Campanalogia

In such peals on five bells where singles are made in the 3d and 4th places at the leadings of the whole-hunt, the extreams may there be made three ways in each peal; viz. every time the half-hunt lieth next to the whole-hunt; secondly, every time it lieth behind; thirdly, every time the half-hunt lieth next the whole-hunt, and also behind: in this last way there are six extreams in each peal, but in other ways only three in each; the extreams being always made when the whole-hunt leads, and betwixt the two farthest extream bells from the half-hunt.

In such peals upon five bells wherein there are three extreams, and made in the 3d and 4th places at the leadings of the whole-hunt; the rest of the singles at the leadings of the whole-hunt may be made two ways in each peal, viz. either in the 2d and 3d, or the 4th and 5th places; if they are made in the 2d and 3d, then the extreams must be made when the half-hunt lyeth behind; but if the singles are made behind, then the extreams must be made when the half-hunt lieth next the whole-hunt, the extreams being always made between the two next extream bells to the half-hunt.

In all the following peals the figures standing by themselves at the title of the peal, are the hunts in the peal there prickt: for instance, in the first cross-peal upon five bells call’d Old doubles and singles, the two figures standing thus 1 and 2, are the hunts in that peal; 1 is the whole-hunt, 2 the half-hunt, and the like of the rest.

All peals of doubles upon five bells, which go sixty changes compleat without any single, by making of two extreams they will go 120. And also all peals of doubles upon six bells, and triples and doubles upon six, which go 360 changes without any single or extreme, by making of two extreams they will go 720. The extreams in all these compleat peals proceeding from one and the same cause, are therefore to be made after one manner, according to this general and infallible rule: Wheresoever any two of the extream bells are in course to make a change, those two bells by lying still will effectually make the extream. So that the making of the extream in doubles upon five bells, necessitates the making of a single change at the same time, by reason that the two extream bells which should contribute to the making of the double change, do lie still; so that the single change is accidental, and very improperly called the extream. When the extreams in triples and doubles upon six bells are made at double changes, then there happens two singles in the peal; but when they are made at triple changes, then those two changes will become double, and consequently the 720 will then go compleat without any single. Upon five bells the first extream must be made within sixty changes from the beginning, and the second extream just sixty changes from the first. Upon six bells the first extream must be made within 360 changes from the beginning, and the second extream just 360 changes from the first. The easiest way in practice, is to make the extremes at the leadings of the whole-hunt; wherein it may be observed as a general rule, That in all peals upon six bells, where the half-hunt dodgeth behind at the bobs, there the first extream may be made either the first, second, or third time: the half and quarter-hunts dodg together behind, and then the second extream must be made the third time those two bells dodg again together behind, after the first extream is made. And also in all such peals upon six bells, where the doubles at the leadings of the whole-hunt are made on the four middle bells, there the first extream may be made either the first, second, or third time the half and quarter-hunts do make a change in the 2d and 3d places, and then the 2d extream must be made the third time those two bells come there again to make a change after the first extream is made. The singles at all these extreams must be made by the half and quarter-hunt. The first extream in any peal may also be made at any place, where two of the extream bells are in course to made a change according to the preceding general rule; and then the making of the second extream may be guided by observations taken from the changes at the leadings of the whole-hunt: for at the leadings of the whole-hunt the half and quarter-hunts always come together to make a change in one place, just at 120 changes distance from one another throughout each peal. Now as the second extream must be made just 360 changes from the first, so the making of it may thus be guided: Look how many changes, or else how many leadings of the whole-hunt the first extream is made after the half and quarter-hunts have made a change together, so many changes or leadings of the whole-hunt must the second extream be made, after the third following time that those two bells do made a change in the same place again. And likewise in all peals, where there are single and double bobs, the same observations will also hold good, in making the extreams either after the single or double bobs as before; there being likewise 120 changes distance between the single bobs and also between the double bobs: so that if the first extream is made at a single bob, the second must then be made at the third following single bob, and the like also at double bobs. And such kind of observations, according to the nature of the peal, will guide the making of the second extream in any peal, either upon five or six bells. Wherein ’tis observable, that the second extream must always be made by the same two bells, and in the same place where the first was made, which two bells will in course lie apt for that purpose; and the rest of the bells will also in course lie in the same places at the second extream where they lay at the first. After the making of the first extream, the method of the peal goeth on as if no extream had been made; and also after the making of the second extream if any remaineth, it also goes on, until in course the bells come round.

