Cyclic Compositions of "Horton's Four"

Below are listed 2951 compositions of spliced Bristol, London, Belfast (F) and Glasgow Surprise Major. They are 7 part (all the work) compositions consisting of 23 leads per part, giving a total of 5152 changes.

The list is a subset of the compositions possible using this plan. It is restricted to compositions:

  • where there are either 5 or 6 leads of each method per part;
  • no 87s occur at backstroke;
  • 4ths place bobs are the only type of call.
  • Explanation of column headings

  • calling: Each letter represents a lead of a method. '/' means bob.
  • part end: Row at the treble's backstroke lead after first part.
  • calls: Number of bobs per part.
  • crus: Number of crus (combination roll-ups (rows ending xx78 where xx are 4, 5, or 6)).
  • 56s: Number of rows ending 5678.
  • 65s: Number of rows ending 6578.
  • 4runs: Number of rows starting or ending with a run of 4 consecutive bells.
  • music: Number of rows ending 2468, 7468, or 7568.
  • com: Number of changes of method.
  • tt: Number of leads which have 7 and 8 coursing as they would in a plain course.
  • score: A number I calculated to put the compositions in order of how good they might be to ring. The calculation used was: (21 - 'calls') * 5 + 'crus' + '56s' + '65s' + '4runs' + 'music' * 2 + 'com'
  • comment: Which compositions score top for a particular column.
  • callingpart endcallscrus56s65s4runsmusiccomttscorecomment
    B/BL/BG/G/L/FBF/F/FB/G/G/FBFLLG/LG/1782345612291331131811848357 
    BG/BF/FF/GB/LL/BG/FFBFL/B/LG/GGL/134567821024901201411858354 
    B/BL/LG/BF/L/F/FL/G/L/G/F/GG/FBFB/LG/1345678214251411181413243353 
    BG/BFFBF/L/FL/LG/G/F/LL/F/L/B/BG/GB/167823451327126142411253347 
    BL/FL/G/G/BFB/G/LL/L/F/F/G/BG/G/BBFF17823456133782136611163346 
    B/LG/L/FB/G/L/FL/BFBFL/GG/F/L/G/B/B/G/182345671517811141514641346 
    BL/FL/G/G/BFF/G/LL/G/B/B/L/BG/G/BFFF17823456133588131611163345 
    BFFLLG/BB/L/F/L/FLL/GB/G/G/BFF/GB/1782345611201121281011258343 
    LG/LL/BL/BG/B/BL/F/FF/L/F/G/G/BFF/GB/134567821425105146211866343 
    B/BL/BG/G/L/FBF/F/FF/G/G/FBBLLG/LG/1782345612281331131810448342 
    B/LG/L/L/BFF/L/G/B/B/L/BG/FL/G/G/FFB/G1823456715201011331112556341 
    B/L/F/LL/FLL/BG/F/G/FBFFB/LG/BG/GB/145678231224116114712661340 
    BG/BG/G/GL/F/L/BL/FFLL/FFB/L/FB/GB/145678231233125113611954339 
    B/BL/BG/L/FF/F/FFL/GG/FB/G/B/LLG/LG/1345678213251331111811150339 
    B/BG/L/FB/G/FF/LL/BFBFL/GG/LL/BG/G/1678234512191201141511839338 
