Mathematics of Bell-Ringing

Total Page:16

File Type:pdf, Size:1020Kb

Mathematics of Bell-Ringing Mathematics of bell-ringing Dr Rob Sturman University of Leeds, School of Mathematics 24th September 2016 Gravity Fields Festival Easy example: on 3 bells, the possible sequences are: 1 2 3 9 > 1 3 2 > > Combinatorics: 2 1 3 => 3 choices for first place, then 2 6 sequences 2 3 1 choices, then 1 choice =) > 3 1 2 > 3 × 2 × 1 = 3! (3 factorial) > 3 2 1 ; 4 bells: 4! = 4 × 3 × 2 × 1 = 24 sequences (around 30 seconds) 6 bells: 6! = 720 sequences (takes about 25 minutes) 8 bells: 8! = 40320 sequences (18 hours, in Loughborough, 1963) 12 bells: 12! = 479; 001; 600 sequences (over 30 years!) Change-ringing Extents Basic idea: Ring every possible sequence exactly once 4 bells: 4! = 4 × 3 × 2 × 1 = 24 sequences (around 30 seconds) 6 bells: 6! = 720 sequences (takes about 25 minutes) 8 bells: 8! = 40320 sequences (18 hours, in Loughborough, 1963) 12 bells: 12! = 479; 001; 600 sequences (over 30 years!) Change-ringing Extents Basic idea: Ring every possible sequence exactly once Easy example: on 3 bells, the possible sequences are: 1 2 3 9 > 1 3 2 > > Combinatorics: 2 1 3 => 3 choices for first place, then 2 6 sequences 2 3 1 choices, then 1 choice =) > 3 1 2 > 3 × 2 × 1 = 3! (3 factorial) > 3 2 1 ; 12 bells: 12! = 479; 001; 600 sequences (over 30 years!) Change-ringing Extents Basic idea: Ring every possible sequence exactly once Easy example: on 3 bells, the possible sequences are: 1 2 3 9 > 1 3 2 > > Combinatorics: 2 1 3 => 3 choices for first place, then 2 6 sequences 2 3 1 choices, then 1 choice =) > 3 1 2 > 3 × 2 × 1 = 3! (3 factorial) > 3 2 1 ; 4 bells: 4! = 4 × 3 × 2 × 1 = 24 sequences (around 30 seconds) 6 bells: 6! = 720 sequences (takes about 25 minutes) 8 bells: 8! = 40320 sequences (18 hours, in Loughborough, 1963) Change-ringing Extents Basic idea: Ring every possible sequence exactly once Easy example: on 3 bells, the possible sequences are: 1 2 3 9 > 1 3 2 > > Combinatorics: 2 1 3 => 3 choices for first place, then 2 6 sequences 2 3 1 choices, then 1 choice =) > 3 1 2 > 3 × 2 × 1 = 3! (3 factorial) > 3 2 1 ; 4 bells: 4! = 4 × 3 × 2 × 1 = 24 sequences (around 30 seconds) 6 bells: 6! = 720 sequences (takes about 25 minutes) 8 bells: 8! = 40320 sequences (18 hours, in Loughborough, 1963) 12 bells: 12! = 479; 001; 600 sequences (over 30 years!) You can only swap neighbouring bells. Easy example: 3 bells: a = (12), b = (23) [positions, not bells] Alternate these changes: All 6 possible sequences gener- ated, and the ringers only have 1 2 3 9 to remember two different opera- > a 2 1 3 > tions, and to alternate them. > > b 2 3 1 => a 3 2 1 6 sequences b b 3 1 2 > > a 1 3 2 > 1 > a b 1 2 3 ; 3 2 Change-ringing A constraint and an opportunity You can’t just move from one sequence to any other! Easy example: 3 bells: a = (12), b = (23) [positions, not bells] Alternate these changes: All 6 possible sequences gener- ated, and the ringers only have 1 2 3 9 to remember two different opera- > a 2 1 3 > tions, and to alternate them. > > b 2 3 1 => a 3 2 1 6 sequences b b 3 1 2 > > a 1 3 2 > 1 > a b 1 2 3 ; 3 2 Change-ringing A constraint and an opportunity You can’t just move from one sequence to any other! You can only swap neighbouring bells. All 6 possible sequences gener- ated, and the ringers only have to remember two different opera- tions, and to alternate them. b 1 a 3 2 Change-ringing A constraint and an opportunity You can’t just move from one sequence to any other! You can only swap neighbouring bells. Easy example: 3 bells: a = (12), b = (23) [positions, not bells] Alternate these changes: 