch he had calJed. It might not have been so good if he had tried the plan when ringing another bell, but with care it will always work ; HO and t.be conductor who studies on paper and in the belfry this kind of variation will gain not only experience, but a lot of ,-aluable information which will be useful to him in many ways. A good illustration of this method of variation is given by one of tho simple.<;t and most famili!l.r of touches. When the Seventh is called In u.nd Out t}u·ee times 168 changes arc pro­ duced. The same thing will happen if the Sixth is called In and Out three times (No. 1) or the Fourth (No. 13). At tho go-off the Second is already in the Hunt and cannot be called In, but it can be called Out and In three times (No. 12). The Third and the Fifth cannot b e used in exactly the same way as Observations. Either could be called In and Out three tirues and the bells would come home, but part of the Plain Course would have to be rung twice, which of course is false ringing. These bells, however, can be used as Observations. In each of the three courses when the Seventh is being called ]n and Out the Sixth is Middle and Before and the Fifth is Before and \Vr·ong. A conductor who h as studied the touch will know when there is more t.han one Observation. He will watch the work of the otbet•s and use it as an auxiliat·y to his main Obser·va­ tion, and when he is ringing another bell can use it for his main plU'pose. \Vhen ringing the Thi.t·d h e must not call himself In ·and Out but he can call himself either Wrong and Before or .\[iddle and Before. In a similar wa.y, although the man at the Hecond could not call a. variation of touch No. 2, by using f!'om his own bell the calling given for the Seventh, he could use the e-qually efficient Observation provided by the Sixth. But this plan of variation not only alters the conductor·'s observation ; it affects the music of the changes which is an even more important thing. 1 n Grandsire Doubles, with its small number of bells and small number of changes, every change is usually rung in a touch, and t.here can be little variety in the music except that it sounds better (e.c;pecially when there is no cover b ell) when 4-:) strike behind in that order at backstroke and not at handstroke. In Grandsire Triples music has a ver·y important part to play and should receive the ringer's cat·eful fl.ttention from the very beginning. The man who trains his ears to understand and appreciate the music is almost sure to become a bet.t.er p1·actical ringer and to find more enjoyment in his art. :n The music of Gra.ndsire Triples is produced mainly by two things: one (which is common in varying degree to all methods) is the rhythm or "beat" of the bells, which largely depends on the way that musically prominent bells com·se each other through the changes. For this, two positions are the most effective. One is when the Fifth, Sixth and Seventh are in plain course ordEJr and come down to the lead, first the Sixth. then the SeventJ1, and then the Fifth. The other (which is called the Tittum position) is even more effective and is when the .Fifth is the first of the three in coursing order and is followed by the Sixth and then by the Seventh. The number of changes which will allow these positions is not large but those touches which contain them always sound well. The other way in which the music of Grandsire Triples is pro­ duced is by the particular bells which strike together in 6-7 at backstroke.. The musical effect is not so susta-ined as in the other instances, but when it does occur the very fact that it is intermittent makes it all the more welcome to the ear, and it has always been especially valued by the best of ringers. It is a distinctive quality of Triples ringing, particularly of G-randsire and Stedman. The musically effective pairs are 4--8, 7-4 and tl-7, and the aim of composers bas always been to include as many of them in touches as possible. This music at its highest is shown by two full changes, l 3 5 7 2 4 0 8 (Queen's) and l 5 2 6 3 7 4 8 (Tittums*) and these two are frequently included not onJy as rows, but as the part ends of touches. Examples of this are shown by touches Nos. 21 to :31. The twelve short touches (Nos. 5-Hl) are given by the lead ends. No. 5 is the shOI'test that can be brought round at hand. No. 15 has always been one of the most populat· of short touches. The calling is easy to remember-it consists of alternately a plain and a singled lead end until the bells come round-and the music is excellent, including Queens and Tittums. There is, however, the temptation for a young conductor to give too much attention to a touch like this and so miss the experience that more difficult touches would give him. Touch No. 8 could be treated as alternately two singled lead ends and one plain lead end but with one of a pair of Singles coming at the start and

• This term is also used in a related but somewhat different seusr. See page 91 et S

(i5) 97 (ti) 11~ (7) 111 (8) 12ti

234567 2 J J ;) I) 7 2:34567 234567 - - - - ~ 572634 2;)37Jf) 253740 s ;)72ti34 .'!67423 - (J 7 2 4 ;) :~ !-) 702453 ;)67423 ~ 435207 6,!7:32:) s 437562 s -±35267 423756 5362J7 4:33270 s 274635 s 764523 52:370+ 4 2 5 (j 3 7 267543 - 357264 - 4.7.362:3 - 764325 s 532467 (32547u) 467352 s 357264 s 475632 - 234;)07 (325476) ±67253 s 234567

(9) 153 -continued (10) 167 -cont-inued 234567 ;)7()32± 234567 - 4tl7523 - 4::!5270 456372 - 752634 423037 253746 435267 765423 - 764523 - 072453 ±23756 s 437265 - :.157264 - 346572 s 764.523 - 524637 (325470) 354.267 - 357264 562743 - 723654 (3 :2 54 7 6) 3:3 (11) 167 -continued (12) 168 -continued 2345o'i - 764352 2345U7 645723 - 2·:3756{ ------()7,1352 - 752fi:~ 4 :! :~ - '1fi273(i s 4 :1 7 2 () !i - :37()542 7 1 (i :1 52 '1 7 56 2 :~ 42357() ~ ;) 7 2 () /l - 2:37;),1_1) ,167352 4 52 t) :1 7 (:i2547li) -

(13) 168 (14) IUS (l:"i) HiK (!G) 196 234-567 2:31567 2 :3 ·l ,; IS I 2:34561 ------25374(\ - 752ti:34 2:i:1741i 25374-li 275(\34 7 6 54 2 :; s 7 () 2 4 5 :1 ·-k 762453 - 46237f) 74()352 71U323 74632;i - 53471_12 - 2 :3 7 G 4 6 s :1 57 2 4 H s 357246 57324() 25:HI74 :.1 2 ;) (J 7 4 325674 527634 265437 H (i J H 7 2 5 362<157 - 4tJ5:127 - 74236G (J 7 4 ;) 3 2 346725 - 734265 7 3 4 52() H :) 2 (J :l 7 { 8 753246 723546 7G3642 :; :1 2 4 ti I t; 267453 752634 - 2674.5:1 H 1. 7 :i (J :1 2 ·-s •132567 - 4U7:3i"i2 24.637:) 4()72:)3 45372G - 234Go7 2345!11 :-; 2 :1 4 5 U I 475632 467253 s 234567

(17) 209 (18) 223 (19) 270 (20) 33.) 234;:>67 234567 2 :1 4 G U 7 234567 ----- ,, s 572634 (i72453 6'74532 ._, 074532 :l 245367 ;) 245367 4 256374 1 256374 I 0723:34 •) G7.2534 2 742U3G 2 742635 2 1GU372 l 456372 l 357264 2 ~157264 2 k 7 (j '.!-52 3 :3 ~ 764523 3 {325·176)1 (3 2 5 ·1 7 6) 1 :IG7264 l 3.'57264 1 l:l2fi476)1 (:{ 2 :> 4 7 6) l 34 (21) 336 (2:2) 0:.31.1 (23) 378 (24) 378

2 ~ 4 5 () 7 :.l :~ -l ;j () 7 234567 234567 ------752634 l H72,lG:3 :.l 462375 3 s 762453 ~ 237G46 :~ :1-lliG72 ti:34762 l s 437G62 4H275:3 •) 7 2 :~ (J G 'l :.! li :2!) ·i 7 3 2 254637 1 374562 l :::)I :2 ·~ tl :l :1 4 6 7 2 ;j 1 s 732,165 2 PL 3 :i 7 2 4 6 1 PL :1 •> 7 2 4 6 2 s 567243 2 PL 52 6 3 7 4

(:.l;)) 4fl2 I :;!I)) ,j(J-f- (27) 50·~ (28) 504

234!>67 :.l :~ 4 G ti 7 2 :~ 4!) 6 7 234567 --- - 342567 ~ s 7 li 2!!) :,1 :! 752634 1 752634 Ci73254 :2 s:.172-l-ti :.! ~~ 4 7 2 6 5 2 527634 4 C:!6573 1 s 7 3 :j:.! 4 ti ( 7G34:')2 3 735246 3 674235 3 3 :') 7 :2 4 (j t 2 '! 7 56 3 1 357246 4 5:26374 1 7(12435 3 :1 G 7 2 4 6 2 (2!J) G4ti (:10) ()7:2 (31) 714 234:3117 23-!Glil 234567 ------4 () :2 :{ 7!) :I :-;:~2741l t> 532746 f) 534702 I. 73i:i624 r; 245367 3 7:3G:.l4n r) 4H7.23G 1 562473 3 35i2ili f) 7 4 2 3 5 -t 735246 2 ;:d (j :l 7 4 l 357246 4 Each of the fureg"inp; e-lev<>n touches (Nos. 21 to 31) to be twice repeated.

(32) 350 (:1:1) 4fi:.l (34) 50:1 (35) 504

234567 2 :~ t ;) (j 7 234G67 234567 ------

:)32746 G 462375 oJ ll724G3 2 462375 3 735624 :> :) :1 4 •7 (j 2 l 346572 1 754236 ::l (537452 ;,) 02:)4.7:3 ::l :3432137 5 627354 1 436275 ;j 2 G n 4. 7 :3 1 .t_ :~;:; 2 6 7 4 326175 ;, 234507 5 PL :! ,, G :l ti 7 PL 3 4 2 5 G 7

3"',) (36) 447 (37) 378 (38) 1008 (30) 1008 234567 234567 234367 234567 ---- ·---- 1372453 :2 462375 3 s 57 2 6 :l! 1 672453 :2 346572 1 534762 1 3!52t.i7 :2 4.7632.'5 5 723654 2 625473 2 G7:3S24 :2 :l 7 4 56 2 3 467523 1 :346723 1 4;)1)27:1 t 573246 5 67452:3 4 743562 5 li 7 4 53 2 :3 2756:34 3 :356274. 1 2:'57643 1 2;)1)37} 1 342567 2 673542 3 432765 •) PL:! 4 3 7 :) 6 2 2564.73 1 574632 1 (40) 1008 s 372645 2 675243 ;) f'ive times ::l34G67 673524 3 :326475 1 repeated. 456273 1 733642 2 7!52634 1 674532 3 ::!67453 1 657423 \) 256374 1 PL 2 :14. 56 7 2 456372 5 742635 2 354207 5 {) 357264 2 253746 ., (3 2 54 7 6) 1 342567 0 Nos. 33, 34, 3.3, 39 and 40 each twice 1·epeateJ.

'.rhe following five blocks (A tu E) are used in the composition of touches :\' os. H to :'56.

A B c 234567 2 3 4 :) II 7 :!:H5G7 ------762634 233741.) :! .) 3 7 4 6 -· 467352 - 6 7 2 4 3 ;~ 27.)1):3-1 436275 - 3 4 6572 2 I) 7 4 53 423567 354267 - 342:367

D 234567 234307

s 572634 s572o34 567423 567423 (546372 - 34:3207 534267 36 A. The Sevcnt.h In and Out ; or the Sixth :\Iiddle and Before. B . The Seventh Before: and Wrong; ur the Sixth In and Out C. The Seventh Right; or the Sixth in ll-7 down. D. The S eventh Before with a. Single, or the Shth Middle with a Hingle. E . I!; the AAme as D with a Bob at Right added.

(H) ::!2-i (12) 2:H (43) <~3(i (44) 33(} 3 3 4 ;) I") ::! 3 '!;, ti 234:)6 2 3 4 5 f.i ------3342li B :3 -l :?. G B c :~542ll B 35426 B ;) -1 ~~ 2 t1 c t "3 :.l fi ll .J.:.l 52 li A 52-13BB 4 2 3 5 lj l:l ,;24a!l c ;) 4 32o A !G236 A 2345tl c 2 3 4 G li H 42356 B 53246 B :.!4256 A 34256 B 23 4 56 A 234 5 6 A

(43) 33Li ( 1li) JJ(j (·17) 336 (48) 448 2:34.')11 2 :1-!:, (j :?.3456 234Gtl - - - 3542GB 42a5H A :3 G 4 2 G B 35426 B 4 :.l 5 2 ll _-\ 2 5 :-:! 4 fj B 4 3G26 A ;)432() c 3::!54li B :1 2 54 {i A :.!2 5 46 .H !3526 c 2-1536 B 24G36 B i) :~ 2 4 (3 A :32546B 52436 A :i243H A 3425(1 B ~4G3tl B 2:~-l:)fi B 2 :~ 4!) (j n 2:~456 A -l523<3 0 5243· () c 23456B

(.H)) ;)04 (:)0) 5()4 (:31) 504 (52) 504 23456 2 :14 5 I) 23456 23456 ---- 35-!26B :3 ;)4. 2() ll 4 2 3 5 (j A 42356A 54326 e :; 4 3 2 li c :3 4 2 56 A ~5346 B .J-3526 c ~ 2 :1 :, fj H 4G236 B 32546 A 32.>413B 25346 n ;)3246 .B 24536 B 2534() c 53246 c 25346 A ~3526B 53246 c :1 4 2 5 (j B :1 2 54 6 A 54326 A 34236 H 45231l R 2 4 536 B 35426 A 42356 c 52436 c G2436 A ,)2436 B 2:~-156 c 2:.!456 ll 23456 B 23456B :\7 (i:i3) 210 (•i4) 294 (G5) 4iH (.36) 532

23456 2~4:')(l 23450 2345U ------~~ 4 52 6 E 53426 D :1 4 3 2 (i E ::14 52() E 4!l326 c 34256 E 42536 ll 42530 R 53426 c 34236 D ~3546 B ~35-!6 B 23458 D + 2 ~~56 E -!8521> n ::, 2 :~ · ~ (i .\ G2:34U D 32G46 ll 2-!3GU H 2:1456 E 2453(1 B ltl•peated. :j2436 A 2 :1 4 5 13 B

{57) 672 (38) 131() 2a456 2345u 13 W H

3 G 4 2 ti Before k \VL'ong. 34520 s 4 3 5 2 (i In &. Out. 4532() · 5 + 3 2 6 In & Out. 5342li 4- 2 3 5 6 Befo1·e & Wrong. :12 450 254311 -- 54236 (59) 546 4 2 5 :~ () 23456 2 3 54 (i ::1 5 246 r; 2 ::1 4 (i 3 4 3 2 6 S Befcwe B Hight. 24350 - 4 5 2 3 B S Before B Right.. 5 2 8 4 6 S BefOl·e B Right. 4.3256 4 2 3 5 6 S Before. Repeated. Ea.ch twice repeated.

