Change ringing - Knowledge (XXG)

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degrees before swinging back in the opposite direction; while ringing slowly, the ringer waits with the bell held at the balance, before allowing it to swing back. To achieve this, the ringer must work with the bell's momentum, applying just the right amount of effort during the pull that the bell swings as far as required and no further. This allows two adjacent bells to reverse positions, the quicker bell passing the slower bell to establish a new pattern. Although ringing up certainly involves some physical exertion, actual ringing should rely more on practised skill than mere brute force. Even the smallest bell in a tower is much heavier than the person ringing it. The heaviest bell hung for full-circle ringing is in

935: 392:. In the down position, the bells are safe if a person touches them or pulls a rope. A bell that is up is dangerous to be near, and only expert ringers should ever contemplate entering a bell chamber or touching a rope when the bells are up. To raise a bell, the ringer pulls on the rope and starts the bell swinging. Each time the bell swings the ringer adds a little more energy to the system, similar to pushing a child's swing. Eventually there is enough energy for the bell to swing right up and be left over-centre just beyond the balance point with the stay resting against the slider to hold the bell in position, ready to be rung. 303: 497: 825: 232: 248: 216: 2302: 1672: 36: 396:

bell, the ringer first pulls the sally towards the floor, upsetting the bell's balance and swinging it on its bearings. As the bell swings downwards the rope unwinds from the wheel and the ringer adds enough pull to counteract friction and air resistance. The bell winds the rope back onto the other side of the wheel as it rises and the ringer can slow (or

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by swinging through a larger arc approaching a full circle, control of the strike interval can be exercised by the ringer. This culminated in the technique of full circle ringing, which enabled ringers to independently change the speeds of their individual bells accurately to combine in ringing different mathematical permutations, known as "changes".

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or wedding. While on these everyday occasions the ringers must usually content themselves with shorter "touches", each lasting a few minutes, for special occasions they often attempt a quarter-peal or peal, lasting approximately 45 minutes or three hours respectively. If a peal attempt succeeds, towers sometimes mark the occasion with a

287:. For convenience, the bells are referred to by number, with the treble being number 1 and the other bells numbered by their pitch—2, 3, 4, etc.—sequentially down the scale. (This system often seems counter-intuitive to musicians, who are used to a numbering that ascends with pitch.) The bells are usually tuned to a 186:

also means they cannot be easily stopped or started and the practical change of interval between successive strikes is limited. This places limitations on the rules for generating easily-rung changes; each bell must strike once in each change, but its position of striking in successive changes can only change by one place.

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Methods of change ringing are named for the number of working bells, or the bells that switch order within the change. It takes a pair to switch, and commonly the largest bell (the tenor) does not change place. For example, there may be six bells, only five of which work, allowing for only two pairs.

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The plain bob pattern can be extended beyond the constraints of the plain course of 60 changes, to the full unique 720 changes possible (this is 6 factorial on 6 bells, which is 1×2×3×4×5×6 = 720 changes). To do this, at set points in the sequences one of the ringers, called the "conductor" calls out

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with a small amount of rope on the wheel. The ringer pulls on the sally and when the bell swings up it draws up more rope onto the wheel and the sally rises to, or beyond, the ceiling. The ringer keeps hold of the tail-end of the rope to control the bell. After a controlled pause with the bell, on or

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Bells have been installed in towers around the world and many rings in the British Isles have been augmented to ten, twelve, fourteen, or even sixteen bells. Today change ringing is, particularly in England, a popular and commonplace sound, often issuing from a church tower before or after a service

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In all cases, the ringer of the bell immediately above (behind) the swapping pair must also be alert, as that bell follows a new bell after the swap. Rarer forms of change calling may name just one of the moving bells, call the moving bell by position rather than number, or call out the full change.

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In change ringing where the order the bells are struck in is constantly altered, it is necessary to time the swing so that this strike occurs with precise positioning within the overall pattern. Precision of striking is important at all times. To ring quickly, the bell must not complete the full 360

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Bellringers typically stand in a circle around the ringing chamber, each managing one rope. Bells and their attendant ropes are so mounted that the ropes are pulled in a circular sequence, usually clockwise, starting with the lightest (treble) bell and descending to the heaviest (tenor). To ring the

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Speed control of a tower bell is exerted by the ringer only when each bell is mouth upwards and moving slowly near the balance point; this constraint and the intricate rope manipulation involved normally requires that each bell have its own ringer. The considerable weights of full-circle tower bells

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The Central Council, by means of its peal records, also keeps track of record length peals, both on tower bells and handbells. (The record for tower bells remains the 1963 Loughborough extent of Plain Bob Major ; for handbells it was set in 2007 in Willingham, Cambridgeshire, with 72,000 changes of

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In method ringing, plain hunt is the simplest form of generating changing permutations in a continuous fashion, and is a fundamental building-block of many change ringing methods. The accompanying diagram shows plain hunt on six bells. The course of two bells only are shown for clarity. Each row in

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The change is made at the next "handstroke" (when the sally on the bell rope is pulled), after the call. In calling, the conductor usually has a strategy or plan to achieve the desired progression of rows, rather than remembering each call, and an example of these is shown in the example on eight

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found that swinging a bell through a much larger arc than that required for swing-chiming gave control over the time between successive strikes of the clapper. Ordinarily a bell will swing through a small arc only at a set speed governed by its size and shape in the nature of a simple pendulum, but

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It is the custom to leave a pause of one beat after every alternate row, i.e., after the ringing of each ‘backstroke’ row. This is called 'open handstroke' ringing (or open handstroke leading). In Devon, Cornwall and parts of Yorkshire, this custom is not followed when call-change ringing; instead

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is used. Ringers stand or sit in a straight line at a single convenient table on which the bells are placed. They pick up a bell each time they ring it, and then put it down. As the bell sequence changes, however, the ringers physically swap the bells accordingly—so the bells move up and down the

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Most ringers begin their ringing career with call change ringing; they can thus concentrate on learning the physical skills needed to handle their bells without needing to worry about "methods". There are also many towers where experienced ringers practise call change ringing as an art in its own

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As of 30 June 2018 there are 7,141 English style rings in ringable condition. The Netherlands, Belgium, Pakistan, India, and Spain have one each. The Windward Isles and the Isle of Man have 2 each. Canada and New Zealand 8 each. The Channel Isles 11. Africa as a continent has 13.