1 2 3 9 > a 2 1 3 > > > b 2 3 1 => a 3 2 1 6 sequences b 3 1 2 > > a 1 3 2 > > b 1 2 3 ; Change-ringing A constraint and an opportunity You can’t just move from one sequence to any other! You can only swap neighbouring bells. Easy example: 3 bells: a = (12), b = (23) [positions, not bells] Alternate these changes: All 6 possible sequences gener- ated, and the ringers only have 1 2 3 9 to remember two different opera- > a 2 1 3 > tions, and to alternate them. > > b 2 3 1 => a 3 2 1 6 sequences b b 3 1 2 > > a 1 3 2 > 1 > a b 1 2 3 ; 3 2 9 The full peal is not generated > by a and b — we need an extra > > change, for example > > > c = (34). => only 8 rows! a > > 1 2 > > > > ;> 3 4 b Change-ringing Plain Bob Minimus Consider 4 bells and let a = (12)(34) , b = (23) 1 2 3 4 a 2 1 4 3 b 2 4 1 3 a 4 2 3 1 b 4 3 2 1 a 3 4 1 2 b 3 1 4 2 a 1 3 2 4 b 1 2 3 4 The full peal is not generated by a and b — we need an extra change, for example c = (34). a 1 2 3 4 b Change-ringing Plain Bob Minimus Consider 4 bells and let a = (12)(34) , b = (23) 1 2 3 4 9 > a 2 1 4 3 > > b 2 4 1 3 > > > a 4 2 3 1 => b 4 3 2 1 only 8 rows! a 3 4 1 2 > > b 3 1 4 2 > > a 1 3 2 4 > > b 1 2 3 4 ; Change-ringing Plain Bob Minimus Consider 4 bells and let a = (12)(34) , b = (23) The full peal is not generated 1 2 3 4 9 > by a and b — we need an extra a 2 1 4 3 > > change, for example b 2 4 1 3 > > > c = (34). a 4 2 3 1 => b 4 3 2 1 only 8 rows! a a 3 4 1 2 > 1 2 > b 3 1 4 2 > > a 1 3 2 4 > > b 1 2 3 4 ; 3 4 b Change-ringing Plain Bob Minimus — full extent a = (12)(34) , b = (23), c = (34) 1 2 3 4 c 1 3 4 2 c 1 4 2 3 a 2 1 4 3 a 3 1 2 4 a 4 1 3 2 b 2 4 1 3 b 3 2 1 4 b 4 3 1 2 a 4 2 3 1 a 2 3 4 1 a 3 4 2 1 b 4 3 2 1 b 2 4 3 1 b 3 2 4 1 a 3 4 1 2 a 4 2 1 3 a 2 3 1 4 b 3 1 4 2 b 4 1 2 3 b 2 1 3 4 a 1 3 2 4 a 1 4 3 2 a 1 2 4 3 c 1 2 3 4 Change-ringing Plain Bob Minor — full peal Change-ringing Extent rules 1 start and end with bells in order musical satisfaction 2 every sequence rung exactly once completeness 3 only swap neighbouring bells physical contraints 4 each bell must move at least every other change keep ringers interested 5 bells do the same work as each other keep ringers equitable 6 the method is palindromic ease of memory? Fabian Stedman 1640–1713 Fabian Stedman: “the father of change- ringing” a contemporary of Isaac Newton (1643–1727) Born in Herefordshire, went to London as apprentice printer in 1655 Learnt bell-ringing at St Mary-le-Bow two publications of bell-ringing a parish clerk at St Bene’t’s Church in Cambridge, 1670 cross-changes Stedman Doubles Stedman Doubles a = (12)(45), b = (23)(45) 1 2 3 4 5 1 2 3 4 5 a 2 1 3 5 4 b 1 3 2 5 4 b 2 3 1 4 5 a 3 1 2 4 5 a 3 2 1 5 4 b 3 2 1 5 4 b 3 1 2 4 5 a 2 3 1 4 5 a 1 3 2 5 4 b 2 1 3 5 4 b 1 2 3 4 5 a 1 2 3 4 5 Stedman Doubles a = (12)(45), b = (23)(45), c = (12)(34) (a parting change) 1 2 3 4 5 3 1 5 2 4 a 2 1 3 5 4 b 3 5 1 4 2 b 2 3 1 4 5 a 5 3 1 2 4 a 3 2 1 5 4 b 5 1 3 4 2 b 3 1 2 4 5 a 1 5 3 2 4 a 1 3 2 5 4 b 1 3 5 4 2 c 3 1 5 2 4 c 3 1 4 5 2 Now known as a single, d = (34) will then allow the other sixty combinations to be rung. Grandsire doubles on 5 bells: a = (12)(45), b = (23)(45), c = (12)(34) =) a(bc)4a Always an even number of permutations, so only half the 5! = 120 possible sequences generated. Need a ‘single’, e.g., d = (45) to generate the other ‘odd’ permutations. Stedman Doubles a = (12)(45), b = (23)(45), c = (12)(34) (a parting change) So the ‘lead’ (ababac)(bababc) = (ab)2ac(ba)2bc gives the permutations 12345 ! 31452 ! 43521 ! 54213 ! 25134 ! 12345 “By this method the peal will go to sixty changes, and to carry it farther, extremes must be made”.