No. 57 can be t·epeated by calling Single instead of the last Bob \Vrong. The number of changes will be 134--l.

No. 59 can be repeated by calling the last course Single Befor·e and Single Right.. The number of changes will be 1064. as (60) 12«30 (ol) 1260 (62) 1260 (63) 121'10

234 5 t) 7 234i'>67 234;367 234567

7 ;) 2 () 3 4 7526:1-.1, l 752634 1 7 5 2 () :l 1 ) ti;)/423 ;) 2:3734() :3 237540 :3 5 2 7 ti 3 ·l •I 7 2 (I 53 4 :I :372:)4(3 4 372346 J 27;)034 1 2 0 7 ;) :; 4 ·1 (i 5 :3 4 7 2 1 6534. 72 1 4 ,; 2 a ti 7 720:3.};) 2 :)36472 l Nine times PL + :2 li :. 7 :l .j 4 :)7(.382 2 725()43 2 repea.t.ed 7:1·152u .,•) :3i"i742;) 1 Single half-way 2671:):3 2 253746 2 and end.

Ea.ch of ::-.ros. <>O to ti2 to be four times repeated.

(134) 1200 (Gil) 12u0

2 :3 4 .> 6 Cfi.Jl 7. 2 3 4 :) li Call 7.

3 .t. :) 2 ti S Before Bob Hight.. -l :-3 i'i 2 li S Before S Hight. 4 ;) 3 2 II Hight. a :> " 2 H Hight. G 2 3 4 () Before &. Wrong. G 4 :1 2 G Right. 3 -l 2 :) (i Before & S Wrong. 4 2 3 ,; li Before & 'Wnmg.

Five ti1nes repeated. B for Five times repeated. S for S Wrong in third and sixth B \Vt·ong in third a.nci sixth parts. parts.

( 1W l 1:2oo (07) 1260

2 :J 4. .) (j 7 C.'a.ll 2. 234;367 Call 4.

:I -l 2 G 6 7 0 u t a.t 1.. 46237;) ln. 2 ti ;3 4 7 5 In. :3()4:;27 Out at ;_), S II 4 2 :) 3 7 Out at 5 with S. 42!367;) In. 7 ti 15 : ~ ·l 2 H.ight. 234o7n Out at 4. :2 :3 7 I G 6 1 n. PL :2 4 3 li 7 i'i Five tin1es repeated. H for B at half-way and enll. Five times t·epeated. 39 (68) 1200 (69) 1260 (70) 1260 (71) 1260 234567 234:)67 234567 234567

---~-

462375 3 462375 :.~ (I 7 2 4 :3 :l 2 s 7 li 2-! 5 :3 2 2746fi33 274653:3 :1 4 6 57 2 1 ·-k 357:2-16 2 362574 1 :l 6 2 57 4 n7:342:i :I :i73246 4 623574 4 743256 ~ !"i46273 I 735246 4 236S74 4 6~7543 1 7aiifl24 •) 4()7523 2 !i26374 G 4 G 7 2 :L3 :l;; 4 2 6 7 li74235 4 l~ach of Nus. G8 to 71 to be 326374 five times repeated. Single fut• Bob half-way and end.

(72) 1260 (73) 12UO (74) l2(i(l 234567 23456713 2 :1 l ;) li 7

s 572634 1 34726G (j 7 2 4 i) :~ ~ *S 435207 ') 475:!0~ *:l -1 I) :) 7 ~ 8fi4267 4 7 52 4 (I :3 72;{(j;)4 2 23374(1 ., 524763 s- 4U7i)~3 342507 3 4235117- H 7 2 4 u 3 :i :1 Five times Five Uows ;i67:L~4 I repeated. repeated. s ~7i"ili4:~ :J Bub for Single at '" Bob for :-lingle s 3 4 2;:; (i 7 ~ in Third and Sixth half-way. and end. Fin3 times Partl'. repeated.

(7iJ) 12fi0 (76) 1~60 (77) 12110 (78) 1260 234i)G7 234667 234507 2:H367

~------4U237ii :3 752634 1 4623/;j :I /;)2634 534762 1 467352 ] :3347U2 ;)~7634 4 735246 5 U74352 4 73G24U ;) :1-Li762 2 :357246 -! 236574 J :1 5 7 2 4 (j ~ 273U45 1 ., 623457 1 302574 4- 74:)562 ,) 342756 3 ;) 5 () 2 7 4 :l 623574 4_ 257643 ,!23756 4 073542 ;~ 7463!)2 2 (j ;, 2 3 7 4 ;) 724ti35 5 25()473 1 2:-{7546 I 526374 (i 2 7 ;) 4 3 5 ,!52367 il 37254() 'b 4 ;j 5 7 2 (i 1 :120074 5 r, •) 524307 4 !173624 524367 " .PLG24367 :1 Kos. 75 to 78 eaclt. twice repeated. 40 Three quarter peals can be had by twice repeating the tlrst part of J ..J. Parket·'s 12-part peal shown on page 52. In No. 6 the thit'd Single must be replaced by a Bob and in each of Nos. 7 and 8 the fit·st Single must be replaced by a Bob in one of the Parts or in all of them.

(79) 12()0 (j '~ 7 3 :; 2 34:>276 234567 4 7 B 5 :! 2 4 ;i7::H,G2 :~ 2 :; 4 a 1 u 1 245673 1 752634 l G4237tl 4 732G64 2 23754U :• G8S742 1 537426 5 7423(\G :; 346327 3 fi4fi237 1 657234 2 34S7tl2 3 875524 2 34672G 2 2 7 :; U 4 G 453276 1 743502 3 4i)23U7 2 254G37 :) s 4 7 2 3 fi :; 7 :; J (j s 2 652743 5 735402 .,.. 4 ;) 7 :l 2 fi :~ 436275 2 24763:) (l342;) 7 I 23·!567 ~) 7324(",(j 3 57U!23 2 From Holt's Original

(80) 1200 (j 7 2 ;) :3 '~ 2 246753 3 2315(17 4 :) (i ~~ 7 2 372546 l 074520 3 24,3765 :; (j 7 2 4 ;j ;; •) 3;)027 -l l ii72643 3·16S72 7 4 :; 6 2 G 2 117;)324 G 67342G ~~ 437fi20 '1 43fi275 \ 54ll27 3 1 (j 3 4 :) 7 2 ;) 7:)4623 2 735624 •) 2 :i (i 7 :l 4. 1 237465 2 2 4 7 5 t) :; 2 032G-l7 :; 652743 2 :l52u47 7 3 (j 4 :l 2 l 376-!id 1 •J 4732H:J ·• 4 ;i 7 2 (I:~ L> 053724 ._, •) 7342().) (j :~ 4 7 2 ;-, 2 4- (j 3 7 :) ~ ()57423 •) 2 .j f) 4 7 ;; 2 l 'I' 2 3 -1 ;) 0 7 3462 r>7 34 27.-.o 1 573024 :2 :!534fi7 :; From llolt's Original 2453tJ7 •) 0723,15 2

41 (81) 1260 2345 67 ------

·) •) :142 5g7 4 ,) 1\ -~ 7 :~ 1 7 I) :::1 4 f) .J. 7 G :::1 0 42 1 :l 7 ;) 2 1\ t !) :; 7 :j 2 (\ ofi 7 234 ;) 2 7 ;) 4;) (\ .) 4 :3 3 67 2 ;) 42 ()35 7 1 (\-! 2 :~ 7 :::1 ~() 4. 7 3 G 1 264 357 4 J 21l37 ;~ 1 ti ·1 2 7 3 5 4 ;) 7 2436 2 7 :~ ,_1. 6 ;") 2 2 ;{ " () :~ 7 ·1 2 7 2 5 4_:1() -i ;~ -1 7 (\;) 2 .1 t) (\ :~ 2 7 4 4 ;_) 37 264 3 7 :i :l 1- 2H :~ :; 7 ;) ti 4 2 3 () 4 5 7 2 3 2 2() 7 :~ ·l ,; 2 4 2 :~ 5 6 7 2 45 67 23 4 (j 7 2 :3 4. :i ·~ :..l :3 t ;) () 7 4

This quarter peal can easily be ca]lf,J by tlw Hells Before (as explained on page fill). Fir·st part-4o 3D () 7 :2 :1 ± ,) Second p:trt.-tiJ> II> :2 :l 4 :) ti 7 Third part-2u i3n 4 .; 1\ 7 2 :~

• Grandsire Triples

(iv) CALLI:><<; TJIE BELr.,;; Hui-:-:D IT not infrequently happens during n touch t hl'l.t sumdhing goe::; wrong and the conducto1· desires tu br·ing th<> bells round. It may be that mistakes have been mad~ in the r-ing-ing, or the!'e has been a miscall, or that. the time ava.ilnble will not permit of the full length started for. but in any ease som•~ special action must be taken, and t.he conduct01· hns to decide what to do. Usually he waits for what seerns to be the fipst convenient oppol'­ tunity and then attempts to forcn t-he bells into rounds. Some­ times it. can be done fairly easily, but g('n(>rally it means a nasty jar in the striking, and a.lways it is. more or less. a confession of failw'e. \Vhen the striking- is t·easona.hJ~, goud. t.his sudden forcing- up of rounds sounds bn.1l and the1·e is little or nothing­ to be said in favout• of it. It is much bette1· t <> let the bells go on until the tin1e available is exhausted, and to set. the bells in the middle of the changes. Jf the final change i;-; on1~ when a com­ bination of the larger bells strikL'S behind, it. '\\"ill not sound at all bad outside the steeple--at an~..- ratP it '\Viii sounll as if it wet·e done intentionally-whereas the for-cing up .,f J·ulmds a]mi)St 4:2 always advertises, even to :t casual hearer, that something bas gone wrong with the ringing. But thet•e is another and a far better way. and that is to call bells round by the ordin11.ry use of Bobs and Singles. It is a thing which ought to be understood and employed by conductors much more than is usual. It is, of course, well enough known by the most skilful men, though it proba.bly is much Jess used than it once was, for the reason t.hat the more advanced bands no'\v practise methods which do not readily afford opportunities for its employment. The average conductor naturally expects the touch he starts fot· to rnn its allotted course. and does not know how to deal with t.be abnormal when it occurs. It is in Minor and Triples ringing that calling r·ound can best be done and wher<~ it gives the best and quickest results. In those methods the bells can be brought home in an a.stonishingly short time from any position and the man who can at any given time do it in Grandsire Triples with the minimum number of calls may claim to be one who really understands conducting. There are not ma.ny such, and so great proficiency is not necessary, for there are plans of calling round in Grandsire which a'fle not difficult to lear·n and to apply in any emergency, and which do not t•equire more than a few caJls·to put int,o operation. These should be undet•stood and use() by everyone who aspires to be a conductor in a belfr~· where Urandsire is pra.ct.ise ability and experience, is not usually very easy ; but., fol'tunately, at the outset it is of no great importance, and when j Ito t.ime eornes that he must tlofinitel~· know, he can find out without. much difficulty.