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For example, while six bells have 720 permutations, eight bells have 40,320; furthermore, 10! = 3,628,800, and 12! = 479,001,600. Estimating two seconds for each change (a reasonable pace), one finds that while an extent on six bells can be accomplished in half an hour, an extent on eight bells

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ringing the bells of a less familiar tower. The setting, the church architecture, the chance to ring more bells than usual, the bells' unique tone, their ease or difficulty of ringing, and sometimes even the unusual means of accessing the ringing chamber can all be part of the attraction. The

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commands such as "bob" or "single", which introduce further variations. The conductor follows a "composition" which they have to commit to memory. This enables the other ringers to produce large numbers of unique changes without memorising huge quantities of data, without any written prompts.

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Change ringing – the history of an English Art. Vol 3, W T Cook & Cyril A Wratten. Pub Central Council of Church Bell Ringers, 1994. P90-93 “A recent examination of a number of call change ‘peals’ still practised at Totnes in the South Hams …including the ubiquitous ‘Sixty on Thirds’

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100 different Treble Dodging Minor methods, taking just over 24 hours to ring) More importantly, perhaps, along with keeping track of the first peal ever rung in a method, the Central Council controls the naming of new methods: it generally allows the first band to ring a method to name it.

1178:, has been published weekly since 1911; in addition to news and features relating to bellringing and the bellringing community, it publishes records of achievements such as peals and quarter-peals. Ringers generally adhere to the Council's rules and definitions governing change ringing. 365:

is constrained to swing in the direction that the bell swings. The clapper is a rigid steel or wrought iron bar with a large ball to strike the bell. The thickest part of the mouth of bell is called the soundbow and it is against this that the ball strikes. Beyond the ball is a

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Plain hunt consists of a plain undeviating course of a bell between the first and last places in the striking order, by moving a place in the sequence at each change, but with two strikes in the first and last position to enable a turn-around as the internal bells change over.

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made it impossible for bell ringers to assemble in belfries. Searching for alternative methods, in March 2020 two ringers from the USA developed software called Ringing Room that mimics the operation of ropes and bells, and permits people to ring together online, in a type of

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In English-style ringing the bell is rung up such that the clapper is resting on the lower edge of the bell when the bell is on the stay. During each swing, the clapper travels faster than the bell, eventually striking the soundbow and making the bell sound. The bell

2371:. The avoidance, where possible, of repetition and the use of hunts, half-hunt and extreme changes are all features of their construction, and together suggest a basically uninterrupted descent from the earlier system, unbroken by the intrusion of change ringing..." 801:

Thus each bell moves one position at each succeeding change, unless they reach the first or last position, where they remain for two changes then proceed to the other end of the sequence. All of the bells are doing this at every change, without any words of command.

448:. This is a repeated sequence of bells descending from the highest to lowest note, which is from the lightest to the heaviest bell. This was the original sequence used before change ringing was developed, and change ringing always starts and ends with this sequence. 1542:

the bands are ringing methods and producing a different change approximately every 2.5 seconds, with a gap between bells of 0.21 seconds. To an expert ringer's ear at this level of competition a variation of a tenth of this would be discernible as a striking fault.

353:, limits maximum rotational movement to a little less than 370 degrees. To the headstock a large wooden wheel is fitted and to which a rope is attached. The rope wraps and unwraps on the rim of the wheel as the bell rotates backwards and forwards. This is 814: 1368:

coming up with plans for a bout of method ringing sometimes like to work their favourite named changes in. The table below lists some popular named changes on eight bells; many of these names are also applicable by extension on more or fewer bells.

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The method is committed to memory by each ringer, so that only a few commands are given by the ringer in charge (the conductor). Learning the method does not consist of memorising the individual sequences, but using a variety of techniques such as:

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where it is customary to include the quality of the rise and lower of the bells as part of the judging criteria. Competitions for method ringers usually start "off the stay"—i.e., the bells are rung up before the competition begins. At the annual

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each different sequence of the bells, known as a "row", is specifically called out by one ringer, the "conductor", who instructs the other ringers how to change their bells' places from row to row. This command is known as a "call".

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And then it repeats. Each bells starts at a different place in this cyclical order. A dodge means just that: two bells dodge round each other, thus changing their relationship to the treble, and giving rise to different changes.

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The names refer to the number of bells which change places in each row. With three bells only one pair can change, and so it is singles. With seven bells there are clearly three pairs with the one left over not moving this row.

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To enable a greater number of changes to be rung without repetition, more advanced methods were developed, many based upon the plain hunt. "Plain Bob" is one of the oldest and simplest of these, and is shown as an example above.

295:, with the tenor bell being the tonic (or key) note of the scale. Some towers contain additional bells so that different subsets of the full number can be rung, still to a diatonic scale. For instance, many 12-bell towers have a 260: 264: 262: 258: 257: 263: 1200:

Scotland 23, Ireland 38, USA 48, Australia 61 and Wales 227. The remaining 6,695 (94%) are in England (including three mobile rings). World-wide there are 985 unringable rings, 930 in England, 55 in Wales and 12 elsewhere.

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roughly when horizontal as it rises, thus projecting the sound outwards. The clapper rebounds very slightly, allowing the bell to ring. At the balance point, the clapper passes over the top and rests against the soundbow.

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could save it from becoming obsolete. But the Central Council of Church Bell Ringers opposed the move, suggesting that it would jeopardise its relationship with church bodies, since bell ringing should be seen as part of

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Since extents are obviously not always practicable, ringers more often undertake shorter performances. Such ringing starts and ends with rounds, having meanwhile visited only a subset of the available permutations; but

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Plain Bob Minor played using synthesised bell sounds. The bells start ringing rounds followed by a plain course of Plain Bob Minor (60 of the 720 changes that are possible on six bells) and finish in rounds

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The example on the right shows called changes eight bells being called using the "down" system. The sequence of calls shown gives three well-known musical rows, which are Whittingtons, Queens, and Tittums.

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Below the bell chamber there may be one or more sound chambers, (one of which is likely to house the clock mechanism if the church has one) and through which the rope passes before it drops into the

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or room. Typically, the rope's length is such that it falls close to or on to the floor of the ringing chamber. About 5 feet (1.5 m) from the floor, the rope has a woollen grip called the

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Call changes on eight bells, with the musical rows Whittingtons, Queens and Tittums. This is not a call change 'peal', but an example of calling changes for a short period for musical effect.