Recommended publications
  • SAVED by the BELL ! the RESURRECTION of the WHITECHAPEL BELL FOUNDRY a Proposal by Factum Foundation & the United Kingdom Historic Building Preservation Trust
    SAVED BY THE BELL ! THE RESURRECTION OF THE WHITECHAPEL BELL FOUNDRY a proposal by Factum Foundation & The United Kingdom Historic Building Preservation Trust Prepared by Skene Catling de la Peña June 2018 Robeson House, 10a Newton Road, London W2 5LS Plaques on the wall above the old blacksmith’s shop, honouring the lives of foundry workers over the centuries. Their bells still ring out through London. A final board now reads, “Whitechapel Bell Foundry, 1570-2017”. Memorial plaques in the Bell Foundry workshop honouring former workers. Cover: Whitechapel Bell Foundry Courtyard, 2016. Photograph by John Claridge. Back Cover: Chains in the Whitechapel Bell Foundry, 2016. Photograph by John Claridge. CONTENTS Overview – Executive Summary 5 Introduction 7 1 A Brief History of the Bell Foundry in Whitechapel 9 2 The Whitechapel Bell Foundry – Summary of the Situation 11 3 The Partners: UKHBPT and Factum Foundation 12 3 . 1 The United Kingdom Historic Building Preservation Trust (UKHBPT) 12 3 . 2 Factum Foundation 13 4 A 21st Century Bell Foundry 15 4 .1 Scanning and Input Methods 19 4 . 2 Output Methods 19 4 . 3 Statements by Participating Foundrymen 21 4 . 3 . 1 Nigel Taylor of WBF – The Future of the Whitechapel Bell Foundry 21 4 . 3 . 2 . Andrew Lacey – Centre for the Study of Historical Casting Techniques 23 4 . 4 Digital Restoration 25 4 . 5 Archive for Campanology 25 4 . 6 Projects for the Whitechapel Bell Foundry 27 5 Architectural Approach 28 5 .1 Architectural Approach to the Resurrection of the Bell Foundry in Whitechapel – Introduction 28 5 . 2 Architects – Practice Profiles: 29 Skene Catling de la Peña 29 Purcell Architects 30 5 .
    [Show full text]
  • About CHANGE RINGING
    All about CHANGE RINGING Provide a pop-up display explaining change-ringing to those attending and visiting the church. Page 6 METHODS RINGING METHODSThe mechanics of a bell It is traditional to start and Theswinging mechanics full-circle of a bell swinging means finish ringing with rounds full-circlethat we meansneed tothat restrict we need its to restrictmove its moveto one to oneposition. position. Not possible: Possible: Possible: Possible: The traditional notation shows each bell as a number starting at ‘1’ for the treble 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 (lightest bell) and running down the numbers to the tenor (heaviest bell). | X | | | | | | X X X | X X X X Bells are usually tuned to the major scale. If there are more than 9 bells, letters 4 8 2Provide 6 7 a1 pop-up 3 5 display 1 3explaining 2 4 5 change-ringi 6 7 8 ng to1 those3 2 attending 5 4 7 and6 8visiting 2the 1 church. 4 3 Page6 5 78 7 The basic method incorporating this rule is called … are substituted, so 0 = 10, E =11, T = 12, A = 13, B = 14, C = 15, D = 16. The1 2 basic3 4 5 6 method 7 8 incorporating this rule is called … X X X X Strokes 2 1Provide 4 3 a6 pop-up 5 8 display7 Now,explaining if change-ringiwe drawng ato linethose attendingjoining and up visiting the the church.