(; n A:-; DSlltE DoUBLEs If tho conductor knows that the changes are in com·s(,, he can call either the S<'..cond or t.hc Thil'

If the Fow·th and Fifth stJ·ike 4-;) at backstroke, when the Third is in the llunt, call the Second into the Hunt with a Single. If they strike i)-4 when the ~econd is in the Hunt, call the Third into the Tlunt with a Single. In either· case no further Cllll is necessary. G-!tA:-.IDSl!tE TrtlPLI·:s (h·andsire Triples is, of all methods, per·haps the most inter·­ esting in which to call the bells r·ound. 'fhe ways of doing it are very varied, but the beginner will do well to study and practise one plan first and to make himself thoroughly acquainted with that before he exper·iments with other plans. The one recommended is not necessarily the quickest or· the one which uses the fewest number of calls. but that does not matter· since the number of leads required will not. in any case be many. G-randsit·e Tr·iples can be brought round either· at handstr·oke or at. backstroke. In the tlr·st case the changes must be out-of­ course; in the second, in-course. To bring up rounds at back­ stroke the first thing is to bring the Sixth and Seventh t.ogether in their right order-that is with the Seventh cow-sing the Sixt.lr, so that they st.rike 6-7 behind at backstroke. Watch the Sixth until it. courses with one bell following it and then the treble. This will be in the lead aft.er it. has dodged in U-7 up and when it is going to dodge in 4-3 up. A Bob at that lead-end will put the Sixth into the hunt. Next watch the Seventh. After one or more leads it will be Before. lt will make Thir·ds l'lacP and when it returns to the front it. will take off the Sixth which is in the 11 unt. Those two beUs are now together, and when they go behind will strike 6-7 at backstroke. If the Sixth were left in the Ilunt. the next lead would, of course. part them again, so a Uob is called which will make the Sixth dodge in 4-5 down and the Seventh dodge in G-7 down. The next lead-end will bl' 7o2 5342()7 But it may be that the 47:J2fili Third is cour·sing before 52374li the Sixth and the FoUl'th -02457i! -675423 after the Fifth. 1 n tlmt G52:347 -i\4(527!) case call the Seventh In­ 1135724 and-Out twice and then H73452 a Single at Home. - 24!357B -753624 As an example of all this, 254007 -467253 shown in the figures given s 204567 45 above, pick at haphazard 1 4 (S 2 5 7 3 to start from. The fir-st job is to get the Sixth into the hunt. and, as it is at present making Thirds place, it is necessary to wait until it has dodged in 4- 5 down, 11-7 down, and 6-7 up. At the next lead-end, when it is going to dodge in 4-i> up, caJI a Bob and that puts the bell into the hunt. Next find out where the Seventh is. At the last Bob it dodged in 6-7 down, so it will be three leads before it makes Thirds place, and follows the Sixth to the front.. When those two bell;; get up behind they will strike o-7 at buckst!'oke, which is a sure sign that at the next lead-end a Bob must be called to fetch the Ri:xth out of the hunt. The followinp; lead-end is the colU'se-end. The Fifth is now t:ow·sing neither iu front of the Sixth no1· after the Seventh, nor is it in the hunt. (:all the Seventh Before­ with-a-Double twice or (which is the sariic thing) the Sixth In­ and-Out twice. 'l'his will bring Lhe t.hr<'e big bells togethe1· in t.heir right positions. The course-end which follow;; i;; easily seen, and as it is 3 ~ 4. 5 fl 7, two Bobs and a Single will b1·ing the changes round. The bells could have been bl'(mght home with fewel' calls and in less number of changes, but the example has only 280, and the conductor who is not pr<>sseu for time will find it instructive anti interesting tci watch how the bells gat.he1· themselves in order into their home positions. The music. t.oo, is almost the be;;t tha.t Gra.ndsire Tt·iples has to give. It is ~xcellent practice for a cnnductor to caJI np some change at random (or get another to do it for him) and then to bring the beils round, using the plan described, nntil he thoroughly understands it. As an alternative thfl f;eventh might have been called into the Hunt and out. again, not at ' t.he lead-end after the Sixth ;:J 2 3 7 .j (; hll.s made thirds place but at -(:17:3423 the lead-end when the Sixth is 4.50327 - 34G275 Befm·e. The Sixth will make - 7 3 4 2 5 (i :l 2 4 5 I) 7 third;; pl11ce and r eturn to the 7~iHI,!G front ; the Sevent-h will dodge ,)(i7 ·123 -7fi3624 in -1-5 down and take it off ti40372 -167253 the lead; and t.he two bells will ij :.l 4 2 (:j 7 /") 2 3 4 5 I) 7 be together in t.he right order. 4G In the example givon this will be the bet.ter pla.n, for the Fiftll is put into the hunt, and it needs but to caJl the Sixth In"and­ Out to bring the three big bells into their home positions. To bring the Fifth home the Sixth was called In-and-Out twice in the first exo.mple, once in the second, and for this, too, there is an alt.ernative. After the Sixth and Seventh aro together in the right Ol'der, instead of allowing the course-end to come up at a plain leo.d before dealing with the Fifth, cn.ll a Bob to ntake t.he Seventh dodge in 4-5 up. That will cut out the course end,· but. if the J<,ifth is Before will at once bring the three large bells into their right cow·sing positions. If the Fifth comes out of the Hunt., another Bob with the Seventh in 1-!i up four leads later will be needed. 4 6 2 :i 7 :\ -:35274H 3 7 5 6 2 4 450327 3G7452 4':.!!i7G2 34o27!i 4732:)1; :324G07

- li 2 4 !) 7 :3 - 7:; :3 G 2 .J 652347 - 4. B 7 2 G :l () 3 !) 7 2 4. s 2 :~ 1 ;j (i 7 H734G2 240:)7~l

1f after the Sixth and Seventh at'(' brought together the l<'ifth is coursing in front of the Sixth (the Titt.um position), tirst call the Seventh eithP-r In-and-Out or TT orne, and then use one of the two a.ltorn:ttives t.o bring th~ Fifth home. By experimental pricking or ringing the student can see for hilllilelf which is the best in certain circumstances, but eithel' will set·ve. To ca.ll the bells l"Ound at handstroke, the foregoing rules require amendment as follows. :For the Seventh substitute the Sixth : for the Sixth, the Seventh ; for the Fifth, the Fourth ; and for the Fourth, the Fifth. When these bells are in their cm-rect positions rounds will occur at handstroke when the Third is in the Hunt and the bells are Out-of-Course. Using the same example as before, call the Seventh into the Hunt. Alter the Sixt.h has made Thirds, <;all the Seventh out of the Hunt. The Fifth is already in its correct position. As the Fourth is in the 47 Hunt it can be brought into Fifths Place by calling the Seventb In-and-Out. As the bells are out of course and the Third is in the Hunt rounds will occm- without any further calls. 46257:\ 423657 764;)23 4563~7 -057264 -73<1256 (325476) 723645 76~304

-457362 ,!35276

GRANDSI.HE TRIPLES (v) PEALS . THE composition of peals of Grandsire Triples has alway;; interested ilie · more mathematical members of the ringing Exercise, and during two and a half centUI·ies a large number was produced. As the problems involved arc abstruse and were imperfectly undet·stood, progress was bound to be slow and much of what was done is now obsolete. Men formed two ideals which they thought were possible. On tho one hand they did not see why the full extent of the changes should not be pro­ dueed by common Bobs only, if a man wet·e elcver enough to find out the right way ; and on the other they recognised the need for peals divided into regular parts with good observations for the conductor, so that Bob calling should not necessarily be a more difflcuJt task in Grandsi.re Triple,; than in such methods as Plain Bob or Treble Dob. But both ideals seemed just out of reach. John Holt almo~t attained them (but not quite) in his two famous and popular compositions. The Original produced all but three leads by Bobs alone, but the peal was very difficult to call. The Ten Part admirably suited the conductor's purposes, but two in-com-se !4ingles (which are foweign to the method as generally practised) had to be used. Holt's peals stood alone and it was not until the last part of the nineteenth century that other men began to know enough t.o produce work comparable to his. Then there was a great denJ of activity which (added to the moderately successful attempts of some earlier men) gave 48 the peals which appear in the first and second editions of Grandsi1·e, and in the Colledions published by tho Central Council of Church Bell Jtingers. These peals have an important place in the development of the science and art of change-ringing, but two things happened which definitely atfected their value in practical ringing and changed the opinions and attitude of the Exercise to the whole question. One was \V. H. Thompson's proof that a peal of Gt·andsire Triples with common Bobs only is not possible; the other was the appearance of .T. .r. Parker's Twelve Part peal. In the earlier times it wa.s considered that the proper way to compose a peal of Grandsire Triples was by Bobs onJy, or (if that could not quite be done by the composer), he might use other calls which might be ordinary Singles, or in-course Bob Singles, or in-course plain lead Sin~les, or fifths place Bobs, or any other "alterat.ions," provided they were fully recognised as regrettable necessities and that the minimum number only was used. To-day it is gener·ally agreed that Grandsirc Tr·iples, like other methods, ha.s a recognised Bub and a recognised Single which alone should be used, and no restriction is placed on the number of either a composer chooses to employ. The Twelve Part is so emphatically the peal needed in pra.ctica,l ringing that it has made obsolete any old rules which appeared to condemn it. Another and distinct style of peal has come down to us from the earliest times. These peals arc made up of three-lead courses in every one of which one bell double dodges in (i-7 down, then in 1-5 up, and then is Before. It does not go into the Hunt, and never dodges in G-7 up nor in wish to study the evolution of Grandsire Triples composition can find the figures of these ail.d other peals in the first two editions of Orandsire ; but a.s tho present book is intended mainly for average practical ringers we have no roon1 for thent here. It happeneu soon after the Exercise was supplied with a large number of new peals of GL'andsire Triples that the gt•eat develop­ ment of 1\{ajor ringing and especially' uf SW'prise :1Iajor ringing began. The essential importance of Grandsire was not lessened, but the method no longer attt•acted so much attention from the most skilful bands and two or tlu·ce peal compositions served all practical pur·poses, especially as one of them was Parker's Tv.relve Part. The first two of the following peal:; are on the tht·ee-Jead course plan. No. 4 is John Holt's famous Ten-part peal. It was for long the one indispensable composition in the art of change­ ringing and, though circumstances have dep!'ived it of that dis­ tinction, it still remains one of the most outstanding compositions and is as worthy of study as ever it was. One point about it may claim our passing attention. 1 t consists of ten parts all of the same length, but it is not a I'egular ten-part peal in the same way that :i\liddleton's Cambridge 8Ul'pt'isc Major is a regular five-part peal or that l'arkcr's twclvo-pa.rt is a regular twelve­ part peal of Grandsire Triples, ot· that scores of peals in many methods are dh•ided intu equal and regul:tl' parts. And this devia.tion from strict regularity is not due to caprice or chance but to the fixed mathematical law~; which control Grandsire Triples composition and decree that it is not possible to have a true extent in two equal and similat· halves '''ith two Singles only whether the~.- be ordinary ur in-course Singles. \Ve are not aware that the law of which this is a part has ever been fully investigated and explained, but it J1as some rathet• important results so far as practical ringing is concet·ned as we shall see presently. 50 The first half of Holt's Ten-part consists of five equal and regular parts. The second half consists also of five equal and regular parts and the two halves a1•e joined by the in-course Hingles, but the caUing of the second half has to be the reverse of that in the first half. C. D. P. Davies made some elaborate investigations into the pla.n on which llolt.'s Ten-part is constructed, the variations of which it is capable, and the other peals belonging to the same syst,em. These will all be found in the early editions of Grandsirc. Reeves's Va1·iatiun (No. 3) diners from Holt's peal only by calling an extra Bob when the Second is Before after the fifth Bob in each Ptwt. (1) 5040 (2) GU463 1 ~ ,:; 4 n :~ 762543 ~5:1764 2:)37()4. 624537

:354267 - Ls :! Cd 2 tl7 -S 74326ii s ------346752 347302 4..)7302 - s 645327 4 7 2 56;~ ;:; 7 2 4 (j :1 542678 7 ~ :~ 4 () c; 123Gti4 24753() 2 :~ -t 7 () G s - 2347GG 423576 - s s 4 :~52() 7 - s -!3:i2u7 -s ----- 326574 s s :.1574()2 ,;:~74112 - s 267.')43 ii723(ic~ :; 7 2 :) G 4 674532 7245():.1 7~-1:3tiii 743526 2 4 G 7 G :~ s - 24ii76:3 632475 s G43267 - s,_ ;:; J :3 2 fl 7 - ·-s 237654 ----- 73524(; 4 :~ 7 G (J 2 -l37Gti2 5347()2 37!i4t32 s - :37:)41i2 k - 436527 752:364 7 52 :3 ti ·l :3425G7 - s s ,)247133 324763 A. J. PITMAN. 423567 - 1-:i -!~3567 - s ,TOHN VICARS. En. TAYLOR. Each five times t·epea.ted. Bob flll' Single half-way and end. 51 (4) 3040 (5) 5040 (a) (~) (a) (~) ~:34;')()7 ~:35476 ~04507 235476 ----- 752634 1 ()42735 1 752634 1 642735 1 347265 2 746523 ;) 34 7 2 () ;j 2 746523 5 24357() 5 :')47362 5 ~ 4 3 3 7 () ;j i54-73G2 .:; !)<12637 iJ :345276 5 :)42li37 ,) 3 ·1 iJ 2 7 6 iJ 765342 1 7(i3!J24 2 7 (j :) 3 .j ~ 7li3324 2 :3 6 7 2 54 ;j 367432 5 -J.27::J36 2 327645 3 ::i4372G 2 2453(37 1 7 :~ 4 2 () ,) :3 453762 2 7 4 5o a 2 ;j :l 4 2 7 56 :"5 I) 3 7 4 2 3 2 274653 1 6472;):3 ;J 7-:1362::-i ;) j ;) (j 3 7 2 :) 672345 ;) 24637:) :) 257364 2 :3 5 ! 2 li 7 i) 376524 5 2:)37413 :) 243657 2 HOLT's TEX PART. HEI':VEs's \'.-\RL\TION. In each of Xos. 4 and :) ca.Jl (a) five times with a Holt's Bob Single (page 23) at end of fifth t.ime: then call (b) five times with another ll olt's Bob Single At end of last time.