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magazine wrote to insist that bell ringing was "an art and a sport", as demonstrated by regular "striking competitions". It was suggested that classification of change ringing as a sport by

2853: 1458: 2185: 1492:. This is particularly effective at the end of ringing down. The bells are in order, and so if not chimed leave a pause, the sequence becomes: 1..4..23.5 where a dot indicates a pause. 1431: 1391: 1506:

Although neither call change nor method ringing produces conventional tunes, it is still the aim of the ringers to produce a pleasant sound. One of the most important aspects of this is

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table and each row is rung in strict sequence from right to left. Ringers in cross and stretch thus do not have responsibility for their own personal bell, but handle each as it comes.

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English style full circle bell with clapper half-muffled. A leather muffle is put over one side only of the clapper ball. This gives a loud strike, then a muffled strike alternately.

1533:(striking errors); the band with the fewest faults wins. These competitions are organized on regional and national levels, being particularly popular among the call-change ringers of 1185:

Much ringing is carried out by bands of ringers meeting at their local tower to ring its bells. For the sake of variety, though, many ringers like to take occasional trips to make a

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and weighs 82 long cwt 0 qr 11 lb (9,195 lb or 4,171 kg). Despite this colossal weight, it can be safely rung by one (experienced) ringer.

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Mathematical abstraction though each row may be, some rows do have a musical or melodic meaning to the listener. Over the years, a number of these have acquired names — they are

2634: 166:, where the ringers are instructed how to generate each change by instructions from a conductor. This creates a form of bell music which cannot be discerned as a conventional 2093:– the sequence of places a bell rings in a method, or the diagram describing the method (the convention being that the treble line is shown in red while the others are blue). 1583:. Various other online platforms for virtual change ringing have also been created, but Ringing Room is the most popular, with over 10,000 people joining in the first year. 1102:, which promised in its subtitle to lay down "plain and easie Rules for Ringing all sorts of Plain Changes". Stedman followed this in 1677 with another famous early guide, 412:

by pulling the tail-end, causing the bell to swing back towards its starting position. As the sally rises, the ringer catches it to pause the bell at its balance position.

1064:: ringers standing in a line each hold one bell, exchanging places in the line so that the changes sound correctly when the bells are rung in sequence from right to left. 1045:

are retained, referring to an upwards and downwards ring of the bell respectively; and as in towers, the ringing proceeds in alternate rows of handstroke and backstroke.

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Ringers can also ring different methods, with different "works" on different numbers of bells - so there is a huge variety of ways of ringing changes in method ringing.

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The bells of St Bees Priory shown in the "up" position. When being rung they swing through a full circle from mouth upwards round to mouth upwards, and then back again.

1172:, founded in 1891, is dedicated to representing change ringers around the world. Most regional and local ringing guilds are affiliated with the council. Its journal, 132: 1344:

The name for 9 bells is pronounced "kate-ers" and comes from the French "quatres". The name for 11 bells also comes from the French and is pronounced "sinks" c.f.

259: 1857:– (pronounced "sinks") methods for working eleven bells (possibly with a twelfth covering) the name deriving from the practice of swapping five pairs of bells. 1072:

Change ringing as we know it today emerged in England in the 17th century. To that era we can trace the origins of the earliest ringing societies, such as the

2597: 2215: 1148:(a method still popular today), rung 2 May 1715. There is some evidence there may have been an earlier peal (also Plain Bob Triples), rung January 7, 1690 at 279:

Today, some towers have as many as sixteen bells that can be rung together, though six or eight bells are more common. The highest pitch bell is known as the

1615:, demonstrates his skill at ringing, and the solution to the central puzzle of the book rests in part upon his knowledge of the patterns of change ringing. 986:

became the only band in history to achieve this feat on tower bells, it took them just under 18 hours.) An extent on 12 bells would take over thirty years.

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bells. Conductors can space out the calls at will, but each row is normally struck twice at least because of the difficulty of calling continuous changes.

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in Bristol, which was founded in 1620 and lasted as a ringing society until the late 19th century. The recreation began to flourish in earnest in the

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The rope is attached to one side of the wheel so that a different amount of rope is wound on and off as it swings to and fro. The first stroke is the

2016:- From rounds all the bells are rung at once for a few strokes before returning to rounds. Done at special occasions such as weddings or New Year. 1566:, not exercise. The council's president, Chris Mew, said: "Where is the glamour of the sports field and where are the David Beckhams of the belfry?" 2524: 1586:

In one Shropshire church, bells can be tied up with their sounds simulated by sensors, so ringers can practise in silence using Bluetooth headsets.

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The plain course of Plain Bob Minor, shown in red. Note that, for clarity, the row at the bottom of each column is repeated at the top of the next.

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Calls are usually of the form "X to (or after) Y" or "X and Y"; in which X and Y refer to two of the bells by their physical numbers in the tower (

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bell is a sharpened 11th (or 4th in the upper, incomplete octave) of the scale. For example, assume the bells are tuned to C-G'. A flat sixth is B

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fitted on trunnions (plain or non-friction bearings) mounted to the belfry framework so that the bell assembly can rotate. When stationary in the

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After starting in repetitive rounds, at a given command, the ringers vary the bells' order, to produce a series of distinct sequences known as

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Memorising the path of the bell, not the numbers of the bells it strikes after. This can be by visualising a tracking line in a method diagram

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Striking competitions are held where various bands of ringers attempt to ring with their best striking. They are judged on their number of

299:, which if rung instead of the normal number 6 bell allows 2 to 9 to be rung as light diatonic octave; other variations are also possible. 1958:– Changing direction for one stroke in bell ringing (although strictly a dodge is taking a retrograde step in the middle of a portion of 1004:

is an extended performance; it must comprise at least 5000 changes (but 5040 on 7 bells). A performance of 1250 changes likewise makes a

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era; an important milestone in the development of method ringing as a careful science was the 1668 publication by Richard Duckworth and

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in a tightly controlled manner to produce precise variations in their successive striking sequences, known as "changes". This can be by

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arrangement. However for method ringing the universal practice is to ring with open handstrokes, even in the South West of England.

1157: 436:– they are generally only chimed, either by swinging the bell slightly or having the bell hung dead and using a mechanical hammer.) 119: 2676: 2569:, (Cambridge, England: Cambridge University Press, 1972), Chapter 24: "Ringing the changes: groups and campanology," pages 451-479. 2488: 805:

This simple rule can be extended to any number of bells, however it repeats the sequence after twice the number of bells hunting.