    [Show full text]
  • A Proposed Campanile for Kansas State College
    A PROPOSED CAMPANILE FOR KANSAS STATE COLLEGE by NILES FRANKLIN 1.1ESCH B. S., Kansas State College of Agriculture and Applied Science, 1932 A THESIS submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE KANSAS STATE COLLEGE OF AGRICULTURE AND APPLIED SCIENCE 1932 LV e.(2 1932 Rif7 ii. TABLE OF CONTENTS Page INTRODUCTION 1 THE EARLY HISTORY OF BELLS 3 BELL FOUNDING 4 BELL TUNING 7 THE EARLY HISTORY OF CAMPANILES 16 METHODS OF PLAYING THE CARILLON 19 THE PROPOSED CAMPANILE 25 The Site 25 Designing the Campanile 27 The Proposed Campanile as Submitted By the Author 37 A Model of the Proposed Campanile 44 SUMMARY '47 ACKNOWLEDGMENTS 54 LITERATURE CITED 54 1. INTRODUCTION The purpose of this thesis is to review and formulate the history and information concerning bells and campaniles which will aid in the designing of a campanile suitable for Kansas State College. It is hoped that the showing of a design for such a structure with the accompanying model will further stimulate the interest of both students, faculty members, and others in the ultimate completion of such a project. The design for such a tower began about two years ago when the senior Architectural Design Class, of which I was a member, was given a problem of designing a campanile for the campus. The problem was of great interest to me and became more so when I learned that the problem had been given to the class with the thought in mind that some day a campanile would be built.
    [Show full text]
  • The Bells Were the St
    1989. At the same time some of the bells were The St. Mary’s and St John’s Ringers The Bells reconfigured and the clock mechanism changed to go The Ringers are a joint band for both White Waltham around the wall rather than across the ringing chamber. and Shottesbrooke, a voluntary group under the & leadership of our Tower Captains, and we belong to the Bell Weight Note Date Founder Sonning Deanery Branch of the Oxford Diocesan Guild Bell Ringing Cwt- of Church Bell Ringers, founded in 1881. 1 4-0-0 E 1989 Recast by Whitechapel at The joint band (St Mary’s and St John’s) of bell-ringers 2 4-3-24 D 1989 Recast by Whitechapel is a very friendly group that welcomes new members. St. Mary’s and St John’s As well as our regular weekly practice sessions and 3 5-3-3 C 1989 Recast by Whitechapel ringing for Sunday service, we sometimes arrange an Churches outing to ring at other towers. 4 6-3-1 B 1989 Recast by Whitechapel 5 8-3-25 A 1989 Recast by Whitechapel We ring bells for: Sunday services and Weddings 6 12-0-9 G 1989 Recast by Whitechapel Special celebrations such as Christmas Day and St. John’s and its bells New Year’s Eve The church is set in the grounds of the Shottesbrooke Estate. The six bells are in good working order and are of some Civic occasions such as Remembrance Day antiquity. Three of the bells date from the first half of the 17th century, with the newest (the treble) being added in Practice evening is Friday 7.30 – 9p.m.
    [Show full text]
  • Change Ringing
    G. L. van der Sluijs Change ringing Bachelor thesis, June 7, 2016 Supervisor: dr. M. J. Bright Mathematisch Instituut, Universiteit Leiden Contents Introduction 3 1 Preliminaries 4 1.1 Change ringing terminology . 4 1.2 Words.................................. 7 2 The existence of an extent 8 2.1 Plain changes . 8 2.2 The Cayley graph . 8 2.3 Existence of an extent using only three changes . 10 3 Grandsire Triples 12 3.1 Description and basic properties . 12 3.2 Thompson’s proof . 14 3.3 The largest possible touch . 16 4 Rankin’s campanological theorem 18 4.1 Rankin’s theorem . 18 4.2 Application to Grandsire Triples . 18 4.3 Application to Double Norwich Court Bob Major . 19 5 The existence and construction of extents 21 5.1 Extent existence theorems . 21 5.2 Existence of Plain Bob Major extent with special bob leads . 23 5.3 Extent construction of Plain Bob Doubles . 23 References 26 2 Introduction This bachelor thesis will be concerned with the old English art of ringing church bells called change ringing. The development of change ringing in the early 17th century was mainly due to the invention of the full-circle wheel on which the bells were mounted. By pulling a rope, a bell would make a rotation of almost 360 degrees with a period of approximately two seconds. The time between two strikes of the same bell could be controlled rather accurately, which made it possible to ring a certain number of bells all after each other and keep repeating this in the same order.