(li) ;')040 (7) 51).11) (~) :)010 234307 234:)07 2 :! 1 :) (j 'i ----- 6 'i 2 1.) :3 2 7::; 2 (l ;) J (i 'i:!. 153 2 G:J6247 2 2:l7G4 () :l s 48()572 l s 27:)436 1 s 5 G 2 4 :3 7 1 72cl(}i);3 2 ()42:37:) 1 3 7 i) 2 4 (i 2 2 4 'i (j 53 4 G36742 l 7 5 :l 2" li 1 ;) li ~ iJ 4 7 1 s 7 2 ;) 4 3 (j l li274G~! l I) 2 8 54 7 4 :l () 7 54 2 2 27tit5J -1 2 :~ li 5 l 'i c1 (a) 42375(:) 2 7 6 2 4 5 :3 472()53 2 67-!G23 l :i37:2-!ll ":2 ~ fi :l J 57 2 1 4:21)73::1 3 s 265437 1 :2 :i () 'i :l 4 1 s 7Ci+J:26 1 7•120li5 ~7:205(\ 1 2 () 7 -~ 3 ;) 2 337()42 s :l (\ 4 57 :2 t\72-!35 -! s 625437 1 7 :2 :l 4 :> (j 2 :i l (j 3 'i :2 37654:2 ·) (lt) :) 1\ 7 3 4 2 2 4li.)372 •! (a) ·i 2 :l (j ;') 7 :2 :2 :3 j 4 6 7 1 PL 4:23765 ~ l'L 243756 1 .Repeat each eleven times, Single for Bub at (a) in sixth and twelfth parts. J. J. l'AHKl:ll'S T\VELVE PART. (9) 5040 2:14.){)7 continued- conl-inucd- IS 7 2-1- ii :l ~ :-; 2.45fl 73 l -1-6 723 5 1 ~ 5 () 7 ;~ 4 :~ 7 32 i'i61 2 n7 4 ~3n 4 1 7 :2 a 5 ls l -1-i'i 7U ii2 l 3:->f\42 7 2 !)(142 ~7 ~ ::!24 765 2 :1-73645 2 7 2 ,, :! ~~ ._!. G 73624 ::it12473 1 2i:i7::lli .J ·I ~ :s 7 !i () 2 · ~ 4 "'"' 7a :>2 4C~ 2 s :l ·I 2 u !) 7 l 4(}3275 -l67fi23 2 ~ 7 5:.J2 u4 2 s 'l !) 4 7 () :~ 1 U7 •~ 523 4 ·1 :! 7 () ,, :~ :~ 7 2 {i :"} 4- I '2:·H4G 7 2 au.~ ;) 2 1 •1 (l 3 G 7 2 1 7 -l2:);)() 1 s !j 7 :l 2 () ·1 1-4 i'i217ti~ 1 :Hi 7254 2 s 7 3 !)024 1 42 3:) 67 1

Piv ~ Limr.s J·P-pcatct.J. Hingle [OJ' Bob half-way a.nd end •

..\. ,f. CoRRIGA~.

(10) 5040 :l :H :; t) 7 --- - cnnlinucd- <:onlinou>d- 7 :i 2 I) :3 I 1 '1.7 f>fi3 :3 7 3 ·I H52 1 J .1 7 '2 tL"i 2 :~51 IS 2 7 1 .) 274133 2 :i 2 :s G 4 1 2 7 :! 1 (I !) 2 :3 ·i:; 6 2 7 1 -t1.i3o2 i H 4fi2H7a 2 7 iii) 6 4. 2 7!i.J a ll 2 i 7 :l ·I 2u!) 2 .~. i)426 73 1 'l. a 7 11 :i 1 r,27fL34 1 275430 3 !-; -1- ;') 2 7 li :l 2 a ·t :> 7 t) 2 2 (j .J. 2 J 7 ;'j 1 :l 7 i(j.) 2 s 72 JH 4!> 1 7C.H2 3 1 2 ;) 2 :! 4. fi 7 2 "() 7 "'2 :l l '":l 4 7 u 2!) 2 fi 1 5 :l .J 2 2 :l ~ !J2t\ 7 1 s :i23764 ~ I '2 (I;):! 7 ~ ~ ::l 7 :1 {) 1- :; 1 · ~7 :>o23 7 i) ·I a :! li :15:2:3()7 2 PL 4:.! :3 ;) 6 7 :$

Five t imes r~pea.tc .J . Single fo1· Bob at • in third a nd sixt.h pa1·ts.

A. J . Con.RTG.-\ N.

5~ (11) 5040 (a) (IJ) (c) (d) :301-Gii7 G34027 432():)7 :i62::JJ7 ------46237.3 3 -!2li573 :\ 8 524;)7() ... 2 4 5 li 7 :\ :3 75"123() 2 7:146G2 2 s :!65724 I 732564 2 5472~\6 4 347652 4 523tl47 ;1 :.\ 2 7 5 (i 4 4 s 63:i724 2 s 2:38'/(J.! 2 625734 :; ~ -1-t\0752 2 476236 1 "1726:')3 34tl572 2 :!.74Gti3 s 254376 1 364572 1 723tiG4 2 3G267 4 l 762435 2 s 52076-! 1 4(i7G23 1 s ti4:37:i2 1 (l 2 7 ·~ 3 5 4 365247 :~ G61372 ;:; 3GG427 3 s 536742 2 2G37G,1 ii 2 :l G 7 6 "I l 4:i37ti2 G 27G436 l G4237G 2 G 1\2 5 51()70:!. !) t\ :) ;1 7 2 -l- 1 :ii337 12 3 2 G (i 7 4 2 ;; 2 ll .i I 7 3 :1 I 3H~7 ...•) 743ilfi2 2 2:i7li43 6G2374 5 40ti7:)2 6 5 ·1-:! 2 7 0

(n) must. be called ont.:e, then (/>) fuur· t.irue:;. t.h,~ part-ends being 026547, :).t:l2(J7, 2654:17 and '1:.~21i:i7, (r) is then called once and (d) four times, the part-ends heing :1 .j. :i G 2. '/. 6 2 3 J 57, 4 ;) ti 2:17 and .2 3 4 50 7. ThP calling of (h) and (d) is the same. (12) 50!0 (a) (ul 2 2 74~u25 !') !')3-1-627 2 632743 1 :)74231l ,, (i 7 2 4 :~ 1 () :~ ;) 7 c! 2 5 43627G 2 62:;::l74 7 4 :; 6 :l 2 !I 27()435 l s 634275 4 s ;~ 4 I) 7 2 5 1 21)7:34!. l 702433 4 !)26734 1 E. BA:I'KES JAMES. In peals Xos. 12 and 13, (a.) must Jir»t be ca.Ued five times and 1-hen (b) five t.inws. ln No. 12 a. Bob must be called instead of a. Single at the ciHl <>f t,he fifth and tenth p11rts: and in No. l:l a Single instea.tl o[ a Hob half-way and end.

(14) 5040 roni'inued- continued- t'OIIfi lilled- 2 :~ 4 .j n 7 :; 1 (j 7 :l 2 7(!324.) '~ ;; 7 (j :i 2 ------6724•)::l 2 :1 2 ,-; 0 7 4. 2 4 57!{ 2 H ~ :.!24•763 2 5:36217 2 7 -1 :3 ,; (\ 2 2 2 6 4 7 :l ;) 2 fj;')!3472 2 s ·) 7 ,j 4. 3 fi s ;) 2764::l 1 G7231l4 s 42()753 1 s 4 0 2 :3 7 G 1 s 1)3;')427 f34n2:-l7 •) 374026 1 7:"i4231i 2 . •) 76548 2 :l 7 () ;) 2 4 2 s :)63274 1 ::ll) 7 4 2 :) 2 i :\ 2 6 :i 7 2 s 7 :'i34G2 ;) 74G326 2 s u4:i·:l72 :; s :1li172S ;, s -t27(),):1 1 267 5::l4 2 s 52 6 7 4 :l L s 7:)32()4 1 s 1)34527 1 s 6G2473 5 s 7H542tl s 2-!76:3::3 1 75()23·1 l s 43 G7 02 1 fi-1 7 2 3 ;) :l fi 2 :) 1 7 s 2•!7:J,)() 1 s 724536 1 s 2 5 ll ::l 4 7 s :; 7 :l 4 (J 2 I (J 3 2 ;) 4 'i 1 (j 57 :3 2 4 1 732•1:)(; I 2 4 :; (J 7 :3 1 :l 2 6 ,-, -1 7 4 s :l4G2:37 l a 2 7 4 5u 4 J:; 2 () 7 :\ -1 7:; :~ -1 2 () 1 7:! :1 54 (I 1 (i -1 ;} ;) 2 7 J :\ (i ~ 7 ;-; 2 I i :i 'i G32 .) 2:37546 4 ·) 4- n 1 :J 2 ;) 'i (j :l 2 i :; !i (i ,; 2-! :~ 7 1 -!:i6723 5 Twice Hepeated. B. D. .PHICE. 55 (li>) Gfl40

l"!HsT Two PARTS. Tl!lRO PART. 234Go7 423G67 conlinucd- s 7 52 4::; a ·> 75423ti -i S 7 U 4- :~ ;-, 2 :) :~ 4 7 :"} 6 2 25764:-1 r; 2 :1 7 ;; li 4- H il23G47 :; 7 2 6 4 :! 4 -!!)2fi37 {7536~ ~ ·1:1G2117::! s 074:1·>2 1 3 7 4 ~ 5 () :i 7~4U3G ~:l(i:j74 4 G ;~ 7 (i 2. :.l G2754:1:, 7 ~ '2 (i :; :~ 2

2 7 4 u 3 :1 :3 :') ll 4 2 7 () l ~ 7 ~~ 2 ;-l ;--) 532:> ij ~7esGJ ,, () 7 :1 i} 4 2 1 s :) :) 4 (i 2 7 1 4 3 ~::; 7 (j 57G234 :"i s (i 7 :1 '2 ::; -l ~ 7 4 :3 (J ;) :~ u :-! I) 7 4 2 :! 4 2 () ;; 7 :1 l 3 7 2:; 4 ~~ _, 2 7 (} 1- :1 !) l 7 :1 -i (\ i) 2 2 () 5 :-! •cl- 7 '2 1 47256:{" H :1 7 2 -l :1 5 376524 :J !174320:; 1 4 n :1 :; 2 :1 G 7 :J 4 t\ :2 ,, ;\ 7 5 <> 4 2 G :; ·l 7 2 ll ;j 5 •1 7 G ~ 3 !i i) I' L ;\ 4o Z ii f) 7 :1 s 2 :; 3 li •l. 7 1 ltcpcated pt•ocluccs ,. 2 :1 5 !i 7 S (I 7 2 4 :) :1 l :1 4- II !i 7 2 7 2 :1 r;;; 4 2 Contim•c the calling of the Third Part li:!74:3rl 5 as from the second sing-le in the Fh·st 7a

35 { lCl) liOLT'S ORIGil\AL.

:i0·10 234507 continued- continued- continued- r-ont-inued- 7 ;'"i ~ 63 4 1 "'.)3:! 7 u t :J54726 3 456372 1 ~7U54H 1 207546 B :! ;:; 4 (i :3 7 G 750642 ;) 67452:3 3 +326:37 2 742305 ~~ 3 7 2 4 (j;j ') 34752() 3 356274 574203 2 637234 2 ."iUIG72 1 u:>3:!47 1 7436~;) 2 63:>·127 2 <:46725 :! ;; 7 ,; 4 2 6 ;j j:J (j :2 ·l 7 4 437623 -1 746235 1 743562 ;) ()~.~~27.) 1 ti-L3B72 3 634572 G ti37452 3 547236 ,, 7;:; (i 3 2 .·~ 2 23fi74;) 1 266734 1 246;):37 1 735462 3 4372i>u 1 (j ·12 :3 ii 7 3 632547 :3 372654 2 20()35 1 37!2.)6 cJ 73H:i42 l 766432 1 :25:3746 3 7:32456 ;; 7-l:32·iti -I ::i:l7:2(H OJ 457263 " ;)32746 4 u!7:l32 l :I;) 7 4 (j :2 ;; :17;) :2 (i l + 634725 :! n 7 ,; -13 2 1 476532 i :2 4 i3!i.; 7 l 2 7:14 ;) (i ;) 25047:-l :2 ;):36724 3 2•'i437U 1 Gi2:HI4 2 jj -!:2;; 7:1 3427:)() 475230 1 5-!237(l 4 4 :~ j (i 7 2 7 ;; u 2 ;) 1 :2 2534()7 :I 274053 5 035742 l ;; ;; lli 7 :2 l ,) ~ i I) 2 :l 2 672:i4:'i 2 ·>32467 2 346327 :-1 4. 7:1:; 2 (i :3 :2 :I;; 7 (i -l •) 2Hi7G53 l ~:I (i 7 ,-; ~ :l 5 ~I U ~ 7 :; 675:124. .) .)32074 1 4·37326 :I ~/4.i3li -; :.~ ~ ():! -l :2 43627:) 1 2 7 5 :H 6 3 03•1257 1 14.~->:Hi .t ~ ~ 7 ;)() :l 2 7 54 62 :l •) 3427()3 3 37642:1 ') (i .) 7:1 12 1 :J.i2tl-i 7 23746;) :2 7-!5326 5 ., 34;i27tl 7 ,I. II;;~ 3 '·' 17 :!:2 () .) :2 liG2743 •) 1)37245 l ;)7:34()2 3 j 17:1132 .-, 7 :; 4 2 () ,; J ~l7 6 4. 52 :2 :16 ,; 7 4 5 213673 l 4. 7 .i :IIi 2 ~ (i 3 7 4. 2:3 2 053724 3 452736 1 132564 •) 2 ~~ -l n 7 .) :11 B2;; 7 ,, 4762!5:~ 1 s :~24567 3 ;);3i-J2t> ;) 'j .i 2 l II :l •) .'i I :l II 2 -l :i :3 Hi 2 7 2 753(124 1 ()43237 l :~-t'ill.i2 2 .1 ,; a ll7 :2 :145027 4 -1 (\7 2 5 :; 3 i (i;)2 4 2 .J- 'j 3 (i .i2 ! li/2;-,:34 •) 64:17;)2 :j i-;234567 1 (17) J. .f. P.\HKEil'S 0:-;r: P.\llT. 5010 •) :1 1 ,; n 7 ----- coniinttrtl- rnllli.ILI.ICJ-