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As an example of calling up and down, consider the following sequence of rows, and the calls a conductor would use to call them:

2980: 2341: 1637:(1992); a group of American women led by a Mrs. Taylor frequently appears practising for or ringing both handbells and changes. 3022: 2306: 1224:"Plain Bob Doubles" is a method rung on five bells whereas "Plain Bob Triples" is the same method rung on seven working bells. 53: 3684: 1496: 100: 57: 2000:– EITHER: when the bells are hanging with the mouth lowermost position, OR: moving towards the front (as in "hunting down"). 1227:

There are two separate ways to refer to the number of bells. One way is used for even numbers, the other for an odd number.

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traditional means of finding bell towers, and still the most popular way today, is the book (and now internet database)

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Normally each ringer has a bell in each hand and sit or stand in a circle (like tower ringers). The tower bell terms of

3794: 3445: 2169:– EITHER: when the bells are raised to the mouth uppermost position, OR: moving towards the back (as in "hunting up"). 1580: 370:, which controls the speed of the clapper. In very small bells this can be nearly as long as the rest of the clapper. 79: 3679: 2022:– to ring haphazardly, either because ringers accidentally try to ring at once, or deliberately for wedding ringing. 943: 726:

Method ringing is the continuously changing form of change ringing, and gets its name from the use of a particular

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Unattended bells are normally left hanging in the normal ("down") position, but prior to being rung, the bells are

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effect to the assembly, and this dynamic is controlled by the ringer's rope. The headstock is fitted with a wooden

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shown in the "down" position, where they are normally left between ringing sessions. This is in the "bell chamber".

946:, Birmingham, recording the details of a notable peal. Thousands of these boards exist in change-ringing belfries. 46: 3674: 3634: 3435: 1627: 1622: 381:(usually around 4 feet (1.2 m) long) while the lower end of the rope is doubled over to form an easily held 86: 3706: 3696: 3669: 3639: 3425: 2950: 2709: 2314: 2225: 2220: 1966:

is an exercise where two bells exchange places on every stroke, sometimes taught to aid learners change from

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Call change ringing requires one ringer to give commands to change the order of the bells, as distinct from

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all the bells plain hunt, until the treble bell is first, and depending where they are in the pattern, they

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There are thousands of different methods, of which two methods on six bells are explained in detail below.

68: 3799: 3749: 3644: 3584: 3410: 3395: 3372: 1445: 2521: 2145:– A device which allows the bell to go over the balance at each end of its swing, but not to over-rotate. 1877:– causing a bell to sound while down by pulling a hammer against it (as a clock would) or by pulling the 3804: 3664: 3377: 3087: 2006:– a touch where all possible changes are rung exactly once each; the number of such different rows is N 1633: 1144:

there is one documenting what is generally considered to have been the first true peal: 5040 changes of

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the permutations, to ring a tower's bells in every possible order without repeating – what is called an

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Method ringing: where after a word of command to start, the changes are rung from memory by the ringers.

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by sounding at the same moment, the bells should sound to a perfect rhythm, tapping out a steady beat.

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discloses a remarkable affinity with the seventeenth century Plain Changes described by Duckworth and

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and looking for visual signposts, such as when the ringer's bell crosses with another particular bell.

3789: 3629: 3624: 3609: 3542: 3494: 3206: 2466: 2421: 1663:(2008) changes are rung in a cloistered monastery for mathematicians to signal different ceremonies. 2441: 481:

The technique was probably developed in the early 17th century in the early days of change ringing.

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a presentation prepared by the Publications Committee of the Central Council of Church Bell Ringers

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Introduction to change ringing and both group theory and graph theory (with references) :

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of the bell and clapper is appreciably below the centreline of the trunnion supports, giving a

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for short); a peal or a quarter tends to last about three hours or 45 minutes, respectively.

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is still considered essential — no row can ever be repeated; to do so would make the ringing

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aired an episode in the fifth season on a series of murders within a bell-ringing team, in "

1642: 1599: 93: 2960: 1891:) – handstroke changes follow backstroke changes with no handstroke gap (unlike open leads) 3614: 3569: 3519: 3400: 2954: 2580: 2528: 2429: 2210: 2139:– the woollen bulge woven into the rope. It is both an indicator and a help with gripping. 1660: 273: 1116:. "Changes" can be viewed as permutations; sets of permutations constitute mathematical 892:

The red bell track shows the order of "works", which are deviations from the plain hunt.

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by their positions in the row). All cause two bells to swap. The first form is used for

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and chimes of bells, though these are more commonly used to play conventional melodies.

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Such names are often humorous; for example, the sequence 14235 on five bells is called

1214: 1153: 1113: 1095: 721: 485: 338: 269: 236: 159: 152: 2917: 2688: 2327: 2151:– a device that is attached to the headstock and works in conjunction with the slider. 3783: 3767: 3711: 3559: 3549: 3293: 3288: 3274: 3112: 2970:

Tintinnalogia, or, the Art of Ringing (by Richard Duckworth and Fabian Stedman, 1668)

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Change-ringing resources, an online compendium of almost everything you need to know

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Bell ringing- the English Art of Change Ringing. Ron Johnson. Pub Viking 1986 P 89.

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in English churches, where it first developed. Change ringing is also performed on

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Central Council of Church Bell Ringers, "Learning plain hunt" retrieved 20.3.2017

962:). The feasibility of this depends on how many bells are involved: if a tower has 488:, where the ringers memorise the course of bells as part of a continuous pattern. 215: 162:

in which the ringers commit to memory the rules for generating each change, or by

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the bells strike steadily without the pause. This latter custom is known as the

813: 742: 178: 35: 2613:. www.cccbr.org.uk. December 19, 2011. Archived from the original on 2011-12-19 699:- bell 1 and 2 stay in place, other bells ascend the odds and descend the evens 3489: 3324: 3148: 3072: 3062: 2985: 2310: 2053: 1133: 1125: 1060:

Some handbell change ringers practice a hybrid of these two methods, known as

939: 859: 780: 17: 2535: 1607:(1934) contains a great deal of information on change-ringing. Her fictional 789:

The "diagram" of change ringing plain hunt on six bells. Two bells are shown.

711:- interspersed light and heavy bells, giving a "tee-tum, tee-tum...." effect. 3502: 3341: 3259: 3216: 3191: 3170: 3163: 3127: 2933: 2200: 2007: 1608: 971: 888:

or sit for two blows if they are just above the treble, then go first again.

137: 3228: 3184: 2827:"The ART Award for Excellence in the Development of Technology in Teaching" 2648: 2562:(New York, New York : W.H. Freeman, 1992), Chapter 13 (pages 199-219). 2493:

Website of St Stephen's, the parish church for the City of Bristol, England

2854:"The chimes they are a'changing at south Shropshire church with new bells" 764:

or by breaking the line into small "work" units which are joined together.