    [Show full text]
  • When Were Church Bells First Used? What Is English Change Ringing
    Guildford Diocesan Guild of Church Bell Ringers When were Church Bells first used? How long do bells last? Saxon churches often had round stone towers like St Peter’s, Yaxham. Four of the bells in this tower are 400 years old Where are bells made? Croyland Abbey, in Lincolnshire, had the first known ring of bells tuned to a musical scale over 1,000 years ago! Johanna Sturdy cast this bell in London in 1460. She is 555 years old. She is one of the bells at Stoke D’Abernon and is rung every Sunday. Bell restoration These French Bell-founders are ‘fettling’ one of the new bells recently installed at Notre Dame Cathedral in Paris. What is English Change Ringing? The simplest sort of ringing is ‘Rounds’, where Much more interesting music is created by con- bells are rung continuously down the musical stantly changing the order of the bells. Ringers scale with 1 being the lightest and 8 being the do not use written ‘music’ for this: instead they heaviest bell: learn a pattern which allows the bells to weave between each other, rather like barn-dancing. 1 2 3 4 5 6 7 8 These methods often have quaint names, like: This would be monotonous after a while, but the music can be varied by the conductor, who calls Grandsire bells to change position. Some musical changes are Plain Bob Although bells last a long time, they do need maintenance. A sponsored abseil was part of the money-raising effort at Epsom Queens: Reverse Canterbury Pleasure Bob Doubles 1 3 5 7 2 4 6 8 Tittums: Double Norwich Court Bob Major 1 5 2 6 3 7 4 8 Plain Hunt Minor There are strict rules for ringing and naming Whittingtons: methods, maintained by the Central Council of 1 2 3 4 5 6 Can you see the pattern here? The challenge is to ring all 720 7 5 3 1 2 4 6 8 Church Bell Ringers.
    [Show full text]
  • Grandsire by J
    Grandsire by J. Armiger Trollope File 02: Grandsire Caters, Grandsire Cinques, History, Bibliography – Pages 83 to 130 This document is provided for you by The Whiting Society of Ringers visit www.whitingsociety.org.uk for the full range of publications and articles about bells and change ringing GH.AND8lRE CATERS (i) TilE Nl!'."l'HOD 12345678!J)Mk 1 2 7 5 9 3 8 4 Dodge l J a e 6~ 9 1 3 5 4 7 6 9 8) Thirds. 2 1 7 !) 5 8 3 (l 4 6-7 down. 231456789 271593846 324165870 725139486 3 4 2 6 1 8 5 9 I 752314968 436281957 ;')73241698 46382917i:i 537426189 04839271:3 354762819 084937251 3-i567829l 869,~73521 436587921 8 9 6 7 4 5 3 1 ~}Pass Treble·. -!U3859712 9 8 7 G 5 4 1 3 ~ in 7 -lj. fi48395172 978561423 ti 8 4 9 3 1 5 2 ?}Pass Tt·eble 7958162c!o3 S ll 9 4 1 3 2 5 7 in G-6. 759182634 ~96142375 :)71928364. 981624735 <i1729384H 91821)7453 15273948() 192876543 1 2 5 3 7 4 9 () 8) Dotlge _______I 2 9 7 8 56 3 4lD o d ge 8 9 2 1 57 3 9 4 8 (l J4_-:i down. 2 1 9 8 7 6 5 4 3 - down. 23137496 ... 2 9 1 7 8 5 6 3 4 52314769S 927158364 [)3241678!1 972:513846 3 5 4 2 (l 1 8 7 g 7 9 5 2 3 1 4 8 6 345628197 7:i!l324168 436582917 :i/3942618 463859271 .)37496281 6483957~1 35-1769821 G8493751~ 3 4 5 u 7 8 9 1 2 8 6 9 4 7 3 1 5 2}l'a.<;;; Tr·ebl·· -!3(),)87192 8 9 6 7 4 1 3 2 5 in f.i-7.