-; .) f) ] 8 3 7 2 () :3 4 1 ti 2 -i ~.l :I .. ·l :J 2 7 4 6 fiB7 2 1 .-. •) 07 I :I ~. ."i :l .j (i :2 7 4 2 3 4 7 () !') 1 7 ~ 3 :I 1).1 ,) li :l " -; ·1 ~ 5 s 7 5 :J (\ :3 4 1 IH 7 ;) :; :2 •) ;) -t li 3 •) 7 :I 2 J 7 t) 4 t) 3 ~ li :2 7 :I :I 4 ;) 7 (j ~ :i .. _, .. 5 3 2() 7 l 3 ·) ,; :\ li 7 .. -; l :l 2 ;) (l 5 •> ·) •) 7 4 526:3 2 ,) ·I 7 ;) 1\ ;) 4 7 II :l ;j :) •) •) 4 57 263 7 I :I (\ .. ,) II l ;) 7 3 5 2 5 -1 :3 7 6 G :2 .. 7 :1 1\ .J ~ -; :\ li :2 ;) ·1 2 ·) •> •) 3 i) 2 () 1- 7 ;) 1\ I 7 ,, ,, :2 :3 7 4 () 3 !) ·) (i 5 :3 7 2 4 ;) :1 li 4 ;) 7 :\ l :.I ~ ;) 7 6 :i :12 (i 5 J 7 :3 ., :\ 2 7 lj ,-, .) 1\ ;) 1 7 3 2 l ,, 2 ::l 7 6 -i G 7 :3 4 ;) •) li ;) :\ 204 7 5 2 7 2 3 4 :3 f) 5 .. :l 7 li -t :2 ;) I 2 :l G 6 7 G 4 2 7 6 ;j 3 ;') 1\ :3 2 7 1 ;J !-) ~ 1 7 :.l (\ ;) " ·) ., ,) -; ;) 1\ 4 :1 7 " '> i -1 lj ~ :\ :2 ;) 1\ -~ :3 7 " 6 4 B2 2 .) .j 7 :.I li ~ ,) .. .1 7 2 :3 (j 3 ~ 4 7 3 ;) 6 1 :l 4 ;; 2 7 (j .. •) 4 (\ 7 :J !') •)" 7 5 ~ .j. 1\ :1 :l ~+:3 lj .) 7 .. 1\ ~ 3 57 5 •) (l :1 7 2 -~ 5 2 :\ .) I 7 1\ '·'•> :I l 1\ 7 :2 5 5 23 () .-; 7 4 :) ,) :23 4 7 1\ 7 I :3 .) 62 5 ·) 53 2 4 (i 7 •J l 2 :) ();\ 7 ,) 1\ -; :\ ;j 4 2 ·1 :-; 7 2 () 5 1\ :2 4 7 .) :1 .) ."i ,1 (j 7 :.12 2 7 3 "·1 () G 2 a 1 ,-; 1\ 2 :3 7 :I 1\ :.l .. 4 27 3 ·) -1 5 7 3 2 6 3 ;) ! 7 1\ :l ,) I :; I\ 7 ;)~ :) •) 3 5 ·1 6 7 2 :) 7 ;) :I ·I li ,) I :3 i 2ti 3 ;)

;_) () ;,; (i 3 8 24 7 ;"') :.\ 7 ~ I " 1\ .. 7 ·1 2 2 2 G 67 3 4 ;.) 1\ .-. :3 .j 7 ~ ·• I .. (i :3 7 2 :; •> •) .j •) ., ,, ., •.> 4 26 7 G 2 7 1\ :I " ·> I 67 5 •) •) ., "- 2 :.I (j 7 ;; -1 ~~ 7 ;) (\ I .) ,) .., 7 4 (i 5 I'L~ :1 I ,-, (j 7 -!

'I' his peal contains only ninety ca. lis.

::;::; (IS) 5040 234;)(37 rnnlin11rtl- rtn!liruu•d- confin11ctl-- continued- s 572634 7 () :i ~ ~:I ,; :l1 ii71i ~ ;) l i'i2 (i 7 3 0 264573 2 465372 :l-t 7 2 fi ;j li2 :1 i'i7 4 2 iJ2 41\7 :l J 1142573 4 234766 1 7130Li:.l :I ,JGI\7 2 :.l L :Hi!'i721 L 3:'36742 1 s 752634 ~ 4 7 :iII :1 1 li24r.:n :~ :H3ii7U 2 423675 2 467352 ;)42J7f) .; 7 ;j tl:l ~4 1 tl!) 2 7 -!3 l ,; (i 4 7 2 3 1 7 54 6 2:1 :J -l2iJ071i .j :.l·l 7 I) ;J 5 2 G 2 li 7 4 :1 4 -~251337 3 3672:i4 7 (j 4:; :12 ·) ;)f\2:)47 1 7 2 ;) :1 (i ,j :; :.lii4037 4 54372() 2 2:'l7:Ju-t 21:; u 7 :1 :I :j672LI a 3721t:S5 2 67524:l 7 6 2:,4 :I :I :.lt\27·15 I :32il4G7 l U53247 .-, 54 6 7:12 0 :l i) 7" () 2 1 1:>32711 2 2;, 0 .1()7 -l :l46G72 3 74526:~ ;; () 2 3 7 ·1 ;) 2 li 2 4 7:; :l L 7426.33 1 2iJ374 6 1 327645 1 ·1 56:.!7 2 2 726:H5 :) 257436 :3 :.!42567 3 7432ii6 :i 7 2 4 (j :I:; 2 li472G3 a 642:.1ii 7 753042 1 627il4H l ,;o7:J:.l-l :12 ti :j 4 7 1 :.l5617;! ;j Ofi7234 i'i 746235 r! 2 4 ;j 7 :lli 2 2 fi :15 4 7 ·1 -liJ2Bti7 :l :146725 2 46723!i 4, :):~2-IU7 :I 7 ;) 2 4 ():I 1 7 il -1 (I:) 2 l 25:·Hi74 2 524367 1 7 -1:; (\ :12 l 11:17 2 'I G 2 :; 2 7 413:1 :.l t) 52 4 ::17 5 413527:3 :1 :3:!. 7:; (\ -1 ·) ;) 21i 4 :~ 7 1 :1,15627 1 746::152 1 3716~2 :3 ·J :>:1 fi2 7 1 12 :)71\0 i) :') 2:34 7 G :~ (j 57 4 2::1 ::1 2 (i 53 7 ·1 1 f):-; -1 7 :12 ;j 7 :.l4 :1!) ti ;) ti 4. G 7 2:3 :H62:)7 1 H2S36 2 :!. 7 II :3 :) 1 ,; 117 .J a 2 2 2::3 G:37 .J 2 HJ:J2G7 ·~ 657:342 ,; ! :!. 0:17 2 :12 57 4. (\ 2 -tG27:lo 1 :3G4o72 3 356274 i) 7 (j;j ;~ 4 2 :; 4:32 () 7 0 :~ 1)4 2 7 5 2 723465 2 -!237!31) 1:!. 7 ;) :I fi ~ :111:.4.7 2 :l "2 :17 () -1 :) !7623 1 354267 :3 liG4:l27 1 21:-37 (\ :-; li 4 G :17 2 2 7 2 G ·!3 () 3 7231\!iJ l 4 213 ;) 7 ;) :; :IH24G7 :\ 7 2 (i;) :14 •) ()47:125 1 3:372 ·113 0 :1:; 4 7 20 7 'l :I :i (i 2 1 457:321i 2iiG734 ~ 46372 ;) 2 2 n:.\4 7 ,; :.l :j 4 7 2 :ll.i r; 2 G-1 7 :3 ,; :.l :14 2 0 7 5 2 3246!'i7 :3 4fl2 :):17 .) fi 2 ;j :14 7 1 :l:j2J 71\ <) 7:)R2U4 <) 76352<1 7 ;) i :IIi 2 :12 () 7 :-; 1 :) 1)4:37:.2 127()53 <) •) 2473:)6 2 H27-~:3:) 17:1 G 2 fi :)26:37-~ 1124375 iJ 5627:'14 •). ,; -1 f) :12 7 2 fi 4:1:; 7 2 ,, 3 s 7 2 n 24()375 4 l'I.2B •!GG 7 1

.J. F. 1'~:1':-llNG.

;)!.) E GRANDS IRE TRIPLES

(vi) Ilor.T's OttiGINAL

ONE of the most popular peals of Grandsire Triples is Holt's One-Part, usually known as Holt's Original, and it is the ambition of most conductors of tho method to call this com­ position. It contains 148 Bobs scattered irregularly throughout the peaL and has two Singles. There are many ways of memorising the tigw·es and, although most conductors will prefer to work out their own system, it is considered that some guidance will not be out of place here. One way is to learn the lead intervals between the Bobs, thus: 1, 3, 3, 2, 2. 3, G, ::l, 1, 3, l, etc. Another is to learn the position of one of the bells at each call throughout the peal. The most satisfactory method, however, is to memorise the bells " Before'' at the Bobs, as explained below. A bell is said to be "Before'' in Grandsire when it is hunting in front of the Treble and is about t.o make Thirds Place--it is the only working bell unaffected by a Bob. Whichever system is used in calling the peal, it is useful to know a number of " landmarks," when some of the must easily recognised lead ends occur. The basis of Holt's Original is the 120 H-Blocks. These are joined together by " omits." There al'e consequently many places in the composition where a Hob is followed by another at the next lead. When this occurs, the bell Before at the flrst Bob is said t.u be called " Befm·e with a Double," and tho majority of those who call the peal do not bother to remember the bell Before at the second of the two Bobs. but learn instead that a llob must be called one lead ~tfter the previous Bob. This reduces t.he number of beUs Befot·e t,o be remembered (excluding the last four calls) from 1 ·tti to !JR. These should now be divided into groups to facilitate memorising and each conductm· will doubtless prcfot· his own an·angement.. TJw following arl'angement divides the compo;~itiun into six sections. each ending with an easily recognis<~d change, but the majority of conductors will probably wish fmthcr to divide each section. Where a flgut·e is shown thus-7n-it means that the Seventh is caJled Befm·e with a Double. 1\Tany cnnductors use the wot·d " one" instead of a " o." liO ,) 3 4 5 4 •1 4 :!o :lD 'io .J-o 4 4-o Go Go 7D 7o 3 3o . . 6 4 5 2 3 7 7o 5 7D 7o Gn 7 ·i :in In :i 7 7 3o 3D 4o 4 4 7o 2 3 4 6 7 5

:in 7 5 :i 4-n a -1 n l~> :; 7 7o :3 4 :3o 5 7 o a 4o 7 3 5n 7 -1 2 4 5 :3 6 7 7 D 7o 4 3 3o :3o :i 3 :Jn :i 2 5 3 4 () 7

7 -lo 4o 7D G :3 :io :)D :l -l Jo 3 7 :~n 3D 7 5 253746 (Plain Course) :lo 3o 7 3 7 7D 7o 7 -l .J u :lu 3s ::;n 2s 234:367

At the Singles the bell shown is in the Before position at the call, but of course makes Heconds Place and goes into the Hunt. The composition can be still further simplified by assuming that all Bobs at·c followed by another at the next lead, with certain exceptions, as follows:-

(1). \Vhen the Second or the kixth is Before a.t the next lead, no second call must be made. It will be observed that (except fot· two of the last four <..:ails) these two bells at·e never called llefore. (2). \Vhen a Bob causes the next bell to be called Before to dodge in 6-7 up or U-7 d<>wn-for a Bob at the next lead would cause it either to g-o into the Hunt or to dodge in 4-5 up. In the first instance the bell could not be called Before. In the second case more than two snccessive Bobs would be used to call it Before. This eann<>t- occur in Orandsire Triples without causing a repetition of cbangns. (3). Ten other places where the fact. that a bell is called Before without a Double must be obset·,·etl. In these c1~ses the next hell Before is neithel' the Seeond not' the Sixth and the bell required Before at the next Bob is not dodging in 0-7. The bells t.o be called Bdore should, therefore, be learned. The following arrangement. is SU!{gested and it must be remembered t·hat each Bob, shown by the Bell Before, is to be followed by a Bob in the succeeding lead, unless the exceptions mentioned in ( 1 ), (2) or (3) above apply. The ten places in paragraph (3) must be memorised and they are shown by the" o" (for omit) following 61 the figure of the bell Before. The sections are of varying length and the change which occurs at the end of each is shown:- :'i3454o4o4 ,),17236 3 3 7 4 ·i 0 4 2 7 3 0 4 5 55773o3 G4:)237 7 5 7 7 i) 7 :J 7 4 2 ;) 6 4fi7:37o7 ii74H32 :~3,l4o4o :i473G2 7:'i75o5 7 ;) :~ G 4 2 -Ll,l-1:::177 ti42:"i73 :>, 4 3 G 7 :1 4 7 :J ., I ,; 7 :1 G 2 4 ~ 7 7 4 7 4:1 0 2 !) :l 3 3 ;) 3 5 3 .. 2 ;i :l -1 G 7 7 4 4 7 I ;>, H 2 7 G ;)355344:3 l32G57 7:l:J75o 2:; :l 7 ·1 0 3 :c~ 7 3 7 7 7 7 -1 o 4 ;~ ;~s •> ~s 2 :1-!- 56 7 Instead of learning that forty-eight of th(' .Uobs must each be followed by anothe1·, it is necessary by this system to remember that only ten single Bobs must. be called and in addition to remembez· the two simple rules set out in ( L) and (:!)abo,· e.

