Campanalogia

In the preceding twenty four changes, every extream change was made betwixt the two furthest extream bells from the hunt. I will therefore here set down an example, where they shall be made between the two nearest bells, to it. First, the treble hunts up (a). The two next notes to the hunt, which are 3.4, must make an extream change (b). The Treble must hunt down (c). The two nearest notes to the hunt, which are 2.4, must make an extream change (d). The Treble hunts up (e). The two nearest extream bells to the hunt, which are 2.3, must make an extream change (f). The Treble hunts down (g). The two next extream bells to the hunt, which are 4.3, must make a change (h). And the like extream changes being made as at (k) and (m), concludes the peal.

The six extream changes, viz. (b.d.f.h.k. and m.) being set down by themselves, will stand in this order, as here you see; where ’tis plain, that 2 3 4 have made the six changes, according to the method of the last six changes on three bells, page 49. where the first change of that six is made between the last two notes thus, 1 3 2. So in like manner is the first here thus, 243, which is the same method with that, though not the same figures.

So that the making of the extream changes two ways in the twenty four, proceeds from the two ways of making the six changes on three bells. This last way of making the extream changes, may, for distinction from the other way, be called mediums; which term is very proper, in regard that the two middlemost of the four notes do always make the extream change. The extream changes in one peal must all be made alike, that is, either betwixt the two farthest notes from the hunt, or else betwixt the two nearest notes to it; but the most usual way is to make them between the two farthest.

Any note may be made a hunt at pleasure, and its first motion at the beginning of the peal may be either up or down. The twenty four changes may be rung sixteen ways according to the aforesaid method, yet the changes to each are still one and the same; but by making each note a hunt, and moving it either up or down at the beginning, and also by making the extream changes two ways, the course of the changes will be so altered, that the same changes shall not come all along together in any two of those sixteen ways. With the hunting of one note it may be rung four ways; for the note may move either up or down at the beginning of the peal; then in its motion either way the extream changes maybe made two ways, as before: so that to make each note a hunt, and with each hunt to ring it four ways makes sixteen in the whole. Wherein ’tis observable, that the treble-note cannot be moved down at first, nor the 4th up; therefore an extream change must first be made, which is as effectual as if either note had moved at first. I have here prickt the twenty four changes three ways, wherein the extream changes are all made betwixt the two farthest notes from the hunt.

The Changes on five Bells.

There are sixscore changes to be rung on five bells; but the Learner may first practice some shorter peals, as the Ten changes, the twelve, the Fourteen, the Twenty all over, the Twenty with one hunt, and the Forty eight.

In the Ten changes the treble must first hunt up (a); the 2.3 must make a change (b). The treble must hunt down again (c); the 3.2 must make another change (d). The ten changes may also be rung by hunting down the 5 to lead; then 3.4 to make a change; the 5 to be hunted up again, and the 4.3 to make another change.

In the Twelve changes the treble hunts up into the third place, then the two first notes make a change; the treble hunts down again, then the two hindmost notes make a change. First the treble hunts into the 3d place (a); the two first notes 2.3 make a change (b). The treble hunts down (c); the two last notes make a change (d); the treble hunts up (e); the two first notes make a change (f); the treble hunts down (g); the two last notes make another change (h).

In the Fourteen changes, the treble first hunts up behind; then the 5 hunts down to lead; the treble then hunts down again into its own place; and the fifth also hunts up into its own place.

The Twenty all over are rung in the same manner as the Twelve all over upon four bells, to which I refer.

In the Twenty changes with one hunt, the hunting note continually hunts up and down through the other notes, and every time it lies either before or behind them, an extream change must be made betwixt the two farthest notes from it. The treble shall be the hunt, and first hunteth up (a). An extream change is made (b); the treble hunts down (c); an extream change is made (d); which course must be continued to the end. The extream changes may also be made betwixt the two next notes to the hunt. Any note may be made a hunt at pleasure, yet still observing to make the extreams as before.

In the forty eight changes, the 5th and 4th are both hunts, and 1 2 3 do make the six changes; the 5.4 do hunt down by turns, and when either of them leads, then one of the six changes is made. First the 5 hunts down (a); one of the six changes is made (b); the 5 hunts up into its own place (c); the 4 hunts down (d); another of the six changes is made (e); then the 4 must hunt up, and the 5 down again, &c. which course must be continued to the end.