3312: 3240: 3221: 3196: 3158: 3153: 3143: 3052: 2317:, is again a 16 but with additional flat 3 and 10. Retrieved 28 May 2008. 2118: 1027: 1021: 982:

should take nearly twenty-two and a half hours. (When in 1963 ringers in

342: 288: 198: 194: 2542: 3415: 2114: 1863:– the metal (usually cast iron) rod/hammer hung from a pivot below the 1655: 1141: 785: 240: 189:

Change ringing is practised worldwide, but it is by far most common on

2548:

Change ringing graphs on polyhedra that can rotated via cursor :

455:

Call changes: where the conductor of the ringing commands each change.

3235: 2969: 319: 167: 144:

in 1910; 5,040 changes were rung in two hours and forty-nine minutes.

2957:, a directory of towers worldwide with bells hung for change ringing 2947: 2715: 474:

right (and even exclusively), particularly in the English county of

2903: 2936:

published by the Council in 2019, superseding its former decisions

1670: 1534: 933: 812: 784: 495: 475: 301: 254: 246: 230: 224: 214: 197:, where conventionally each ringer holds two bells, and chimed on 131: 2939: 2309:

is listed as having 16 bells, with additional sharp 6, 9 and 13;

1034:, including the longest peal ever rung, are by handbell ringers. 3107: 3047: 3031: 2776: 2662: 1031: 1000: 929: 141: 3004: 2925:, a wide-ranging and well-organized compendium of ringing links 2442:"Framework for Method Ringing - Fundamentals of Method Ringing" 2270:

in a 12-bell ring is in fact the flattened 7th of the scale. A

1807:– starting to raise in peal by adding an extra bell each time. 1082: 974:) possible permutations, a number that becomes quite large as 357:

and quite different from fixed or limited motion bells, which

29: 2911: 1486:

because it is the tune of the refrain to the children's song

950:

For some people, the ultimate goal of this system is to ring

173:

Change ringing originated following the invention of English

2129:

with a leather pad on one side of the clapper. Very rarely

1364:. Both the conductors directing call-change ringing and the 1030:, and is quite popular in its own right. Many record-length 823: 2995: 1759:– the commonest type of call in most methods or a class of 1221:

with bell towers in the UK are fitted with only six bells.

794:

the diagram shows the order of striking after each change.

676:, The first-called bell moves after the second called bell. 669:, The first-called bell moves after the second called bell. 2928: 2922: 1990:– a method with five working bells, possibly with a sixth 1213:. Doubles is the most common group of methods rung in the 268:

6 bells being rung to call changes in All Saints' Church,

2186:

The Australian and New Zealand Association of Bellringers

1699:) – The part of a bell's cycle started by pulling on the 3000: 2714:, Central Council of Church Bell Ringers, archived from 444:

The simplest way to sound a ring of bells is by ringing

306:

Mechanism of a bell hung for English full-circle ringing

2738:) define back rounds slightly differently, as 76543218. 2520:

Introduction to change ringing and group theory :

2303:

Search on Dove's Guide for towers with 13 or more bells

1707:; also: the position at which the back bells come into 3279: 3250: 3226: 2711:

County Lists from Dove's Guide for Church Bell Ringers

2555:

Some literature on the mathematics of change ringing:

2541:

Change ringing as directed graphs on polyhedra :

2400:. Central Council Education Committee. 6 October 2000. 2266:

This again may seem counter-intuitive to musicians. A

2040:– the hole in the wheel where the rope passes through. 1471:(so named because of the ti-tum ti-tum sound it makes) 661:

Thus it can be seen how these ways of calling differ:

27:

Art of ringing a set of bells in mathematical patterns

3182: 3168: 1112:

underpinnings of change ringing have been pursued by

528:, and the second form swaps the two bells mentioned. 1209:

A method of ringing for these bells would be called

3720: 3528: 3388: 3302: 3136: 3038: 2280:

allowing F-F' to be a scale. The sharp second is F'