OB.AND1:iiHE THIL'LEH

(vii) CO~ll'O:'

I~HANGE ringing is a practical art. based on, and stdctly con­ trolled by, a mathematical science. Due to this there are somt' fundamental things knowledge of which is essential to a com­ poser, important t.o a competent conductor, and desirable to an ordinary skilled ringer. These things are clementat·y and ve1·y simple, but, just because they a•·e simple, they arc vet·y difficult, to explain. Complex things can be explained in terms of simpler things, but with the simplest all t·hat. can usually be done is t-o state tbe facts and leave the reader to use his brains and his imagination as best he can, r·eminding him that simple things are not. always the easiest to unde•·;;tand. Any order in whkh a numhe1· of bells can be sounded, or· in which the figures which represent them on paper can be written down, is termed a Row, and change ring-ing is the production of various Rows by moving t.he bell;; llmong each other. 'fhis 62 movement is t.he essential thing in the art and comprises all that the ringer calls the " work " of a method-hunting, dodging and place making. It is produced by interchanging one or more pairs of bells, as we saw in the chapter on Pricking the Changes (page 9). A Change is the movement which produces one Row from another and the term covers, not only the movement, but also the new Row which results from it. Row and Change are technical ringing terms, but their meanings are essentially the same as in ordinary speech. On any given number of bells there is a definite number of Rows and of these Rows half can be produced from rounds (directly or indirectly) by transposing an odd number of pairs of hells, and the others by transposing an even number of pairs. On this distinction depends what is called the Nature of the Rows-half of them are Oud (marked -) and half are Even (marked + ). The succession of the Nature of the Rows in Grandsire on ti ve, seven and nine bells _is as follows:- 1 2 :3 4 5 + 1 2 ;~ -t G G 7 + 1 2 3 4 G G 7 8 9 + ------~ 1 3:; 4 + ~1:3547H - ~1:l:34769l:l + ~ !1 1 4 5 + 2 :l 1 4!) (i 7 + 2 3 1 4 5 6 7 H 9 + 3:! 4 1 5 + :l 2 4- 1 IS 5 7 - 32410:)879 + 34251 + :l 4 2 0 1 7 :i + 3-12018;)!)7 + 4 :~ 52 1 + -b 3 u 2 7 1 G 4:~6281957 + 4 :) :3 1 2 + -l () 3 7 2 :i ] + 40382917G + etc. etc. etc. On five bells every elutnge in tho plain course is a double one. and as the same thing happens when Bobs are made, all the rows are even and their Natw·e is unaltered until a Single is made: after which they remain all odd until the next Sinf{le. This happens too in Caters wherc, except at a Single, all the changes are quadruple. But on seven bells the changes are triple ones and, except at Singles, the rows are alternately of opposite Nature. This distinction is of great importance to the composet• ; but for the conductor and the pt·actical ringer (and to a large extent for the composer as well) a modification of it is of greater importance. When the ba.ckstroke rows of the Treble's whole pulls on the front are even, the changes are said to be I n-cow·se. 63 When those rows are odd the changes are said to be Out-of· course. To put it in other words. when the Nature of the lead ends and the succession throughout the leadR are the same as in the plain course the changes are Jn-course. When they are opposite the changes arc Out-of-course. Thus, not only are the plain courses of Doubles and Caters and a.ny other changes added to them by Bobs, Jn-course. but so also are the plain cow·se of Triples and any changes added to it by Bobs, although the number of odd rows is equal to th<: number of even rows. The terms In and Ont-of-('ourse han: been used by write!'s loosely and as if they were the equivalents of even and odd; but in their original meaning and in theil' usc in the belfry there has always been the distinction. It should be kept in mind . .Movement in change ringing is cyclical. 1t is movement which starts from a row and is always t.endinf.l,' tu t•eturn to it again. We saw in the chapter on Pricking t·he ('hanges that when all of a given number of bells plain hunt ft·om rounds they t·eturn to rounds again after twice as many changes as there are bells. We saw too that each of the bP.lls has a cyclical path and the order in which they follow one another is their Coursing Ordet·. The movement which pt·oduces one of these Hunting Course:> can be of two kinds, it can be Fot•ward Hunting or Backward Hunting. Forwat·d Hunting is when from rounds the even bells go down and the odd bells go up and the leading in front is a.t hand and backstroke. Backward llunting is when the odd bell:> go down and the even bells go up and the leading is at back and handstroke. Forward. 13ack ward. 1 2 3 4 1 2 3 4 2 1 4 :3 1 :3 2 4 2 4 1 =~ :: 1 4 2 4 2 3 1 :; 4 1 2 4 3 2 1 .J. :l 2 1 3 4 1 2 .J 2 :3 1 3 1 4 2 :.! 4 1 3 1 3 2 4 :.! 1 -1 :l 1 2 3 '! l 2 :3 4 ln theory there is no difference between these two except in dil'ection-one is the opposite of the othet·. In the belfry there 64 is a marked practical

2 ;~ 4- G (i 7 •) :3 i) 4 7 li

2 G :l 7 4 6 •)

2 (i 7 4 5 :3 ., 1 ii 4. 7 0 G

1 2 ·1 (.1 :l 7 5 21 40tiG7

l ~ 1 :1 4 :"> 6 7 lt is important to notice this, for an exactly similar construction gives us the Q Set. ().) In studying the composition of pooh:; of Grandsire Triples it; is necessary to understand thoroughly th~ Law of Q Sets. This is one of the most; important and must. widely spread in the science of change ringing and it will be well to examine it first in its simplest form. If we make a Bob at the end of the plain c: ourse of Bob Majut· we produce tht' backstroke row 1 .J ~ :l G (l 7 8. The band­ !:ltroke r-ow next before it is 1 ~ 4. 3 u G 8 7, and it follows that we cannot in any part of our touch ol' peal, without falseness produce 1 2 3 4 G 6 7 8 at a plain lead end, for that would need tho handstroke t·ow 1 2 4 3 6 5 ~ 7 which has already appeared. The handstroke t·ow of the backstroke row 1 2 :3 4 G t:l 7 ~ brought up by a Bob is 1 3 2 4 u G 8 7, and it further follows that l 3 4 2 5 6 7 8 cannot be produced at a plain lead end for that. would need the handstroke J :l 2. 4 H G ~ 7. Therefore if 1 4 2 3 5 u 7 8 is brought up by a Bob, thEm 1 3 4 2 56 7 8 and l 2 3 4 5 G 7 8 must also be brought up by Bobs; and conversely if one is brought up A.t a plain lead end then all three must be brought up n.t pln.in lead cnus. \Ve must. have one oe ot.her of the two following:-

2-!3 Li :'iS7 :1 ~ l. i fi :) 8 7 -l 2 3 G 6 7 'f-\ :l 4 2 i G Li 7 ~

-13~ 6587 4 :l 2 11 (} 5 8 ; 3-lo2 Gu7H C:!3 5ll78

:l :! .J. (j 5 8 7 2 4 :1 i fl :) 8 7 ~3-! 507H 2 :1 1 I,,() 7 8 In Wl'it.ing uown tho figures of a composition it is usual to ignore the handstrokes. and so the tlu·ce backstroke 1·ows which are related in this wa.y 4 2 :l - H 4. ~ -- 2 :1 4 are calleu a Q Set. These Q Sets c11.n appe,w in any positions at which Bobs may be made (in Bob :Major, for instance, at t.he Wrong and Middle as well as at the Horne as shown ab< •ve) and the members may be widely separateu in a composit,ion, but t.heir relationship is alwn.ys the samt:>.

The three bells (2, :l, 4) which ar<~ affected by the Bobs, g o through the two ~h,es (one forward 11nd the ot-her backward) and we remember t-hat Richaui Dnckwor·th in J'intinnalogia (j(i (A.D. 1668) place;; tltc beginning of change ringing at the in\•ention of the Sixes abL>Ilt the year HllO. Two things must be said in comment on what we have written so far. 1<1rst. when in a tt·tw composition all the members of a Q Set appeat·, then if one is bobbed all must be bobbed, or if one is plained, all must. be plained ; yet it is possible to bring one up bobbed and anot-het• plained ; but in that case the third cannot be bad at. all. F••1· instance :3 4 ~ G 13 could bo brought up bobbed and 2 3 4 fi () plained : but then ± 2 3 fi (l could not be pro­ duced without. falseness. Secondly. when Hingle~ a.t·e used as well as Bobs fUI·ther and ext-ended Q Sets a1·e sometimes possible.

2 4 8 I li ;. :! 4 ;~ ! ll G :~ 2 4 I u ,-; ') { I •) •J _L :_ : I, ,,- n • ~ " I .,.- ('• 3 4 2 1 5 ti ---;-- - 1- .J- :3 :! · H :; -~ :-3 :?. • u ;') - ~! 2 1 _:~; ---1-- 1 :2 :~ : fi ;. 8-12 6:) . :! ; 1 1 ~ ~ - •) ,I •J! ,-I' :l 2 4 G li S - • " I " > ,! 2 i 1 -~~

a ~- 2 u ,, ~- t>':- 1 i-,..) .)- -4.:~2jfili s :?. n 1 ! :> ti

1 2 3: ()!) 248•Gh --1-- 2:14~();:; ·> ' S ·>.;..,~ ·> . .t jI .).- •.~ ) 1t will be nct:Pssat·y t." t·deJ· somewhat to these particulat' Q Sets pt·esently. lmt t.he~· have no pt•actical value in Grandsii·e 'Tt•iples. vVe can now ttu·n t.o Gt·andsire Triples. The Q Sets t.here are in principle exactly like the :{-member Q Sets of Bob l\fajor, but in actual use they appear to be more complex. This is due to the fact that tlH' B same Com·sing- Ot·der. (\7 A B ;) 1 i 7 2 6 3 ·1 .)117~634 15'76~43 lili273(),J,

31,67423 ;)} 1 237413 15 ()·!732 15 :32471)

:11!4o37~ .~--; 1 :~ 4 ~ fJ 7 L>i43627 J G 1 :l G 2 7 '---- ;j}'l :cl•!267 .~ l ~~i:l7 ~ 13 3247() --:----l:)j()17:J2 ;)} 23746 ;) 1 1 (i 7 -1 ~ :J 1r> 27304 };) : 7fi2+:~ A shows the backstroke and hn.ndst.roke rows which are pro­ duced when a Bob is made in the first lead of the pla.in cow·se and at the four other Bobs which complete the Q Set. '.rhe same bell (the Pifth) is called Befot·e. ll shows the rows which would be ptoduced if the lead ends were all plained instead of being bobbed. _;Ul these changes ar·P made at backstroke and hand­ stroke in the interior of the leads, and as it is the custom to designate any call by the backstroke r·ow at the Treble's whole pull on the front, we set these Q Sets down as follows:- Bobbed. l'ln.in. 7;)26i.l4 2 ;j :~ 7 ·1 () G:i7423 :l:J42t\7 -tG6372 ·l ;) (I g 7 2 :3i'i42ti7 fi G 7 4 2 :3 263746 7:i2()34 vVhPn \Villiam H. Thompson WI·ote his Xnlc on Grandsire Triples (see pagps !2iH.l) he used as the designation of a Q Set the backstroke lead ends of the leads previous to the Bobs being made and he would have written this Q Set as follows:- Bobbed. !'lain. 234667 ~ :3 4 :) (j 7 723546 :1 4 6 G 7 2 (i72534 -! () 7 :) 2 :3 4G7G23 () 7 2 i) :l 4 34(i372 72:3340 68 In this he followed Shipway and was himself followed by C. D. P. Davies and other writers. This was understandable in Grandsire Triples, but the plan does not adapt itself to other methods and it is well to have one which is common to chango­ ringing generally. \Vhen we examine this Q Set of Grandsit'e Triples and com· pare it with the Q Set of Bob ?IIajor we can see that in all essentials the two are alike. In Bob Major three bells are affected by a Bob and the Q Set consists of the Sixes (backward and forward) on three bells. 1 n Gra.ndsire 'l'riplcs five bells are affected by a Bob and the Q Set consists of the 5-bell Hunting Course (back­ ward and forward). \Ve can also see that when in a t.rue com­ position all the membe1·s are included (as they must be in a peal) if one is brought up bobbed all must be bl'Ought up bobbed; or if one is brought up plain, all must be brought up plain. In compositions shorter than a peal it is possible to produce one member bobbed and another plain, but then some cannot be produced at all. \Ve saw that in HPh Major it is possible to have Q Sets formed by a combination of Bobs and Singles and plain leads. Very useful those Q Sets are in composition, but ther·e is no equivalent to them in Grandsire. This is due to the fact that the ordinary Grandsir•~ Hingle is not ma.de in the same change as tho Bob. Jt, is in addition t.o the Bob and is made at the next change at backstl·oke. The Bob, which in practice is a part of the Single, is in composition quite separate feom it and takes its place as a member of a Q Set of llobs.

