• Rob Coley
    Hello - I'm an academic researcher, currently working on a project that has led me to investigate some aspects of change ringing.

    I'm particularly interested in the patterns of change ringing and the 'factorial' number of bell towers. I'm trying to get a sense of the sheer complexity involved in ringing the changes of a large number of bells.

    I don't have the reference to hand (I think it was probably in George Grove’s Dictionary of Music and Musicians), but I've read that it would take around thirty minutes to continually ring the changes of six bells, three and a half hours to ring each permutation of seven, and more than a full day to ring eight. I assume that the other figures I have noted down are purely hypothetical - over 100 days to ring the changes of ten bells, almost 38 years to ring twelve!

    Does this sound correct? Any clarification and/or further sources on this would be very much appreciated.
  • John de Overa
    There is a good explanation here, including a table of how long it would take to ring all the permutations of different numbers of bells.

    The Mathematics of Bell Ringing
  • Rob Coley

    Thanks for this. Interestingly, the figures given by Prof Hart in this lecture are lower than those in Grove's Dictionary and the gap becomes exponentially larger as the number of bells increases.

    This, I presume, is simply due to a difference in the estimated time taken to ring each row. Hart's table is based on 2 seconds per row, Grove doesn't provide any figure.

    Do you have any thoughts on this? I'm comparing 19th and 21st century estimations here - it is simply a case of different estimations or could ringing have occurred more slowly in the past (assuming that pace/rhythm isn't dictated by the bells themselves)? Apologies if this is a stupid question!
  • A J Barnfield
    Of course it all depends on how fast you ring. Ringing on higher numbers tends to be slower partly because the bells tend to be heavier and partly because you have more bells to fit into each row. Have a look on BellBoard for some typical speeds. These days I seem to ring at about 30 changes per minute. A bit back on light eights 33ish felt comfortable. Some folk like hanging it out.

    Not sure how speeds have changed over time. Probably a bit faster now with modern bearings and fittings.
  • A J Barnfield
    ... on higher numbers the bells tend to be rung closer together than on lower numbers but overall the rows do spread a bit...
  • John de Overa
    As @A J Barnfield said the numbers you'll find are all just estimates, how long a peal takes depends on the number and size of the bells, the state of the installation and probably the air temperature and age of the ringers as well!

    You can get an idea of the current peal speeds from this link to BellBoard, in the last column. If you want to play with the numbers you can export them as CSV via the link at the bottom of the page.

    For historical records, you could dig around in Felstead, but I don't seem to be able to find any times on there, although they are commonly recorded on old peal boards in towers.
  • Rob Coley

    Thanks very much @John de Overa and @A J Barnfield, this is really helpful. Much appreciated.
  • A J Barnfield
    Some modern rings of bells seem to be very flexible as to speed and can be rung well easily quickly and slowly. Some rings of bells seem to have their own fixed speed, as do some ringers. The range of peal speeds at Shirley is most interesting.

    I expect we will get folk along soon with a wide range of statistics.
  • A J Barnfield
    ... you have started me looking now...
  • Rebecca Banner
    And of course the same combination of permutations rung on handbells (usually with two bells per ringer) often takes a lot less time - see https://bb.ringingworld.co.uk/view.php?id=1458352 for an extreme example.
  • Alison Hodge
    Rob - From your questions, I deduce that you may not be a bell ringer. So as this is a topic of interest then I strongly advise that you consider joining a group and learning to ring. You will find advice on how to do this here: https://cccbr.org.uk/bellringing/learn/

    Regarding your academic research, I don't know where you are doing your project or at what level - for example, are you a school student, university research student or academic staff? Academic research must show "originality"; but the answers to your questions are known to ringers (as you can see from the reponses already) even though not known to you. So for us to be able to help fully, perhaps you could let us know the aims and context of your project. We may then be able to offer responses that are more appropriate for your research goals.
  • Gareth Davies
    Here's an historical perspective.

    Nicholas Saunderson was the Lucasian Professor of Mathematics. His 'Elements of Algebra' was published posthumously in 1740. One of the questions he posed for students was 'In what time may all the changes on 12 bells be rung, allowing 3 seconds to every change'. The answer he gave was '1437004800 seconds, or 23950080 minutes or 399168 hours or 45 years, 27 weeks, 6 days, 18 hours'.

    In January 1788 the Cambridge ringers rang a peal of 6600 changes on 12 bells in 5 hours and 5 minutes. The newspaper report of the achievement said 'On Monday 21s was rung by the Society of Cambridge Youths, at the Tower of St Mary the Great, in this university, a true and compleat peal of Bob Maximus, in 5 hours and 5 minutes, consisting of 6600 changes; which for the regularity of striking, and harmony throughout the peal, was allowed by the most competent judges that heard it, to be a very masterly performance; especially as it was remarked, that in point of time, the striking was to such a nicety, that in each thousand changes, the time did not vary the 16th of a minute, and the compass of the last thousand was exactly equal to the first, which is the grand scope of ringing. 
The time of ringing this peal shews that the late Professor Saunderson’s calculations is pretty accurate, respecting the time it would take to ring the whole number of changes on twelve bells, which he stated at 45 years, 27 weeks, 6 days and 18 hours, without intermission'.
  • DRJA Dewar
    I've been away from ringing for some years now, but recall ringing on higher numbers (mainly 12), with 'closed handstrokes' - whereby there is not a small gap left bewteen the start fo every other row. This could, over a peal or more, make a small difference to the total peal length. (I have the impression, from somewhere, that this practice may have died out a little.)

    Furthermore, compositions for peals on seven would be 5040 rows to obtain the 'extent', and no more because that would necessarily make the peal 'false', by means of repetition. On higher numbers it becomes easier to devise compositions which tend towards 5000 rows.

    With compositions for odd numbers of bells which actually produce the changes, it is 'usual' to provide an n+1 bell (usually the heaviest) in each row. Thus, a peal of triples (i.e. seven bells actually changing in each row) would have eight bells ringing, with the heaviest not participating in the changes but always sounding (and striking) at the end of each row. (Personally, for me, a bete noir.)

    The other issue related to timings is that on almost any weight of bells, and provided excellent striking is maintained, there is a premium for faster ringing to enable more time in the pub afterwards. (Of course, not completing the peal enables further rounds to be consumed.)
  • Peter Sotheran
    Yes,. The times will vary according to the weight of the bells and a few other factors.
    6 bells: 18-30 mins to ring all the 720 changes on 6 bells
    7 bells: 2½hrs to 3 hrs to ring all 5040 changes
    8 bells: 18-20hrs to ring 40,320 changes - I believe it has been achieved 3 times in recorded history.
    9 bells: forecast is about 7 or 8 days

    Handbells can rung approximateley twice as quickly and therefore take about half of the above guideline times.
  • Rob Coley

    Thanks Gareth, that's fascinating. Do you happen to have a source for the newspaper report?
  • Rob Coley

    Thanks for this - very helpful and much appreciated.
  • Gareth Davies
    Hi Rob. The article appeared in the Cambridge Chronicle & Journal, Issue 1317, 19 January 1788. A copy is attached.
  • Rob Coley
    That's wonderful - very much appreciated!
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