boring for those ringers whose bells do not change position for long periods. Stedman's achievement was to develop methods – then known as "cross-changes" – which could relatively quickly produce an "extent" by changing more than one pair of bells at a time. For instance, starting with rounds on five bells (12345) one might move to 21354 then to 23145 and so on. The aim of producing an extent without repeating a change apart from rounds at the start and finish could now be realised more artistically and with more interest for the ringers. One of the very earliest methods, known as "Doubles and Singles" in Tintinnalogia, accompanies this article. The diagram shows the course of the lightest bell (1) and one other bell (in this case 2). All bells other than the 1 follow the same course as the 2 but start in different places. The "plain Course" of Grandsire Doubles, still commonly rung today, is also shown. As more bells were added to towers, Stedman's methods were adapted to higher numbers. Since the number of possible changes varies with the factorial ( n! ) of the number of bells, it became impractical to ring extents on numbers above 7 (the extent on 10 bells would take around three months). Any performance of 5,000 (approximately 7!) changes or more became recognised as a peal, but still with the traditional restrictions that no change may be repeated and that a bell may exchange only with one adjacent in the row. Nowadays many hundreds of methods are practised; all, in some degree, owe a debt to Stedman's pioneering work which has value as well in mathematics (group theory) as well as bell-ringing. See also Albert J Pitman John Holt (composer) References Change ringing – the history of an English art, three vols., General Editor: J. Sanderson. Chapters on Stedman by John Eisel in Vol 1. External links Go Stedman! A bell-ringing anniversary – British Library music blog Fabian Stedman: The First Group Theorist? Arthur T. White The American Mathematical Monthly Vol. 103, No. 9 (Nov., 1996), pp. 771–778 1640 births 1713 deaths Bellringers People from Herefordshire 17th-century English mathematicians