In all compleat peals of doubles upon six bells there may also moveable extreams be made, which are made according to this rule; wheresoever any two of the extream bells are together, and in course to lie still, those two bells by making a change will thereby make the extream, which is as effectual as the fixed extream, the reason and ground of both being one and the same. There are also two of these extreams in the peal, and the second always made 360 changes from the first, and the making of it guided by such kind of observations as before. When moveable extreams are made, then there will be two triple changes in the 720; but when fixed extreams are made, then two singles.

The art of cross-pricking may receive a being from this consideration. As every compleat peal of plain changes upon one number comprehends the compleat peals on all lesser numbers; so likewise every compleat cross-peal must of necessity do the like, although their cross course permits it not to be done so regularly and demonstrably as the former. From whence may be inferr’d, that every note in a cross-peal must of necessity lie as many times in one place, as the rest of the notes are capable of making changes; and also that two or more of the notes must jointly lie in the same places as many times, as the remaining number are also capable of making changes: this being a certain touchstone to prove all cross-peals after they are prickt, and must be held as a principle on which to ground such methods of pricking, that the course of all the notes may demonstrably tend to produce those effects. And from hence it is, that the whole hunt immediately derives the manner of its uniform motion through the courses of each peal. And the changes in every course are as so many guides to conduct the rest of the notes in such sort, that they may be prepared to lie at the last change of the course in apt places for each succeeding course to receive them, and to perform the like. Now as the changes in all the courses of a peal are made alike, except as before; so in the composing of cross-peals, by pricking of one course may soon be discovered, whether or no a compleat Peal will from thence arise.

The Twenty four, Doubles and Singles on four Bells.

This peal consists equally of double and single changes; one change is double, the next single, and so throughout. 1 is here the hunt, and 2.3.4 extream bells. Every double change is made on the two first and two last bells, and every single on the two middle bells, except when the 1 leads, and then behind which is call’d extream. All the bells have a direct Hunting course up and down until 1 leads, and then the bell in the second place lyeth still, whilst the two hind-bells make a dodg; which being made, all the bells proceed again in their Hunting course. The three changes of (a.b.c) are the three extream changes.

Old Doubles and Singles. 1 and 2.

One change is double, the next single, and so by turns. The treble hath a direct hunting course, as in plain changes. Every double change is on the four first bells, and the treble is one of the two bells that makes every single change, except when it leads, and then the single is in the 3d and 4th places; but when 2 lies next the treble, then the single is behind, which is call’d extream. Every time the treble leaves leading, the two first bells continue slow dodging, until the treble comes down and displaceth them. And when the treble moves down out of the 5th place, the bell that comes into it lies still there, untill the treble comes thither again, except when the extream change is made behind. Every bell lies twice together in the 3d and 4th places, except when the treble leads, and also when it hinders them in hunting.

This old peal may be rung by a new course, which differs from the former only in the single changes that are made every time the whole-hunt leads, viz. every single may be made either in the 2d and 3d, or 4th and 5th places. If they are made in the 2d and 3d, then the extreams must be made when the half-hunt lies behind; but if they are made in the 4th and 5th places, then the extreams must be made when the half-hunt lies next the whole-hunt, the extreams being always made in the 3d and 4th places.

London Paradox. 1 and 2.

One change is double, the next single, and so by turns. The motion of the treble is after this manner; in hunting up, first, it makes a dodg in the 2d and 3d places, then it lies twice in the 4th place, and four times behind; in which manner also it hunts down again, and then leads four times. The rest of the bells have a like course and motion with that of the treble, untill the treble leads. Now ’tis observable, that every single change is made in the 2d and 3d places until the treble leads, and then in the 3d and 4th places; but when 2 lies next the treble, then an extream behind. The changes at the leadings of thewhole-hunt have an absolute dependency upon the course of the twenty four changes, doubles and singles upon four bells; and the extreams to be made as many ways as in that peal, which are here guided by the motion of the half-hunt.

Phœnix 5 and 4.