    [Show full text]
  • Contents of the Southwell and Nottingham Guild of Church Bellringers Library
    Contents Of The Southwell And Nottingham Guild Of Church Bellringers Library BELLRINGING BOOKS / BELL MUSIC AND OTHER RINGING MEMORABILIA All of this collection is in the ownership of The Southwell and Nottingham Guild of Church Bell Ringers It is located at Saddlers Cottage, Farm Lane, East Markham, NG22 0QH Note: Errors may have been inserted but every effort has been made to be correct. Last Update 18th January 2021 1 CONTENTSU OF THIS LIST ITEMS IN PAPER FORMAT – BOOKS AND LEAFLETS CENTRAL COUNCIL PUBLICATIONS 3 A.R.T. - ASSOCIATION OF RINGING TEACHERS 9 JASPER SNOWDON CHANGE RINGING SERIES 10 SHERBOURNE TEACHING AIDS 11 GENERAL BOOKS ON BELLS 12 LEAFLETS AND/OR ARTICLES FROM BOOKS 19 CHURCH GUIDES, CHURCH BOOKS AND PARISH MAGAZINES 21 RELIGEOUS BOOKS AND NON BELLRINGING 23 NEWSPAPER ARTICLES 24 VARIOUS GUILD AND ASSOCIATION BOOKS 25 DEDICATION OF BELLS SERVICE SHEETS 33 RINGER’S FUNERAL SERVICE SHEETS 33 ITEMS OF NON-BOOK FORMAT GRAMAPHONE RECORDS 8 INCH RECORDS 33 10 INCH 78’s 34 12 INCH 78’s 35 7 INCH 45’s AND 33’s 36 7 INCH BBC SOUND EFFECTS CHURCH BELLS 38 7 INCH BBC SOUND EFFECTS CLOCK BELLS 40 10 INCH 33 1/3rpm RECORDS 42 12 INCH 33 1/3rpm CHURCH BELLS 43 HANDBELLS 44 CARILLON CHURCH BELLS 51 SCHULMERICH ELECTRONIC CARILLON BELLS 54 OTHER VARIOUS TYPES OF BELLS 56 NON RINGING RELIGON 58 COMPACT DISCS BELLS VARIOUS AND COPY OF RECORDS 59 DOCUMENTS – MS WORD AND OTHER FORMATS 69 BOOKS IN PDF FORMAT 70 VHS PAL VIDEO 75 DVD’S 75 CASSETTE TAPES 76 PROJECTOR SLIDES AND LANTERN SLIDES 76 COMPUTER PROGRAMS 77 BELLRINGING MEMORABILIA 78 LIST OF BRITISH TOWER BELLS ON RECORDINGS 81 LIST OF FOREGN BELLS ON RECORDINGS 82 LIST OF HANDBELL TEAMS ON RECORDINGS 84 LIST OF CHURCH BELL CARILLONS ON RECORDINGS 89 LIST OF ELECTRONIC CARILLON BELLS ON RECORDINGS 91 Note: The Whitechepel Foundary closed down in 2018 The Library can be used by all ringers and must be authorised by the Guild Librarian in the first instance.
    [Show full text]
  • Handbell Software for Kalamazoo College Change Ringing Guild
    Handbell Software for Kalamazoo College Change Ringing Guild Marlisa Pennington Supervised by Prof. Pam Cutter of the Computer Science Department. 2016 A paper submitted in partial fulfillment of the requirements for the degree of Bachelor of Arts at Kalamazoo College. Contents Acknowledgments iv Abstract v 1 Introduction 1 2 Changing Ringing 101 1 3 My Project 7 4 Process 10 5 Notable 14 6 Future 16 7 Conclusions 18 A Plain Bob Minor Blueline Figure 19 B Bell Class Code 20 C Method Class Code 23 D Band Class Code 25 E SoundEffect Enum Code 37 F HandbellApp Class Code 40 List of Figures 1 Circle of Work . .6 ii 2 UML Diagram . 13 3 GUI .................................... 15 iii Acknowledgments Great thanks to the entire Kalamazoo College Guild of Change Ringers and especially Margaret Miller and Linda Woodford who have been my teachers from the very beginning and have taught me everything I know about change ringing. Much thanks to Dr. Pam Cutter. I could not have completed the work I have done without her help. Thank you to the entire computer science department, for being such a welcoming environment to learn in. iv Abstract Handbells are a tradition on Kalamazoo Campus that is struggling to maintain enough members. A portion of the cause of this problem is the difficulty in learning handbells when there are not enough experienced ringers available to teach it. In order to minimize any possible lack of teachers, this Senior Individualized Project attempts to write software in java that allows a single ringer to learn handbells with only a computer.