In the Sixscore changes, four of the notes do make the Twenty four changes, and the fifth note hunts continually through them: so that the course and method of the Sixscore is in effect the same with that of the Four and twenty. For as the Four and twenty comprehended the Six changes on three; so in like manner the Sixscore comprehend the Four and twenty changes on four, and the Six changes on three. Therefore in the Sixscore there must be two hunts and three extream bells; one of the hunts is term’d the whole-hunt, and the other the half-hunt, The three extream bells do make the Six changes in the same manner as they were made before in the Four and twenty changes upon four bells, and are here also call’d Extream changes: the half-hunt and three extream bells do make the Four and twenty changes in the same manner as the Four and twenty changes on four bells were likewise made: and the whole hunt continually hunts through those four bells, and every time it either leads or lies behind them, one change must then be made in the twenty four. 1 shall here be the whole-hunt, 2 the half-hunt, and 345 extream bells: so that 2345 must make the four and twenty changes. Every extream change shall be made betwixt the two farthest extream bells from the half-hunt. First, the treble hunts up (a). One of the twenty four changes must now be made; and therefore 2 which is the hunt in the twenty four, must begin its motion through the extream bells (b). The treble hunts down (c); the half-hunt must proceed in its course (d); the whole-hunt hunts up (e); The half-hunt proceeds forward (f); the whole-hunt moves down (g). The half-hunt should now proceed, but having finished its course through the extream bells, therefore an extream change must now be made betwixt the two farthest extream bells from it, which are 3.4 (h). The treble must hunt up (i); the half-hunt must now begin its course again through the extream bells (k); treble hunts down (l); the half-hunt proceeds in its course down (m); treble hunts up (n); the half-hunt proceeds in its course down (o); treble hunts down (p); the half-hunt having finished its course, therefore an extream change must be made betwixt the two farthest extream bells from it, which are 3.5 (q). The treble hunts up (r). The half-hunt begins its motion again through the extream bells, and first it moves up over 4th (s). The whole hunt moves down (t); the half-hunt must proceed in its course, and therefore must move over another note (v). And this method being observed, will produce sixscore changes, and then the bells will in course come round. Now ’tis observable, that the changes at (b d f h k m o q s v x and z), being set down by themselves, that is, the 1 to be excluded, and the changes on 2345 to be set directly under one another in the same successive order as they were made, it will thereby appear, that those four figures have made twelve changes of the twenty four, according to the method of the first twenty four changes on four bells before set down. And whereas here are just half the sixscore changes prickt down, so likewise here are just half the four and twenty changes made therein: and the remaining part of this sixscore being likewise prickt, the remaining part of this four and twenty would also appear therein, which part being added to the former twelve, would make up the twenty four changes compleat; and the method of them the same in all respects with the first twenty four changes on four bells, page.

In the sixscore changes there is a whole-hunt, a half-hunt, and four extream bells. The half-hunt and four extream bells do make the twenty changes in the same manner as the twenty changes were made upon five bells with one hunt. page 61. The whole hunt hath a continual motion through the other five notes, and every time it leads and lies behind them, one of the twenty changes must then be made. In this example, treble is the whole-hunt, 2 the half-hunt, and 3456 extream bells; therefore 23456 must make the twenty changes wherein 2 is the hunt, and every time it lies either before the four extream bells, or behind them, an extream change must then be made, which here shall be betwixt the two farthest extream bells from the half-hunt. The treble hunts up (a). One of the twenty changes must now be made, therefore 2 being the hunt in it, must begin its course through the extream bells (b). The treble hunts down (c); The half-hunt proceeds forward (d); the treble hunts up (e); the half-hunt proceeds forward in its course (f); the treble hunts down (g); the 2 proceeds forward (h); the treble hunts up (i); the half-hunt should now proceed forward, but its course through the extream bells being finished, therefore an extream change must be made betwixt 3.4, which are the two farthest extream bells from it, (k). The treble must hunt down (l); the half-hunt must now go its course again through the extream bells, and first it moves down under the 6th, (m) &c. which method must be continued to the end. Any note may be made a whole hunt at pleasure, or a half-hunt also. And the extream changes may be made betwixt the two nearest extream notes to the half-hunt; but withall observing to make all the extreams in one peal alike. There are four extream changes in each peal, and thirty changes distance from one to another.