2099:– an agreed/named sequence of changes that forms a 2034:– the smaller bells which are rung first in rounds. 1631:(1997), features bell ringers in her earlier novel 745:of the bells' striking order proceeds. For example 408:close to its balancing point, the ringer rings the 177:tower bell ringing in the early 17th century, when 60:. Unsourced material may be challenged and removed. 1703:(rope end) in the tower, or with the bells raised 1689:– the heavier bells (so tend to limit the speed). 219:Bell ringing at St Mary and St Gabriel’s Church, 140:, Cambridgeshire, commemorating the ringing of a 2633:: CS1 maint: bot: original URL status unknown ( 871:A "plain course" of plain bob minor is shown in 329:of steel or wood. Each bell is suspended from a 1779:") the appropriate point in the method (e.g. a 1717:– the leather lined metal strap from which the 1136:mounted on the wall of the ringing chamber; at 2301:, a twelve bell tower with 3 semi-tone bells. 1120:, which in turn can be depicted via so-called 3322: 3016: 2589:Arthur T. White (1987) "Ringing the cosets," 2424:, from the Central Council records committee 451:Two forms of ringing changes have developed; 8: 3475: 1984:where the structure is the same if reversed. 1160:. Today over 4000 peals are rung each year. 705:- descending odd bells then descending evens 227:, England. This is in the "ringing chamber". 2572:Arthur White and Robin Wilson (March 1995) 2052:– move one place at a time up or down (see 1940:is made sometimes, but not every time, the 136:Peal board at St Peter and St Paul Church, 3023: 3009: 3001: 2929:The Central Council of Church Bell Ringers 432:(Whilst heavier bells exist – for example 2348:. Central Council for Church Bell Ringers 1733:– the load-bearing assembly on which the 1444:(an apocryphal story says it appealed to 120:Learn how and when to remove this message 2991:Animation of English Full-circle ringing 2908:, a DVD documentary about change ringing 2163:– the highest-pitched bell in the tower. 1737:(and so the whole bell) turns about its 1375: 1286: 1229: 1026:Change ringing can also be performed on 533: 2649:Landmarks in the History of the Society 2247:"The History and Use of Semitone Bells" 2237: 2157:– the lowest pitched bell in the tower. 2046:– the stroke when the sally is gripped. 1871:of the bell when the bell stops moving. 1767:takes place or some bells are not just 2981:Change Ringing Wiki - Info for ringers 2626: 2522:Mathematics and Music: Change Ringing 2342:"Liverpool:Cathedral Church of Christ" 1851:– loops cast onto older bells' crowns. 1797:, but does not check the ringing as a 1775:); also can mean (usually called the " 1170:Central Council of Church Bell Ringers 1076:, which claims to date to 1612 or the 885:or perform dodges in the 5-6 positions 857: 3735:Glockenmuseum Stiftskirche Herrenberg 2748:Jamieson, Sophie (19 February 2014). 7: 3729:Dove's Guide for Church Bell Ringers 2560:Another Fine Math You've Got Me Into 2346:Dove's Guide for Church Bell Ringers 2087:and a place short of the last place. 1783:) to modify the sequence of changes. 1683:– at or near last place in a change. 1193:Dove's Guide for Church Bell Ringers 882:perform "dodges" in the 3-4 position 400:) the rise of the bell if required. 58:adding citations to reliable sources 2677:"72000 Treble Dodging Minor (100m)" 2598:Steinhaus–Johnson–Trotter algorithm 2536:"The Mathematics of Change Ringing" 2216:Steinhaus–Johnson–Trotter algorithm 2113:For commemorative services such as 1741:. Modern hanging means the bell is 1124:, which in turn can be mapped onto 310:The bells in a tower reside in the 2391:"The Learning Curve: Call changes" 2070:(ringing first) at its backstroke. 1845:, that is often the first learned. 1510:— not only should the bells never 25: 2961:Some recordings of change ringing 2833:. Association of Ringing Teachers 2543:Bell-ringing methods as polyhedra 2010:, where N is the number of bells. 1905:), or produce rounds prematurely. 1540:National 12 Bell Striking Contest 1158:Ancient Society of College Youths 1048:Occasionally, a technique called 875:, which has the characteristics: 2489:"THE ANTIENT SOCIETY OF RINGERS" 2028:– at or near the start of a row. 1825:to its limit, stopping the bell. 1108:Throughout the years since, the 1088:Society of Ringers of St Stephen 858:Problems playing this file? See 839: 683:, the bells simply swap position 34: 2802:"Ringing Room – a User's Guide" 2586:, vol. 79, no. 484, pages 5-16. 2307:Christ Church Cathedral, Dublin 1919:, while the other bells ring a 349:, which, in conjunction with a 325:The bells are mounted within a 322:to enable the sound to escape. 151:is the art of ringing a set of 45:needs additional citations for 2944:, the Council's weekly journal 2914:– introduction for non-ringers 1915:) ringing at the end of every 1867:of the bell, that strikes the 1640:The British television series 1422:Back rounds or Reverse Rounds 1: 3761:Freedom Bell, American Legion 3337:Russian Orthodox bell ringing 2986:- Video of plain hunt ringing 2591:American Mathematical Monthly 2180:Index of campanology articles 1881:against the side of the bell. 1653:In the science-fiction novel 1495:Called changes are listed at 3740:Liberty Bell Memorial Museum 3466:Bells of Notre-Dame de Paris 2934:Framework for Method Ringing 1897:– return to rounds to end a 1590:In literature and television 1150:St Sepulchre-without-Newgate 3675:Saarlouiser Glockengießerei 3280: 3251: 3227: 3183: 3169: 2880:"Glossary of ringing terms" 2579:September 20, 2009, at the 2330:. Whitechapel Bell Foundry. 2286:, giving G-G' as the scale. 