One change is double, the next single, and so by turns. Every bell leads twice, and lies behind four times. Every single is made in the 2d and 3d places, until the 5th comes behind, and then in the 3d and 4th places; but when the 4th leads, (the 5th being behind) the single is in the 2d and 3d places.

London pleasure. 1 and 2.

This peal in the former printing of it was prickt another way, but I have here transposed that Course, which in my opinion renders it more easie and practical.

Mr. Tendring’s Peal, call’d Grand Paradox. 1 and 5.

One change is double, the next single, and so by turns. The motion of the whole-hunt is after this manner: first, it moves up into the 2d and 3d places, lying twice in each; then it moves up and makes a dodg behind, and then lieth still one change in the 5th place; then it makes another dodg behind, and so moves down into the 3d and 2d places lying twice in each as before, and then leads four times. Every other bell hath a like course and motion with that of the treble until the leadings of the treble, and then observe, that every time the treble goeth to lead and leaves leading, the double change is made on the two first and two last bells, except when it goeth to lead if the half-hunt lies next it, and then not. Every bell leads four times, and every single is made behind. The change wherein each bell leaves leading, is always made on the four first bells, except as before.

Every bell leads four times, and lies behind twice, except when the extream is made behind; and twice in the second place, except when the extream is made before: and note, when the treble is before the fourth stroke, the single is in the 2d and 3d, the next time the single is behind; but at other times the single is in the 3d and 4th places. When any bell leaves leading the double change is on the two first and two last, and the extreams are made by turns, first behind, then before, and so on to the end, for there are six extreams.

New Doubles.
1 and 2.

The changes are all double, except one single at every leading of the treble. The treble hath a perfect hunting course as in plain changes; and when it moves up from leading, the two first bells dodg untill it comes down again and displaceth them. Every bell that comes into the 3d place lies there twice, and then moves up behind; but the bell which lies there when the treble leaves leading, moves down. Every bell lies twice behind, except at the changes wherein the treble goeth to lead and leaves leading. Every time the treble leads, a single change is then made in the 3d and 4th places; but when the 2 lies next the treble, an extream behind.

Reding Doubles. 1 and 2.

The treble hath a direct hunting course as in plain changes, and when it moves up from leading the two first bells dodg until it comes down again and displaceth them; and whilst they dodg before, every bell that comes down into the 3d place lies there twice, and then moves up again behind. But after the dodging all the bells go a direct hunting course up and down, until the dodging again hindreth them as before. Every bell lies twice behind, except when the treble leaves leading if the 2d lies next it, and then the double is made on the two first and two last bells; by which means the two hind-bells then make a dodg, which happens in course once in twenty changes, that is, every second time the treble leaves leading. By this method it will go sixty changes, and then an extream must be made. The extreams in this peal may be made according to the preceding general rule set down in the Introduction. Here the first extream is made at the end of sixty changes, the bells lying 1 3 2; and when they come to lie so again, the second extream must be made; the extream is made behind, two of the extream bells lying there, and the single is made in the 2d and 3d place at both the extreams.

Grandsire. 1 and 5.

The treble hath a direct hunting course as in plain changes, and every other bell hath also a like hunting course with that of the treble except when the bobs hinder. The bobs are double changes, and made on the two first and two last bells according to this rule, viz. every time the treble goes to lead and leaves leading, a bob-change is then made, except the 5th lying next it makes a change there with it, and then not. Now ’tis observable, that once in twenty changes, that is, at every second leading of the treble, the 5th lies next it, and consequently there is but one bob-change then to be made, but at other times two; so that at one leading of the treble there is but one bob-change made, at the next leading there are two, and so successively by turns, which for distinction may be call’d single and double bobs, The two bells that dodg behind at a bob continue there dodging until the treble comes up and displaceth them, and at every bob-change the bell in the 3d place lieth still, and then moves down to lead. By this method it will go sixty changes; and to carry on the course extreams must be made, there being two in the peal. The manner of making an extream I have at large shewed in the Introduction, and the extreams may here be made in any place according to the general rule there set down. The easiest way in practice is to make them at the leadings of the treble; at any single bob it maybe made behind, two of the extream bells lying there, and to lie still whilst the bells in the 2d and 3d places do make the single change: at any double bob it may be made in the 2d and 3d places, so that the single must there be made behind. If the first extream is made at the single bob, the second must be made at the third following single bob; or if the first is made at a double bob, the second must be made at the third double bob following, as in this peal here prickt, where the first extream is made at a double bob, and the second also made at the third following double bob.