The method of the Seven hundred and twenty, hath an absolute dependency upon the method of the Sixscore changes on five bells; for five of the notes are to make the sixscore changes, and the sixth note hunts continually through them, and every time it leads or lies behind them, one of the Sixscore changes must then be made. The method of the Seven hundred and Twenty is in effect the same with that of the Sixscore: for as the Sixscore comprehended the Twenty four changes on four, and the Six on three; so likewise the Seven hundred and twenty comprehend the Sixscore changes on five, the Twenty four changes on four, and the Six changes on three. Therefore here must be three Hunts, and three Extream bells: the three Hunts are thus distinguished; one of them is call’d the whole-hunt, another the half-hunt, and the other the quarter-hunt. The Half-hunt, Quarter-hunt, and three Extream bells, are to make the Sixscore changes; the Quarter-hunt and three Extream bells are to make the Twenty four changes, and the three Extream bells are to make the six changes, which are here also called extream changes, and made in the same manner as before I have shewed upon four bells. In this example here prickt, treble is the whole-hunt, 2d the half-hunt, 3d the quarter-hunt, and 4 5 6 extream bells. Now ’tis observable, that 4 5 6 are to make the six extream changes, which will divide the seven hundred and twenty into six equal parts; the 3 4 5 6 are to make the twenty four changes, wherein the 3d is the hunt, (but in the seven hundred and twenty ’tis call’d the quarter-hunt;) and 2 3 4 5 6 are to make the sixscore changes, wherein the 2d is the whole-hunt (though in the 720 ’tis call’d the half-hunt,) by which ’tis evident, that the treble continually hunts through these five 2 3 4 5 6, the 2d through the four 3 4 5 6, and the 3d through these three 4 5 6; which are assigned for the respective hunts to hunt through, from the beginning to the end of the peal. First the treble hunts up (a). Now one of the sixscore changes must be made, therefore the 2d being the hunt in the sixscore, must begin its course through the other four notes (b). The treble hunts down (c); the 2d proceeds in its course (d); the treble hunts up (e). The 2d proceedeth forward in its course (f); the treble hunts down (g); the 2d proceeds forward (h); the treble hunts up (i); the 2d, which is the half-hunt, should now proceed forward, but having finished its course through the four bells, therefore the 3d, which is the quarter-hunt, must begin its motion through the extream bells (k). The treble hunts down (l). The half-hunt must now begin its course again through the four bells, and first therefore it moves down under the 6 (m). The treble must hunt up again, and then the 2d must move down under another bell, which method must be observed untill the 2d has moved quite down through the four bells again, and then the 3d must proceed forward by moving over another of the extream bells; which method must be observed in the motion of the three hunts, until the quarter-hunt hath moved up behind the extream bells, and then the whole and half-hunts, having gone their course again through the bells, an extream change must be made: after which the whole, half, and quarter-hunts proceed again in their course as before.

The letter h standing by the figures signifies half-hunt, that is, the motion of the half-hunt in that change; and likewise q the quarter-hunt. Here are the first sixscore changes of a seven hundred and twenty; wherein ’tis observable, that all the changes at h and q being set down by themselves in the same successive order as they were made, that is, the 1 to be excluded, and the changes on the other five figures to be set down directly under one another, and the extream change at last, it will thereby appear, that the five figures have made twenty changes of a sixscore, according to the method of the example on five bells, page 63. with this only difference, these are made on 23456, and those were made on 12345; but the five figures of each have both alike course, the 2d and 3d going the same course in this, as the treble and 2d did in that. Now whereas the sixscore changes here prickt down are a sixth part of the seven hundred and twenty, so likewise are the twenty changes, here made by 23456, a sixth part of the sixscore: and then consequently, the seven hundred and twenty changes being all prickt, the sixscore changes on 23456 would plainly appear therein, in the same manner as twenty of them appear in this sixscore. Therefore more need not be said of the method of the 720, since the method of the sixscore changes on five bells being well understood, will be a sure and certain guide to the Learner: only this one thing farther; in ringing of this peal with any hunts, the second extream change being made between the two bells which made the first extream, will always bring the bells round at the end of the twelvescore. But after twelvescore are made, they cannot in course be brought round until the end of the 720.

The 720 changes may be rung one thousand nine hundred and twenty several ways, which is thus demonstrable. There are six times five figures to be produced out of six, and not twice five the same: as 12345. 12346. 12356. 12456. 13456. 23456. and with each five the sixscore changes may be prickt one hundred and sixty ways, as before I have shewed on five bells. Now to each five add the sixth figure which is wanting, as to 12345 add 6, to 12346 add 5, to 12456 add 3, to 13456 add 2, and to 23456 add 1. And the sixth figure which is added, being hunted through all the several sixscores which the other five figures make; for instance, the 6 through the 160 several sixscores which 12345 make, and the 5 also through the 160 several sixscores, which 12346 make, and the like of the rest; will produce as many seven hundred and twenties as there are sixscores, that is, six times one hundred and sixty, which amounts to nine hundred and sixty. Then the note that hunts through the other five, may hunt two ways through each sixscore, that is, up and down, which will double the former number, and make nineteen hundred and twenty in the whole.