1581:networked music performance 958:(or sometimes, formerly, a 3821: 3600:Pieter and François Hemony 2177: 2062:– the change on which the 1813:– allow the bell to swing 1667:English bell-ringing terms 1497:MAW Call Change Collection 1068:History and modern culture 1019: 944:St Martin in the Bull Ring 927: 778: 719: 466: 208: 3436:Ivan the Great Bell Tower 2593:, vol. 94, pages 721-746. 2567:The Fascination of Groups 2056:, treble bob hunt, etc.). 1817:, out of control, so the 1749:, but were traditionally 1628:To Say Nothing of the Dog 1289: 1232: 730:to generate the changes. 3670:John and William Rufford 3426:Great Bell of Dhammazedi 2905:The Craft of Bellringing 2584:The Mathematical Gazette 2315:Perth, Western Australia 2226:Whitechapel Bell Foundry 2221:Veronese bellringing art 2076:– a method in which the 1217:, since the majority of 492:Call change instructions 283:, and the lowest is the 2611:"Bells and Bellringing" 2196:Change ringing software 1164:Organisation and extent 1074:Lincoln Cathedral Guild 924:Peals and quarter peals 3750:National Bell Festival 3580:Gillett & Johnston 3476: 3411:Bell of King Seongdeok 3396:List of heaviest bells 3373:Bolognese bell ringing 3323: 3073:Bell tower / Campanile 2918:Call changes explained 2858:www.shropshirestar.com 2465:. 2006. Archived from 2428:June 13, 2008, at the 2328:"500 Years of History" 2133:with pads both sides.. 1676: 1233:Even numbers of bells 947: 828: 818: 790: 753:in the next sequence. 546:Call, if calling Down 501: 361:. Within the bell the 307: 276: 252: 244: 228: 145: 3755:Ringing organizations 3378:Veronese bell ringing 2912:Discover Bell Ringing 2178:Further information: 2125:, the bells are rung 1901:(e.g. "come round at 1674: 1290:Odd numbers of bells 937: 827: 816: 788: 634:to swap bells 1 and 3 612:to swap bells 2 and 5 589:to swap bells 4 and 5 566:to swap bells 2 and 3 499: 305: 267: 250: 234: 218: 205:Technique and physics 135: 3645:Glockengießerei Otto 3610:Franciscus Illenfeld 2735:Some sources (e.g., 2574:"The hunting group," 2456:"Company of Ringers" 2206:John Taylor & Co 1711:order at backstroke. 1016:Changes on handbells 543:Call, if calling Up 54:improve this article 3745:Liberty Bell Museum 3655:Petit & Fritsen 3441:Japanese Peace Bell 3351:Full circle ringing 3332:Ellacombe apparatus 2831:ringingteachers.org 2755:The Daily Telegraph 2469:on October 29, 2006 2299:Worcester Cathedral 1551:In 2016 readers of 1489:Pop Goes the Weasel 540:Conductor's intent 506:call change ringing 463:Call change ringing 427:Liverpool Cathedral 355:full circle ringing 3795:Culture of England 3605:Christopher Hodson 2953:2016-10-10 at the 2718:on 10 October 2016 2527:2010-07-04 at the 2123:Remembrance Sunday 1944:is going from one 1677: 1648:Ring Out Your Dead 948: 829: 819: 791: 502: 308: 277: 253: 245: 229: 146: 3777: 3776: 3508:World Peace Bells 3406:Bell of Good Luck 2975:Project Gutenberg 2685:The Ringing World 2663:The Ringing World 2550:Minimus Polyhedra 2461:Lincoln Cathedral 2422:Online peal board 2398:The Ringing World 1763:(in which either 1621:, who frequently 1613:Lord Peter Wimsey 1605:Dorothy L. Sayers 1576:COVID-19 pandemic 1564:Christian worship 1554:The Ringing World 1476: 1475: 1342: 1341: 1285: 1284: 1175:The Ringing World 1146:Plain Bob Triples 1138:St Peter Mancroft 1110:group theoretical 1054:cross and stretch 966:bells, they have 873:diagrammatic form 844: 659: 658: 549:Call if swapping 265: 130: 129: 122: 104: 16:(Redirected from 3812: 3688: 3546: 3481: 3328: 3285: 3256: 3232: 3188: 3174: 3025: 3018: 3011: 3002: 2977: 2891: 2890: 2888: 2886: 2878:Harrison, John. 2875: 2869: 2868: 2866: 2864: 2849: 2843: 2842: 2840: 2838: 2823: 2817: 2816: 2814: 2812: 2798: 2792: 2791: 2789: 2787: 2773: 2767: 2766: 2764: 2762: 2745: 2739: 2733: 2727: 2726: 2725: 2723: 2706: 2700: 2699: 2697: 2696: 2687:. Archived from 2673: 2667: 2666: 2665: 2658: 2652: 2651:, from the ASCY. 2645: 2639: 2638: 2632: 2624: 2619: 2618: 2607: 2601: 2515: 2509: 2508: 2506: 2504: 2495:. Archived from 2485: 2479: 2478: 2476: 2474: 2452: 2446: 2445: 2438: 2432: 2419: 2413: 2408: 2402: 2401: 2395: 2387: 2381: 2378: 2372: 2364: 2358: 2357: 2355: 2353: 2338: 2332: 2331: 2324: 2318: 2293: 2287: 2285: 2284: 2279: 2278: 2264: 2258: 2257: 2255: 2253: 2242: 1964:Dodging practice 1815:over the balance 1721:used to be hung. 1643:Midsomer Murders 1600:The Nine Tailors 1465: 1464: 1463: 1461: 1438: 1437: 1436: 1434: 1418: 1417: 1416: 1414: 1398: 1397: 1396: 1394: 1376: 1295:Number of bells 1287: 1238:Number of bells 1230: 908:make 2nds place. 846: 845: 826: 629: 607: 584: 561: 557: 534: 266: 125: 118: 114: 111: 105: 103: 69:"Change ringing" 62: 38: 30: 21: 3820: 3819: 3815: 3814: 3813: 3811: 3810: 3809: 3780: 3779: 3778: 3773: 3716: 3682: 3570:Kashpir Ganusov 3565:Royal Eijsbouts 3540: 3530: 3524: 3520:Yongle Big Bell 3401:Balangiga bells 3384: 3298: 3132: 3040: 3039:Background and 3034: 3029: 2967: 2955:Wayback Machine 2900: 2895: 2894: 2884: 2882: 2877: 2876: 2872: 2862: 2860: 2852:Tooley, David. 2851: 2850: 2846: 2836: 2834: 2825: 2824: 2820: 2810: 2808: 2800: 2799: 2795: 2785: 2783: 2781:ringingroom.com 2775: 2774: 2770: 2760: 2758: 2747: 2746: 2742: 2734: 2730: 2721: 2719: 2708: 2707: 2703: 2694: 2692: 2675: 2674: 2670: 2661: 2660: 2659: 2655: 2646: 2642: 2625: 2616: 2614: 2609: 2608: 2604: 2581:Wayback Machine 2529:Wayback Machine 2516: 2512: 2502: 2500: 2487: 2486: 2482: 2472: 2470: 2454: 2453: 2449: 2440: 2439: 2435: 2430:Wayback Machine 2420: 2416: 2409: 2405: 2393: 2389: 2388: 2384: 2379: 2375: 2365: 2361: 2351: 2349: 2340: 2339: 2335: 2326: 2325: 2321: 2294: 2290: 2282: 2281: 2276: 2275: 2265: 2261: 2251: 2249: 2245:Bryant, David. 