This peal will go with any hunts, and to begin it on the four hind bells; but then in ringing it at half-pulls, the first change being made at back-stroke to prevent cutting compass, the bells at the end of the peal will come round at a fore-stroke change. Therefore the better way is to begin it on the four first bells, which may also be done with any hunts, excepting 1.3, 1.5. and 2.3, 2.4, 2.5, wherein the first change of each may be a bob. And observe, that in any way of beginning it, the bells must all proceed in such a perfect hunting course as the first change directs them, until the first bob comes to be made.

Old Triples and Doubles.

One change is triple, the next double, and so by turns, except one single at the end of every sixty changes. Every triple change is made on the two first, the two middle, and two last bells; and every double is made on the four middle bells, except when the hunt leads and then on the four hind bells. Treble is here the hunt, and hath a direct hunting course up and down as in plain changes: the rest of the bells have also a direct hunting course up and down except when the treble leads, and then each bell that was hunting up (except that in the 2d place) makes a dodge with the next bell below it, and then proceeds forward again in its course up; and each bell which at the same time was hunting down, makes a dodg with the next bell above it, and so proceedeth forward in its course down; which method will carry on the peal five courses of the hunt, that is sixty changes as they are here prickt.

In the 120 there is also a half-hunt; and when the whole-hunt leads and the half-hunt lies next it, a single change must then be made, either in the 3d and 4th, or 5th and 6th places; but observing when the half-hunt comes again to lie next the whole-hunt, another single change must be made in the same place where the first was made. These single changes are called extreams, there being two in every sixscore, and the last of them always falls out in course to be made just 60 changes from the first, that is, at the fifth leading of the whole hunt after the first extream.

In the 240 there is also a half-hunt; and when the whole-hunt leads, and the half-hunt lies next it, a single change being then made in the 4th and 5th places, will bring the bells round at twelvescore, there being four singles in the peal, one of which falls in the course at the end of every sixty changes.

In the 720 there is a whole, half, and quarter hunt, and every time the whole-hunt leads and the half-hunt lies next it, a single change must then be made in the 4th and 5th places as in the twelvescore; but when the quarter-hunt lies next the half-hunt, that is, when the three hunts come together before, (which always happen at the end of every twelvescore) then the single must be made behind, which is call’d extream, there being three of them in the peal.

The sevenscore and four triples and doubles are the same with the former except at the leadings of the treble, and then a single is always made in the 3d and 4th places; but when the 2 lies next the treble, an extream is made in the 4th and 5th places. This peal is grounded on the twenty four doubles and singles, the four middle bells making them at the leadings of the treble.

Grandsire Bob. 1, 2 and 4.

The general method of this peal is the same with that next before, but with this difference; whereas in that peal singles were made at the end of every sixty changes to carry on the course, in this there are double changes made in their stead, which are called Bob-changes, and made when the treble leads in the 2d and 3d and the 5th and 6th places, whereas at other times the double is there made on the four hind bells.

The Practitioner may observe these rules in the ringing of it, viz. whatsoever bells he followeth when he hunteth up, he must follow the same bells again, and in the same order, the next time he hunts down, as in these changes here prickt; where the treble in hunting up first follows 2, then 4, and then 6; and when it comes behind, first it follows 2 again, then in its hunting down it follows 4 and 6 in the same order as when it hunted up; which is also observed in the ringing of any other bell, but with this difference betwixt the whole-hunt and the rest of the bells, viz. Every time the whole-hunt leaves the treble’s place and hunts up, it followeth different bells from what it did in its former hunting up, as may be seen in this example: where in its first hunting up it first follows 2, then 4, then 6; whereas in the next hunting up it first follows 3, then 2, then 4. But the first time any other bell leads after a bob, whatsoever bells it then follows in its hunting up, it follows the same bells likewise and in the same order every time it hunts up, and consequently every time it hunts down unto the next bob; as in this example, where 2 in its first hunting up, first follows 4, then 6, then 5, and likewise when it next hunts up it follows 465 as before, &c. But when the whole-hunt is the second bell which he follows in hunting up, he must follow it again when he next lies behind.