~[embers of a Q Set may appear in a composition in varying orders and at widely diiTcrent intet·vaJs.

In Bob ~lajoJ', n.nd in similar symmetrical* methods wit.h a plain hunting Tt•eble, there arc 120 rows in which the Treble, Seventh and Eighth al'e in their home positions. Half of them at·e even and half are odd ; and from each of them a course of 112 changes ea.n be pricked in the same way that the plain com·se is pricked h·om rounds. Half of these NaturaJt Courses

• A ~ymmetrical method is one in which lbc changes are produced from the. lead end going backwards in the sn.Jile way as they are from the lead head gojog forwards. t They are also termed P Blocks. uu .are In-course and half are Out-of-course, and together they comprise the full extent of the changes which are available for ringing the method with the tenors together. But primarily they are independent round blocks and to be used they need to be joined together and to the plain comse. B(lbS are the means -of doing this. 'l'lte simplest an9. most. typical t.ouch is the t.hree comses joined togethel' by Bobs at Home. First the plain course is rung : then a Bob puts the changes into the comse 4 2 3 5 G ; t.hen, after that is rung in full, a second llob puts the changes into the course 3 4 2 5 6 ; and finally at the end of that a third Bob produces rounds t.he last row of the plttiu course. Three complete round blocks have been joined into one by a Q Set of Bobs. In similar fashion a Q Set of Bobs at a Wrong ot· a :Middle would add two or more Natural Com·scs to the J-coursc block and produce a 5-course block. So we conld go on, adding by means of Q Sets to om· block two Natural Courses at a t.ime. The added courses may begin with course end and finish with course -end ; or they may be from Wrong to \-Vrong, or from Middle t.o Middle ; but they always appear as complete round blocks. \Ve started with one round block (the plain course) and at every operation we added twi> more. Our made-up block (how­ ever we arrange the Q Sets) must. compt·ise an odd number of Natural Courses, and as the extent of the In-com·sc changes consists of sixty Natural Courses (an even number) clearly it cannot be had by Bobs alone. 'J'he most we can do is to collect into one block .'iU of the available ()0 Natural Cow·ses and to leave one ovet•. This is the simplest. expression of the mathe­ matical law which decrees that a peal of (handsil'e Triples with common llobs only is not possible. But half the t.otal number of Natural CotU'ses of Bob 1\lajot· ~re out-of-cow·se; to include them the Nature of the t•ows must be altered, and for that Singles are needed. We can put a Single into our :39-com·se block, double it and so produce a block of 118 Natural Courses. There still remain outside the two omitted Natw·al Courses, one In-course, the other Out-of-course. B~· means of two Singles we can join tl,le In-course one to the Out· of-course half of our large block, and the Out·of-cow·se one to the In-course half. Or we can use the compound Q Set which 70 will join together four round blocks. This shows that Singles have two distinct uses. They can alter the succession of the Nature of the rows and so make Out-of-course changes available, and they a.re a.Iso necessary to include In-cours~ changes. To set down all the available changes in the independent Natural Courses provided by the method, and then to join them together by Q Rets of Bobs (and Singles where necessary) is the simplest and most obvious way of composing extents. Hut it is not t.he only way, and the problem can be more complex. Bobs are not merely means of joining together round blocks. They can have other uses. If from each of the Natural Course Ends of Bob Major we prick a course with Bobs at \V, )-I and H, we find that the full number of changes is gr·ouped into twenty­ four similar and independent 5-course round blocks. If each course is pricked with Bobs at Wand .M the same thing happens. Tf the Bobs arc at \V and R, or at l\'I and R, sixty 2-course blocks are produced. Tho Q Sots of which these Bobs at•e members are all bobbed, hut thay do not act as links which join round blocks together. The members arc separated and in different blocks. We have now a number of independent round blocks, instead of a number of Natura.I Courses, as the material for om· com­ position and the problem is to join these blocks together. For that we can use Q Sets of Bobs (if there are positions to make them in), or Q Sots of omits, or both Q Sets of Robs a,nd Q Sets of omits. Omits in composition can have the same uses and value as Bobs. The problem of joining togcthct· the members of one of these sets of round blocks is simila.t· to what, we have been discussing. An odd number can only be joined by Bobs or omit.s and one block (which may be one of the group or a full Natura.I Course) must be left over. .Singles again are necessary to produce the t\~dent. When we tur·n t•> Grandsire Tr·iples we find that what we have been saying will fully npply, only it must be adapted to the peculia1· charaderistics of the method. There are sixty even rows in which both the Treble and tbe Seventh a.re in their hon1e positions and if from each of them a Natural Com·se is pricked -1200 of the possible 5040 changes will be gTouped into sixty indPpendent r•mnd blocks. In audition t,he Seventh must be in 71 the Runt in twelve Natural Courses. So the material for com­ position consists of seventy-two independent Natural Courses or P Blocks (as it is usual to call them in Grandsire Triples). Our means of joining these together consists of Q Sets of Bobs: \Ve start with the plain course. In it we make a llob, and when we have completed the Q Set we have produced a round block made up of five complete P Blocks joined together. We started with one and to it we have added four more. In this block we make a Bob and when we have completed the Q Set anothet· four are added. So we can go on until we have unly three 1' Blocks left and no bobbing can gather them in.

All this is strictly simiiH.r to what happens in Bob ~Tajor except that four 1' Blocks a.re added at a time instead of two and three are left ovet· instead of one. But something a litt.Je diJierent is possible. If in the large block there are tlu·ec members of an unbobbed Q Set. and if the two remaining members are nne each in two of the remaining l' Blocks, wo can Bob the Q Set and the two P Blocks will join up with t.he large block. \\ie can add P Blocks to the large block cithet· four at. a time or two at. a time, but we can never add an odd nurnbet·, and so we alway» have at least one that cannot he absm·bcu. There is an alternative way of setting down the material fol' composing a peal. 1 t can be grouped into 120 ll Blocks. _-\ B Block is a. round block of three leads produced by making a Bob at. every lead end, and the problem of joining together the 120 is similar to that of joinin!-l' together the seventy-two P Blocks, except that omits grouped in Q Sets must be used as the links instead of Bobs. However the omits are a!'l'anged one B Block cannot be absorbed and we must use some other means. Ordinary Grandsire Singles 11t'e not necessat·y Lo alter the Nature of the Rows as they aJ·e in Doubles and (fur extents) in Caters, and alternative calls have from the earliest days been looked upon as allowable. lly means of Fifths Place Bobs Shipway composed a peal adapted from Holt's Ten-pat·t in which the changes throughout arc tl'iples, and vV. 11. Thompson investigated and greatly developed the irlea* : but. though it has its value in composition. it bas never taken any place in pt·actical

• Shipway Reprint Ill p. 8S. Thompson, A Syslt·m nj Pl·als nf Vnion- Triplts. C1awl~ .sire 2nd Edition. Central Council Report on Calls. 7'2 ringing. John Holt in the Ten-pat·t. used two In-Course Bob Singles and these with the ordinary Singles may be reckoned the st.andard Singles of the method though the latter at present are almost exclusively used. Between the uses of the two kinds of Singles there is an impot·tant difference. ·when P Blocks are the basis of a peal In-course Singles al'e necessary. 'When B Blocks are used ordinary :Singles may be employed. The essential difference between the two cln.sses of round blocks is that, while the n Blocks are symmetrical about the path of the Treble, the P Blocks ar·e not so. B Bl<)cks can exist in two forms, one fn-course th<' other Out-of-course, and both forms contain the same rows. A P Block can exist in one fo1·m only. It is possible to set the 50.1-0 changes do·wn in seventy-two Out-of-course P Blocks. but they a1·e useless for composition as rounds appears a.t. a handsh·oke. A B c D 2 3 4 :-; 6 7 ;; 2 54 7 li :2 :; .t56 7 :3 2 ;) 47 6

-~------~

·) ;) 7 G 2 4 :3 4 0 7 :I ;) 2 7 :3 0 J .J 3 G2 7 5 "•) 7 5 2 G3+ lj i :l 7 ;) 2 :i :~ 7 4ii :I 1 2 u 5 7 ----- li 4. 3 7 2 ;) 7 G 2 (i :3 .J 7 2 ti 5 4 a ll :37 4 5 2 ') 4 ., I lj 7 3 5 ;; 7 li 2 .. 2 7 i'i ii :3 4 :l (i 4 7 2 5

--~--

•) •) :~ 5 4 7 (j :3 J :) li 7 (i 2 4 7 :~ :) 7 :3 ;j ti 2 4 ., •) .... :J 4 5 ti I :; -· .) ~ 7 n 2 13 7 4 G :; :3 7 65 4 2

------~-- 4 2 ;~ (j G 7 :) :; 27 4 () '> 4 (l :3 7 5 :~ J 7 2 G 4 ------:; 2 5 4 7 (i 23 4 :-; G 7 2 :~ 4 5 fj 7 :l 2 ;) 4 7 G

A. is a H Block prickPd fl'<~lll 2 :~·I.) G 7. H is one 1)l·icked ft·om :1 2 ;) ~ 7 II. and it will be see-n t.hat the r-ows in the first are the same as in the other except that they appea1· in rcvet·se (l!'der. Cis a P Block pricked ft·orn 2 ;! 4 5 () 7. D is one prick~d f1·orn :3 2 54 7 li. ln this casE1 the l'UWS are quite different except ftw one lead. H would be possiblt> to use a form of P Block with ordinary S inglt"s if all the changt'::< \H\I'e I'eversecl so that the bell 7:l coursing in front of the T:rehle became the Bell-in-the-Hunt, and the Bobs were made after the Treble ha•l led instead of before. Holt.'s Ten-part has in fact been rung wit.h the second half re\·ersed in this manner· and two eommon Singles, but that must be looked upon as a d<'parbu·P from the st.andarcl method. If in om· composition we t1nd anywhet·e t.ha.t. we have a B Block left over which cannot be included by Bobs. we can add it at a convenient place between two common Singles. The rows will be the ones we need but they will conw in reverse order. If a P Block is missing we cannot add it with common Sinl'les for, though ono missing lead will a.ppea.t· in r<:versed form, all the rest of the block will be quite other than what we need. We can see from these t.hings why the common Single is to-day used so much more freely than it unce was. a n•l Wt' can see tho reason for those blocks of bobbed leads between .Singles which are familiar in Holt's Original, Parker's Two>h·e-part, and other peals. Besides the plan of composing b:v joining t.ogdher P Blocks or B Blocks by means of Bobs and Singles nrt·anged in Q Sets, there is a.not.her plan which t.ak(•.S ns hack to tht> very beginnings of the art and science of chang(' ringing-L·nmposing by means of Hunts. Jt is the plan by which the migina.I Plain Changes were produced, it plays its pa.t·t in many compositions, and an excellent example of it occm·s in t.he threo>-lead course peals of Grandsire Triples.

The general plan of llunts is thi;;-Fh·st. of all thl'!'C is the Whole Hunt (usually the Treble) whieh has a path which takes it regularly through every position. Then there is the I falf Hunt which falls regularly into every position t•elativc to tho \VhoiP Hunt. Then the Quat•ter Hunt which falls regula.rly into (W('t·y position relative to the 'Whole Hunt. an

1006000 1000600

1600000 1 0 6 0 0 0 0

J 0 0 0 0 0 6 1 0 0 0 0 () 0

The Sixth has occupi<~

1 0 0 7 0 6 0 1 0 7 0 () ti 0 1 7 0 0 0 () 0 000760 J 0 0 0 0 U I The seventh, the (-.luar·t,et· 1 lunt, has now eonnpleteu its 1·evolutlon.

But we cannot llHtk<~ furthe1· alterntions in tltc number and positions of the Bobs. 1f we c'lid we should upsd the Half and Quarter Hunts. l:;o we must usc Singles to fix t-he pat.h of the Fifth, the llalf-Qum1.P.t· 1 lunt. 'rhcre are various ways of doing it. and we produce ;)-cours<~ hlocks with the followin~-: pn.t·t-<~nds :- o:,oo67 0 () :, () ti 7 ;)00067 ll 0 (I !j () 7 7G F Next. we must use Singles on 2 3 4 to produce the part-ends:- 4 2 :.l;) (j 7 3425U7 2 3 1 G u 7 and, finally, by making ot· omitting two Hingles on 2, ~1, one in each half-p0,aJ, we complete the composition. 'l'he making m· omitting of Singles is independent of the Bobs which at·e not affected. After t.hc gene!'al principks of composition have been studied and understood. there remain t.hc many and dil'ficult problems presented by various classes of peals in different numbers of parts. These matters have betm dealt with thoroughly and in great detail in t.be two eady editions of (;randKi.rc. They are available the1·e fn1· the student, but t.hey aJ·e outside the scope of the present book. The composition of touches dill'e1·S in m11ny important. respect.s ft·om that of peals. There is less l'BStraint. of detinite 1'\\le and mo•·e fr·cedom of choiee. ln practice it is laJ·gely a mattct· of experi­ mental pricking directed by inct·Pasing knowledge and expe!'icnce.

