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Method ringing (also known as scientific ringing) is a form of change ringing (the practice of ringing a series of mathematical permutations on tuned bells, rather than a melody). In method ringing, the ringers are guided from permutation to permutation by following a specific algorithm, called a ''method.'' Where the treble bell follows exactly the same pattern as the other bells it is called a ''principle''. The underlying mathematical basis is intimately linked to group theory. The practice originated in England and remains most popular there today; in addition to bells in church towers, it is also often performed on handbells. ==Introduction== Understanding the conventions of change ringing is necessary to discuss method ringing. Among these are ways of referring to bells: the one highest in pitch is known as the ''treble'' and the lowest the ''tenor''. The majority of belltowers have the ring of bells (or ropes) going clockwise from the treble. 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 counterintuitive to musicians, who are used to a numbering which ascends along with pitch.) The bells are usually tuned to a diatonic major scale, with the tenor bell being the tonic (or key) note of the scale. The simplest way to use a set of bells is ringing ''rounds'', which is sounding the bells repeatedly in sequence from treble to tenor: 1, 2, 3, etc.. (Musicians will recognise this as a portion of a descending scale.) Ringers typically start with rounds and then begin to vary the bells' order, moving on to a series of distinct ''rows''. Each row (or ''change'') is a specific permutation of the bells (for example 123456 or 531246)—that is to say, it includes each bell rung once and only once, the difference from row to row being the order in which the bells follow one another. Since permutations are involved, it is natural that for some people the ultimate theoretical goal of change ringing is to ring the bells in every possible permutation; this is called an ''extent'' (in the past this was sometimes referred to as a ''full peal''). For a method on bells, there are (read factorial) possible permutations, a number which quickly grows as increases. For example, while on six bells there are 720 permutations, on 8 bells there are 40,320; furthermore, 10! = 3,628,800, and 12! = 479,001,600. Estimating two seconds for each change (a reasonable pace), we find that while an extent on 6 bells can be accomplished in half an hour, a full peal on 8 bells should take nearly twenty-two and a half hours and one on 12 bells would take over thirty years! Naturally, then, except in towers with only a few bells, ringers typically can only ring a subset of the available permutations. But the key stricture of an extent, uniqueness (any row may only be rung once), is considered essential. This is called ''truth''; to repeat any row would make the performance ''false''. Another key limitation keeps a given bell from moving up or back more than a single place from row to row; if it rings (for instance) fourth in one row, in the next row it can only ring third, fourth, or fifth. Thus from row to row each bell either keeps its place or swaps places with one of its neighbours.〔Ringers sometimes experiment with ignoring this rule, making a "jump change."〕 This rule has its origins in the physical reality of tower bells: a bell, swinging through a complete revolution with every row, has considerable inertia and the ringer has only a limited ability to accelerate or retard its cycle. A third key rule mandates ''rounds'' as the start and end of all ringing. So to summarize: any performance must start out from rounds, visit a number of other rows (whether all possible permutations or just a subset thereof) but only once each, and then return safely to rounds, all the while making only small neighbour-swaps from row to row.〔These rules dramatically limit the options open to a method-maker. For example, consider a tower with four bells. An extent includes 4! = 24 changes and there are, naturally, 24! possible orders in which to ring each change once, which is about 6.2 × 1023. But once we limit ourselves to neighbour-swaps and to starting and ending with rounds, only 10,792 possible extents remain. (())〕 It is to navigate this complex terrain that various ''methods'' have been developed; they allow the ringers to plot their course ahead of time without needing to memorize it all (an impossible task) or to read it off a numbingly repetitive list of numbers. Instead, by combining a pattern short and simple enough for ringers to memorize with a few regular breaking points where simple variations can be introduced, a robust algorithm is formed. This is the essence of method ringing. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Method ringing」の詳細全文を読む スポンサード リンク
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