CHANGE RINGING

traditional English art of ringing a set of tower bells in an intricate series of changes, or mathematical permutations (different orderings in the ringing sequence), by pulling ropes attached to bell wheels. On five, six, or seven bells, a peal is the maximum number of permutations possible (120, 720, and 5,040, respectively); on more than seven bells, the full extent of possible changes is impracticable, so that 5,000 or more changes are said to constitute a peal. The number of possible changes on any series of bells may be determined, using the mathematical formula of permutations, by multiplying the number of the bells together. On 3 bells, only 6 changes, or variations, in the order 1 2 3 can be produced; on 5 bells, 1 2 3 4 5 = 120; and so on up to the astronomical total of 479,001,600 changes on 12 bells. A touch is any number short of a peal. In ringing a peal, no bell moves more than one place forward or backward in the ringing order in each successive change, nor is it repeated or omitted, nor is any sequence (change) repeated. A set, or ring, of 4 bells is known as Minimus, or Singles; 5, Doubles; 6, Minor; 7, Triples; 8, Major; 9, Caters; 10, Royal; 11, Cinques; and 12, Maximus. A complete peal of 4 bells (24 changes), requires about 30 seconds; one of 12 bells (479,001,600 changes), about 40 years. A system of permutation is called a method; the entire ringing fraternity, the exercise. Groups of swinging bells in English church towers date from the 10th century, and, at least by the 15th, orderly ringing took place involving changing note patterns. This practice evolved from first rendering descending scales (called rounds). The practice was stimulated by the Reformation in England, and it remains particularly associated with the Anglican church. By the 17th century, intricate mathematical formulas had evolved. Change ringing was originally a gentleman's recreation. Its early participants, aristocrats and intelligentsia, often students, were later joined by ecclesiastics, labourers, and others. Women were excluded, and participation was a mark of social status. The first society, or ringing organization, the Ancient Society of College Youths, was founded in 1637. The earliest treatises on the subject were Fabian Stedman's Tintinnalogia (1668) and his Campanologia (1677), which introduced his Grandsire Method and his Stedman's Principle (a method). When swung, change-ringing bells rotate slightly less than 360. A bell is gradually swung back and forth until it reaches a nearly vertical balance position with the mouth of the bell uppermost. Handstroke (a pull on the rope that rotates the bell almost 360 to the other balance position) alternates with backstroke (a pull on the rope that returns the bell to its initial position), two successive revolutions constituting a whole pull. In the ringing sequence a bell makes three basic movements. (1) It hunts, or changes position one place forward or backward and continuing in the same direction. Hunting up is moving toward last place, called behind; hunting down, toward first place, in which a bell leads. (2) It dodges by suddenly reversing coursetaking a step backward in the hunt, then proceeding in the original direction. (3) It makes a place by remaining in the same position it occupied in the previous change (also called lying still); this term refers to a bell in an inside position, rather than at lead or behind. A bell's movement is its duty, and various methods are identified by the duty given each bell. In plain hunting, a bell moves change by change toward last place, where it lies behind for an additional stroke; it then moves toward first place, where it leads for a whole pull, or two strokes. Change-ringing bells are relatively short waisted, with their axis at midwaist for easier swinging. They are tuned in just intonation (pitches derived from certain ratios rather than from equal division of the octave). Until the end of the 19th century, tuning of their partials (component tones) was not seriously undertaken and so lacked uniformity. The largest and last bell in a ring is the tenor; the smallest, the treble. Most tenor bells range from several hundred pounds to two tons; that of the Cathedral Church of Christ, Liverpool, weighs 4.6 tons. The two founders, both English, who cast bells for change ringing are the Whitechapel Bell Foundry and John Taylor and Company of Loughborough, Leicestershire, Eng.