    B/BG/L/FB/G/FF/LL/BFBFL/GG/LL/GB/G/1678234512161201101512539338 
    BG/BFFBF/FF/LL/GB/GL/L/F/L/B/BG/LG/13456782122679115911854338 
    B/BL/LG/BF/L/F/FL/G/L/G/F/GG/FBBB/LG/1345678214241411181411843338 
    BG/BF/G/LG/BFBLLL/F/G/L/B/G/F/F/L/GB/1567823414231201151013344338 
    BL/FL/G/G/BFF/G/LL/G/BFBL/L/B/G/F/G/B/167823451530128117712661337 
    BL/FL/G/G/BFF/G/LL/G/BFBL/L/F/G/F/G/B/167823451530128117712661337 
    BL/BL/F/FL/FF/GG/FBFL/L/BG/G/BG/GB/167823451230116120611262336 
    BL/BFF/G/G/G/BG/L/L/F/FL/L/FL/B/BG/GB/178234561518121153129850336Most runs of 4
    LLL/BG/FFB/G/G/F/L/F/FL/FBL/GB/GB/B/156782341324132129411864334 
    BL/BFF/G/F/G/BG/L/L/F/FL/L/FL/B/BG/GB/1567823415181121371211250334 
    BL/LL/G/G/BFB/G/LL/L/F/F/G/BG/G/BBFF1782345613378213769763333 
    B/BL/F/FL/L/GGL/B/G/F/G/FL/FBB/LG/BG/1678234514291221101012552333 
    BG/BL/F/L/FFBF/L/BG/L/L/GG/F/L/BG/GB/1678234514271231101012650333 
    LG/L/FB/BG/BBFL/F/F/L/GGL/G/BFF/GB/182345671234116107212578332Most tenors-together
    B/BG/B/B/GB/L/BFF/L/GG/FL/G/LG/L/FFL/167823451422122122712562332 
    B/BL/G/BG/BL/FLL/FF/GL/G/G/L/F/FB/B/G1567823414271511021711847332 
    B/LG/L/L/BFF/L/G/B/B/L/BG/FL/F/G/FFB/G167823451520921171113256332 
    BFF/LL/G/F/GB/LL/FL/BG/B/BL/F/G/F/G/B/167823451523821211112659332 
    BG/BF/G/LG/BFFLLL/F/G/L/B/G/F/F/L/GB/1567823414231201151012644331 
    BG/FF/G/LG/BFBLLL/F/G/L/B/G/F/F/L/GB/1567823414231201151012644331 
    G/F/F/G/LG/L/BF/L/FL/LG/BG/FL/FB/BG/B13456782142345111713950331 
    B/B/BFL/F/GB/LL/F/G/FBFL/G/BG/L/LG/G15678234133914898312565330 
    B/B/BLL/F/GB/LL/F/G/F/FL/G/BG/FB/LG/G134567821438158110311862330 
    L/F/G/B/LL/BF/GB/L/FL/BG/BF/FF/GB/GL/145678231423810107713361330 
    BG/FF/G/BG/L/L/FBL/FL/F/L/G/B/L/BG/GB/145678231523120115813350329 
    BL/LL/G/G/BFF/G/LL/L/F/F/G/BG/G/BBFF1782345613388213769063327 
    F/G/BG/FL/BG/FBF/G/L/B/L/FBL/L/BG/L/F/1345678215338297514756327 
    FL/L/L/G/G/B/L/FL/BFF/G/FB/B/G/FL/G/B/B145678231629421291011857327 
    B/BG/L/FB/G/FF/FL/BFBFL/GG/LL/BG/G/1678234512171001061511839326 
    B/BG/L/FB/G/FF/FL/BFBFL/GG/LL/GB/G/1678234512141001021512539326 
    BG/BG/GB/LL/GG/BF/F/L/FL/B/BF/FFLL/14567823123574121510465326 
    B/BL/F/FL/FB/BG/F/G/B/LG/GL/F/GB/LL/G182345671430152931312552326 
    B/B/G/L/F/FF/F/FB/GB/BG/L/FL/G/B/LG/LG/1345678216201001052411844326 
    BFL/B/LG/BG/L/F/L/F/G/G/B/BG/FF/F/L/GB/182345671622103130512648326 