GHANDSIHE 'fHlPLES (viii) PnooF

ONE of the essentials of change ringing is that in any touch no change shall be 1·epeated. Proof is the ptoccss used to ensm·e whether or no this essenti;tl has been observed. In Grandsit•c Triples, until a Single is called, all the rows aJ·c ;Liternately odd and even (see page ii:l). Consequently, in

(i) (ii) (iii) F.".LSE Even rows at Odd rows at TOUCil Tt·cble's lea.d ( +) Treble's lead (-) 2 3 4 5 6 7 2:34G07 2 5 3 7 4 (I 2 ;j 3 7

A comparison of th.: otlcl rows in column (iii) reveals that ther·e is duplication in t.hn lh·st and fourth rows. 'l'his could not be readily apparent fr·orn t.tw backstroke lead ends in column (i). For purposes of proof, peals of Gra.ndsire Triples may be grouped into two classes. Those in which 1-T olt's Singles are used a.nd those using Golllmon Single,;. ln the former, the odd and even sequenGe uf th

THE 72 COURSE ENDS OF GHAKDSIRE TRIPLES.

~34567 324657 1~35()7 ;;~:Hi47 623457 723546 235647 325467 425o:n .):?-!3ti7 u24.337 72435(:) 236457 :~26547 426357 :):?()4:i7 li25347 725436 243657 342567 4326;)7 ,; ~~:? 4 (j 7 ti32547 7 3 2 4 51) 245367 :34:'5627 435207 :i34o27 1134257 7345213 246537 346257 ·136527 :386247 635427 73524() 253467 352647 452367 ;;J-2()37 642357 7 4 2;) 3 () 254637 354267 153627 .)4:~207 043527 74325() 256347 356427 ,~56237 ,j iii :l 2 7 fi4S237 745326 263547 3()2457 46253/ G li 2 :l4 7 li52437 7523,16 264357 364527 163257 ;) 60-i 2 7 653247 753420 265437 365247 465327 GlH.237 654327 754236 In the second class, all ex tents of lhandsir~ Triples using common Singles are based on t.he 120 H Blocks (see page 72) and for purposes of composition OJ' proof it. is preferable to work from these rather than from the seventy-two full cow·ses. The lead ends of these B Blocks give us all the 360 In-course changes with the Treble leading. ·Each B lllock, however, has an Out-of­ cuur·se variation ·obtained by transposing <·ach of the three lea•l ends by 57 (i 2 ,~ :~ and t•eversing; t.he r

2:34i'iU7 :i 7 ti :H.:\ ;~ 2 5 4 7 6 7 5 2 () :i 4 (i 4 3 7 2 ;-, fi+:3725 46785:? :32;i47ti ;; 7 li :2 4 3 78 If the whole forty-two changes of each of A and C above are written out in full, it. wiH be found that identically the same rows are produced. Therefore one or the other may be used in a peal. It is this fact which enables us to use common Singles in extents of Grandsit·c Triple!;. There is no easy way of proving Grandsire Triples. In a One-Part composition every lead end must be checked and care must be tu.ken to transpose all Out-of-Cow-se lead ends by G 7 6 2 4 3. If the composition is in several parts the B Blocks should first be arranged in as many groups as there are parts, so that only one part need be checked. The first row of the fh·st B Block in each group should give the part ends. If the composition has some Out-of-course part ends (e.g. Parker's Twelve-part) these and all the rows in that group must be trans­ posed by 5 7 6 2 4 3. It is, however, simpler to consider onl)' the In-course part end>! and to prove two parts starting from an In-course and an Out-of-course part end respectively, thus treating the composition as a six-part instead of a twelve-part.

The table on pages ~0-81 is arranged for the proof of Parker's Twelve-part (Seventh Observation). (See page 52 for the com­ position.) It will be observed that the first row in each of the collllllS B to F is t.ransposed in turn by each of the rows in column A to obtain the corresponding rows in columns B to F. This gives us the 360 Jn-course lead ends. There are sixty rows (twenty B Blocks) in each column. In column G of the table on page 82 are the sixty lead ends of the first two parts of t.he composition. The Out-of-course rows in this column are transposed by 5 7 G 2 4 :; to give in column H their In-course equivalents. In column J is given the position in the table on pages 80-81 of each of the sixty In-com·se lead ends (from columns G or H as the case may be).

It will be seen that in column .J all the numbers from 1 to 61) occur. Therefore, no two lead ends from these two parts of the peal are to be found on the same line in the table. Since the six columns A to F start from the six In-course part ends of the peal, and the subsequent rows are all produced in the same way and no row is duplicated, the composition is true. 79 THE 360 LEAD ENDS 0:1!~ GRANDSillE TRIPLES, BASED ON B BLOCKS A B c D E F 1 2 3 4 5 6 7 243657 324657 3 4 2 5 6 7 423567 4 3 2 6 5 7 2 752634 7 6 2 5 4 3 7 6 3 5 2 4 753642 7 5 4 6 2 3 7 6 4 5 3 2 3 4 6 7 3 5 2 3 5 7 4 8 2 457263 2 6 7 4 5 3 367254 257364 4 235647 246537 326547 345627 425637 436527 i) 76243.'> 752:346 753426 763245 764325 754236 6 547362 637452 6 4 7 2 5 3 :)27463 537264 627354 7 2 3 6 4 5 7 245367 325467 846257 426357 4 a 5 2 6 7 8 7 4 2 5 3 6 7 3 2 6 4 5 7 4 3 6 2 5 723546 734526 724635 9 057342 5 6 7 4 3 2 567243 657423 6 5 7 2 3 4 567324 10 25:3467 264357 362-!:)7 3 5 4 2 6 7 452367 -i G a 2;:; 7 ll 7 4 2 6 5 3 7 3 2 5 6 4 743562 723o54 7 3 4 6 5 2 724563 12 ::l ti 7 5 ·! 2 457632 2 5 7 6 -! 3 467523 26753-i 3 5 7 6 2 4 13 :L346:37 263547 3 6 4 5 2 7 3:)26,17 ,!;)3627 -!62537 00 14 7623::>+ 7 ;) 2 4 6 3 753264 7 (j :l 4 ;) 2 7 (j 4 2 5 3 7:54362 c l;) !:~7:)02 :i47B:i2 427():):~ 2 4 7 :; (j :l :i 2 7 5 (j ± 2376:)4 Hl 2 .) I) 3-! 7 2 {i :) 4 :l 7 :l li :) 2 .j 7 :l 5 ti -! 2 7 -! ;) ll 2 ~~ 7 -1- () :) :i 2 7 17 ; :l 2 4 :) I) 7 + 2 :! () :; 723-!(i.) 7 -1 :l 2 :i () 72±3:ifi 7 :i +. 2 6 5 IH (i ! 7 :i :{ 2 :) :! 7 (j + ~ :; 4 7 li 2 i! (i 2 7 j ,l :1 I) :1 7 ;) 2 cJ. i)27U3-l ]!) ;; 2 :~ (j J 7 ti 2 4 5 :! 7 t>:l2 :i±'7 :) :1 4627 ;'j l 2 (i :! 7 6-! :1:; 2 7 :W 765423 7 :) (i H 2 1 7 ;) (j-! 3 2 7()i)23! 7 u 5 :l 4 2 7:>6243 2l 347265 4 3 7 2 5 (j 2 4 7 3 5 0 !27:365 2::l7-U35 32745() 22 524367 6 2 3 4 5 7 6 3 4 2 3 7 532467 5 4 3 2 6 7 6 4 2 3 5 7 23 7 3 !i 6 2 4 7 4 (i 5 2 3 72653c1 745632 7 2 5 tl 4 3 7 3 6 5 4 2 24 4 (j 7 2 3 5 357246 457326 267345 367425 2:>7436 2;) :)26437 li 2 5 3 4 7 (3 3 5 4 2 7 5 3 6 2 4 7 546327 645237 26 7 4 5 3 2 6 7 3 6 4 2 5 746235 7 2 5 4 3 6 735246 726345 27 6372-l:) .'547236 :)27346 G4732:3 62743;) 5 3 7 4 2 6 28 5623-!7 6 2 4 3 7 6 !i 3 2 4 7 563427 564237 6 5 4 3 2 7 29 735462 7 6 3 5 2 7 2 6 4 5 3 745263 7 2 5 3 6 4 7362:34: 30 2-!7li:35 2 7 5 4 li :3 4 7 5 2 (j 327li13 J 3 7 ti 2 5 -!27.J3li 31 234675 243576 32<1;)76 342675 423675 432576 32 562734 6 5 2 7 4 3 653724 563742 564723 654732 33 4 7 5 3 6 2 376452 4 7 6 2 5 3 275463 375264 276354 34 235476 2 4 6 3 7 5 326475 3 4 5 2 7 (I 4 2 5 3 7 6 436275 35 64273;) 532746 543726 623745 634725 524736 36 5 7 6 3 4 2 675432 675243 576 •!23 5 7 6 2 3 4 675324 37 23657·! 245673 8 2 5 (l 7 4 3 4 6 5 7 2 426;373 4 3 5 6 7 2 38 4 5 2 7 3 6 362745 4 6 3 7 2 5 25374(i 3547213 264735 39 674352 573462 57-!263 672-!53 6 7 3 2 5 -! 57236 ·1 40 25367-! 26L'573 36:L>74 3 5 4 6 7 2 4;32673 4 6 3 5 7 2 41 4 (l 2 7 5 3 35275-! 4 3 3 7 6 :3 ~637;")-! 3 6 4 7 5 2 25-!763 42 3 7 4 5 13 2 473652 2 7 t 6 5 3 4 7 2 5 6 3 273564 372654 43 25-!376 263 ,175 3 6 4 2 7 5 352-176 !53276 462375 .u 6 3 2 7 5 .j. 5±276:~ 523764 643752 62±753 53±762 3 7 6 5 2 ± 2 7 5 6 3 4 oc ±5 4 7 6 5 3 2 3 7 5 6 4 2 4 7 5 6 2 3 2 7 6 5 4 3 ..... 46 256 •173 26537± 365472 B 5 6 2 7 4 456372 :165273 47 34275(3 432765 243765 423756 234756 32-!765 48 673 5 42 574632 572643 () 7 4 5 2 3 672534 573624 49 523476 624375 632475 5 3 4 2 7 6 5 ± 2 3 7 6 643275 50 6 4 5 7 2 3 536724 5 4 6 7 3 2 625734 6 3 5 7 4 2 526743 51 376245 475236 2 7 5 3 4 6 4 7 6 3 2 5 2 7 6 4 3 3 375426 52 524673 623574 !i34572 532674 54367~ 6±2573 53 3 6 5 7 2 1 4 5 6 7 ~ 3 2 5 () 7 :1 1 4 6 5 7 3 2 2 1> 5 7 -1 a 3;')15742 5.J. J. 7 3 2 6 ;; 37425() ·1 7 2 3 ii (j ~ 7 .J. 3 6 5 3 7 2 4 6 5 ~ 7 3 J 5 (j :)5 5 2 6 3 7 4 ti25473 63i)274 5 3 (I * 7 2 5 -! 6 2 7 3 li45372 56 435726 346725 426735 2!5736 325746 236745 57 674235 573246 574326 672345 673425 572436 58 5 6 3 2 7 4 65-1273 652374 564372 5 6 2 4 7 3 6 5 3 4 7 2 59 425763 326754 436752 235764 345762 2 4 6 7 5 3 60 ~74fl2fi 47~!126 2 7 4 fi 3 6 472635 2 7 3 6 4 5 372546 TAllL.E FOl{ PROOF OF PARKE It'S TWELVE-PART

G H J G H J 234[)67 l A 4236:)7 675432 36 B 752634 2 A. 7 6 4 5 ~ :l 532746 35 B 7 6 54 2 ~ ~ 20 A 75U342 324765 47 F 746352 29 B 735264 ~46753 59 F 23754(1 30 B 427635 OG3472 58 F :)62437 473G2U GO B 654327 28 F :)40723 723564 llB 03574:! 50 E 375246 ~64357 lOB 2764::15 51 E 327<354 645372 55 F 2 4 7 56 :l 15 D 36247!') -!5732(; 24 c 25437() 43 A :~40:)27 :372364 :3 9 }<' 235fl47 4A 753246 2647:35 ::.!8 F 762431> 5A 62745:3 435672 37 p 5 4. 7 ~~ 6 ~ 6A 64237!'5 357624 12 p 53 4 2 7 (i 49 D fi34527 572643 4~ c 523647 19 A o53742 724635 8 }<' 5U2734 32 A 276453 435267 7 F 47530:! 33 A 247365 356274 46 D 437256 21 B 234576 567243, !J c 423t:I7G 31 E 253647 674235 57 A 462537 13 F 762453 43G720 ;:;o A 754362 14F 746325 ~~ 52 7 6 4 4-1 B 73524U 26 E 537240 2134573 40 B 627435 27 E 265437 HlB 456327 37246G 54 E 74236!'> 17 B 734-236 265743 53 E 537642 18 B 627534 .>43672 52 E 625437 4'7::lt1:)2 12 B 546327 25 E 642753 7 ;{ 5 () 2 4 23 A !3~14762 44 F 376542 324367 22 A 27fi034 45 F 357264 2 4 6 :l 7 ij B4 H 2()7

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