2244: 2243: 2239: 2234: 2211:Margery Sampson 2182: 2176: 1911:– a bell (e.g. 1697:Backstroke home 1669: 1661:Neal Stephenson 1592: 1572: 1549: 1504: 1459: 1457: 1456: 1455: 1432: 1430: 1429: 1428: 1412: 1410: 1409: 1408: 1392: 1390: 1389: 1388: 1358: 1219:parish churches 1206: 1204:Number of bells 1166: 1070: 1024: 1018: 932: 926: 865: 864: 856: 854: 853: 852: 851: 847: 840: 837: 835:Plain Bob Minor 830: 824: 811: 783: 777: 724: 718: 627: 605: 582: 559: 555: 494: 471: 465: 442: 375:ringing chamber 320:louvred windows 274:North Yorkshire 255: 213: 207: 126: 115: 109: 106: 63: 61: 51: 39: 28: 23: 22: 15: 12: 11: 5: 3818: 3816: 3808: 3807: 3802: 3797: 3792: 3782: 3781: 3775: 3774: 3772: 3771: 3764: 3757: 3752: 3747: 3742: 3737: 3732: 3724: 3722: 3718: 3717: 3715: 3714: 3709: 3704: 3699: 3694: 3689: 3677: 3672: 3667: 3662: 3660:Richard Phelps 3657: 3652: 3647: 3642: 3637: 3632: 3627: 3622: 3617: 3612: 3607: 3602: 3597: 3592: 3587: 3582: 3577: 3572: 3567: 3562: 3557: 3555:Andrey Chokhov 3552: 3547: 3534: 3532: 3529:Bell founders 3526: 3525: 3523: 3522: 3517: 3516: 3515: 3505: 3500: 3492: 3487: 3485:Sigismund Bell 3482: 3473: 3468: 3463: 3458: 3456:Maria Gloriosa 3453: 3448: 3443: 3438: 3433: 3428: 3423: 3418: 3413: 3408: 3403: 3398: 3392: 3390: 3386: 3385: 3383: 3382: 3381: 3380: 3375: 3370: 3369: 3368: 3366:Method ringing 3363: 3356:Change ringing 3348: 3347: 3346: 3345: 3344: 3334: 3329: 3320: 3315: 3306: 3304: 3303:Ringing styles 3300: 3299: 3297: 3296: 3291: 3286: 3277: 3272: 3267: 3262: 3257: 3248: 3243: 3238: 3233: 3224: 3219: 3214: 3209: 3204: 3199: 3194: 3189: 3180: 3175: 3166: 3161: 3156: 3151: 3146: 3140: 3138: 3134: 3133: 3131: 3130: 3125: 3123:Striking clock 3120: 3115: 3110: 3105: 3095: 3090: 3085: 3080: 3075: 3070: 3065: 3060: 3055: 3050: 3044: 3042: 3036: 3035: 3030: 3028: 3027: 3020: 3013: 3005: 2999: 2998: 2993: 2988: 2983: 2978: 2964: 2963: 2958: 2945: 2937: 2931: 2926: 2920: 2915: 2909: 2899: 2898:External links 2896: 2893: 2892: 2870: 2844: 2818: 2793: 2777:"Ringing Room" 2768: 2740: 2728: 2701: 2668: 2653: 2640: 2602: 2595: 2594: 2587: 2570: 2563: 2554: 2553: 2546: 2539: 2532: 2510: 2499:on 3 July 2007 2480: 2447: 2433: 2414: 2403: 2382: 2373: 2359: 2333: 2319: 2296:Dove entry for 2288: 2259: 2236: 2235: 2233: 2230: 2229: 2228: 2223: 2218: 2213: 2208: 2203: 2198: 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In this way 722:Method ringing 720:Main article: 717: 716:Method ringing 714: 713: 712: 706: 700: 685: 684: 677: 670: 657: 656: 654: 652: 650: 646: 645: 642: 639: 636: 631: 624: 623: 620: 617: 614: 609: 601: 600: 597: 594: 591: 586: 578: 577: 574: 571: 568: 563: 551: 550: 547: 544: 541: 538: 493: 490: 486:method ringing 467:Main article: 464: 461: 460: 459: 456: 441: 438: 339:centre of mass 337:position, the 270:Kirkbymoorside 237:St Bees Priory 209:Main article: 206: 203: 160:method ringing 149:Change ringing 128: 127: 42: 40: 33: 26: 24: 18:Change-ringing 14: 13: 10: 9: 6: 4: 3: 2: 3817: 3806: 3803: 3801: 3800:English music 3798: 3796: 3793: 3791: 3788: 3787: 3785: 3770: 3769: 3768:All the Bells 3765: 3763: 3762: 3758: 3756: 3753: 3751: 3748: 3746: 3743: 3741: 3738: 3736: 3733: 3731: 3730: 3726: 3725: 3723: 3719: 3713: 3712:Geert van Wou 3710: 3708: 3705: 3703: 3700: 3698: 3695: 3693: 3690: 3686: 3681: 3678: 3676: 3673: 3671: 3668: 3666: 3663: 3661: 3658: 3656: 3653: 3651: 3648: 3646: 3643: 3641: 3638: 3636: 3633: 3631: 3628: 3626: 3623: 3621: 3618: 3616: 3613: 3611: 3608: 3606: 3603: 3601: 3598: 3596: 3593: 3591: 3588: 3586: 3583: 3581: 3578: 3576: 3573: 3571: 3568: 3566: 3563: 3561: 3558: 3556: 3553: 3551: 3550:Bilbie family 3548: 3544: 3539: 3536: 3535: 3533: 3531:and foundries 3527: 3521: 3518: 3514: 3511: 3510: 3509: 3506: 3504: 3501: 3499: 3497: 3493: 3491: 3488: 3486: 3483: 3480: 3479: 3474: 3472: 3469: 3467: 3464: 3462: 3459: 3457: 3454: 3452: 3449: 3447: 3444: 3442: 3439: 3437: 3434: 3432: 3429: 3427: 3424: 3422: 3419: 3417: 3414: 3412: 3409: 3407: 3404: 3402: 3399: 3397: 3394: 3393: 3391: 3389:Notable bells 3387: 3379: 3376: 3374: 3371: 3367: 3364: 3362: 3359: 3358: 3357: 3354: 3353: 3352: 3349: 3343: 3340: 3339: 3338: 3335: 3333: 3330: 3327: 3326: 3321: 3319: 3316: 3314: 3311: 3310: 3308: 3307: 3305: 3301: 3295: 3294:Tubular bells 3292: 3290: 3289:Tintinnabulum 3287: 3284: 3283: 3278: 3276: 3275:Standing bell 3273: 3271: 3268: 3266: 3263: 3261: 3258: 3255: 3254: 3249: 3247: 3244: 3242: 3239: 3237: 3234: 3231: 3230: 3225: 3223: 3220: 3218: 3215: 3213: 3210: 3208: 3205: 3203: 3200: 3198: 3195: 3193: 3190: 3187: 3186: 3181: 3179: 3176: 3173: 3172: 3167: 3165: 3162: 3160: 3157: 3155: 3152: 3150: 3147: 3145: 3142: 3141: 3139: 3135: 3129: 3126: 3124: 3121: 3119: 3116: 3114: 3113:Ring of bells 3111: 3109: 3106: 3103: 3099: 3096: 3094: 3091: 3089: 3086: 3084: 3081: 3079: 3076: 3074: 3071: 3069: 3066: 3064: 3061: 3059: 3056: 3054: 3051: 3049: 3046: 3045: 3043: 3037: 3033: 3026: 3021: 3019: 3014: 3012: 3007: 3006: 3003: 2997: 2994: 2992: 2989: 2987: 2984: 2982: 2979: 2976: 2972: 2971: 2966: 2965: 2962: 2959: 2956: 2952: 2949: 2946: 2943: 2942: 2941:Ringing World 2938: 2935: 2932: 2930: 2927: 2924: 2921: 2919: 2916: 2913: 2910: 2907: 2906: 2902: 2901: 2897: 2881: 2874: 2871: 2859: 2855: 2848: 2845: 2832: 2828: 2822: 2819: 2807: 2803: 2797: 2794: 2782: 2778: 2772: 2769: 2757: 2756: 2751: 2744: 2741: 2737: 2732: 2729: 2717: 2713: 2712: 2705: 2702: 2691:on 2015-10-16 2690: 2686: 2682: 2678: 2672: 2669: 2664: 2657: 2654: 2650: 2644: 2641: 2636: 2630: 2623: 2612: 2606: 2603: 2599: 2596:See also the 2592: 2588: 2585: 2582: 2578: 2575: 2571: 2568: 2565:F.J. 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