    [Show full text]
  • Swan Bells Foundation Inc
    Swan Bells Foundation Inc. Annual Report 2018-2019 Annual Report 2018-2019 TABLE OF CONTENTS CONTENTS Statement of Compliance ...................................................................................................................................... 2 Overview ................................................................................................................................................................ 3 Executive Summary ........................................................................................................................................... 3 Opeational Structure .............................................................................................................................................. 5 Board Members ..................................................................................................................................................... 6 Senior Officers ................................................................................................................................................... 7 Swan Bells Foundation Inc Organisational Structure 2018-2019 ........................................................................... 8 Performance Management Framework ................................................................................................................. 9 Outcome Based Management Framework ....................................................................................................... 9 Agency Performance ..........................................................................................................................................
    [Show full text]
  • Treble Dodging Minor Methods: Ringing the Cosets, on Six Bells
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Discrete Mathematics 122 (1993) 307-323 307 North-Holland Treble dodging minor methods: ringing the cosets, on six bells Arthur T. White Western Michigan University, Kalamazoo, MI 49008. USA Received 13 July 1992 Ahstruct A general theory is developed to analyze Treble Dodging methods, for change ringing extents, on n=2 (mod4) bells, and then specialized to six bells, by means of Schreier right coset graphs of comparatively low order. The theory is then applied to the eight Treble Bob Minor methods, the six Delight Minor methods, and the fifteen Surprise Minor methods that appear in the book Diagrams. In each case all possible extents of the form [ W(P, B)]” are obtained and exhibited, where P and B denote the plain and bob leads, respectively, and W(P,B) is a word in these two letters. This application is then extended to all 152 Treble Dodging methods appearing in Collection of Minor Methods, Fifth Edition and beyond, to the classification and construction of additional Treble Dodging minor methods, as appearing in Collection of Minor Methods, Sixth Edition and in Treble Dodging Minor Methods. 1. Introduction The aim of this paper is to present a relatively efficient means of analyzing, by the use of Schreier right coset graphs, Treble Dodging methods of change ringing extents. The analysis is particularly simple for Treble Dodging Minor methods, and the general theory is applied to all twenty-nine such appearing in Diagrams [ 12).
    [Show full text]
  • Swan Bells Exhibit Questions Middle Primary School Worksheet Welcome to the Bell Tower! Look Around Or Ask a Guide to Answer the Following Questions
    Swan Bells Exhibit Questions Middle Primary School Worksheet Welcome to the Bell Tower! Look around or ask a guide to answer the following questions. Ground Floor The Royal Ascot Clock was made in 1896 for a famous racecourse in England. What keeps the clock ticking? Electricity, batteries, or gravity? (circle one) Level 1 The bell in front of the lift is the oldest bell in Australia, and is originally from Hampshire, England. When was this bell made? ____1550______ All levels There are many different kinds of bells from all over the world in this building. Name 2 different types of bells and where they come from. ________________________________________________ ANY TWO OF THE BELOW Types of Bells and Their Origins - Bell Tower, Perth, Western Australia Ground Level Tubular bells, from Prestatyn, North Wales and Hardwick, Northamptomshire, England. Level 1 Oldest bell in Australia, from Upton Grey in Hampshire, England. Level 2 Kul kul, from Bali. Camel bell, from Kenya. Swan Bells Exhibit Questions Middle Primary School Worksheet Cup Bells by James Brigeman, from Albourne, England. Crotal bells by Edmin Seller, from York, England. Turret clock and bells, from St. Ethalburga’s church, London, England. Other turret clock and bells, from the South of England. Grandfather clock by John Dent (maker of Big Ben), from London, England. Buddhist bells from Burma. Buddhist hand bells (with no clapper) from Java, Indonesia. Gansadans/Whirling gongs, from Burma. Elephant bells, from India/SE Asia. Hindu bells (aka Ghanta, or Puja), from India. Singing bowls, from Tibet/Nepal/India/Bhutan/China/Japan/Korea. Crotal bell/Tree of Shinto Music bells, from Japan.
    [Show full text]