    B/BL/G/LL/B/L/B/BF/F/L/L/G/F/FF/G/G/B/GG/156782341822132153129750326Most runs of 4
    G/FBFL/FF/F/GG/BB/L/BL/BG/L/L/GB/GL/182345671325107961112540325 
    GB/L/BL/BF/L/GL/BG/BG/F/FFL/G/BG/FL/15678234132023781814651325 
    B/B/BFL/F/GB/LL/F/G/F/FL/G/BG/FB/LG/G13456782143914898312562325 
    B/BG/B/B/GB/L/FFF/L/GG/FL/G/LG/L/FFL/167823451422122122711862325 
    GL/G/BG/FB/L/G/FF/LL/F/G/BL/BL/BF/GB/1456782314228494814654325 
    B/BB/GG/F/GB/GB/BF/G/LL/FLLL/FFFL/15678234112392105199745324 
    BL/FL/G/G/BFF/G/LL/L/F/G/G/B/B/G/BBFF15678234142682133810462324 
    B/B/BFL/F/GB/LL/F/G/FBFL/G/GB/L/LG/G15678234133914898311865323 
    F/LL/GG/FBF/F/L/G/L/G/B/BFLL/B/GB/BG/167823451415901201311838323 
    B/BL/GB/G/F/L/FF/GB/GG/LL/F/L/F/FB/B/G182345671530152120411861323 
    BL/FL/G/F/LL/BF/L/FFB/L/F/G/BG/G/GB/B/1678234515191521101411952323 
    BL/FL/G/G/BFF/G/LL/G/BBBL/L/F/G/F/G/B/167823451530128117711261323 
    B/B/G/L/FFB/L/G/BG/BL/L/G/BG/L/G/FL/F/F1456782316231001031513236323 
    B/LL/BG/L/FF/F/FFBB/GG/FBBLLG/LG/156782341022103101179748322 
    BBLLG/BF/L/FB/G/GGL/BFFL/F/F/L/GB/1823456711201001021411254322 
    B/B/G/G/F/G/F/FLL/FL/BG/FBFBBL/LL/G1456782312221111121011152322 
    BG/BL/BL/LG/BG/FFBF/G/F/FLL/LG/G/B/156782341226106117311259322 
    BL/GB/B/G/L/F/F/G/BBF/L/L/FBF/G/LG/LG/134567821517120971713237322 
    LLG/GL/BFL/F/GB/LL/F/GB/BG/G/BBFF1678234510397299411167321 
    B/B/BLL/F/GB/LL/F/G/FFFL/G/GB/L/BG/G156782341338158110310465321 
    BFFBB/G/B/G/F/L/LG/GB/L/FL/F/FLL/GB/182345671324112120611258321 
    BG/BG/G/G/FL/LL/FF/FL/GL/FB/L/FB/GB/156782341327125852011245321 
    BL/G/FB/BG/BG/FF/FL/L/GG/L/F/FBL/GB/134567821319111982011238321 
    L/G/B/G/F/FFLLG/BF/GB/BG/FL/FL/L/GB/17823456131776901812547321 
    G/F/F/G/BG/L/L/L/FFB/LG/BG/FL/FB/BG/B13456782142445120412550321 
    F/LL/G/BG/FB/B/L/FFB/G/L/BL/G/F/FL/BG/13456782151694882113247321 
    B/G/GB/BBFLLL/FL/G/GG/FL/G/B/BFFF1567823410278312759064320 
    LG/L/FB/BG/FBF/G/BFBFLL/G/F/LL/GB/13456782111995721313959320 
    G/F/F/G/BG/L/L/L/FBB/LG/BG/FL/FB/LG/B13456782142445112413250320 
    G/F/F/G/BG/L/L/L/FFB/LG/BG/FL/FB/LG/B13456782142445112413250320 
    G/F/F/G/LG/L/BF/L/FBB/LG/BG/FL/L/BG/B13456782142745102413951320 
    L/BG/G/L/GL/F/L/FL/B/BF/GB/L/G/B/BFFF145678231415321121412556320 
    B/BG/FB/L/G/L/BL/G/F/FL/FL/BG/FL/BG/G/167823451519100114413945320 
    B/BG/FB/L/G/L/FL/G/F/FL/FL/BG/FL/BG/G/167823451519100114413945320 
    L/F/GG/L/B/G/F/L/L/BG/GB/B/BL/FL/FF/GB/17823456162281130811849320 
    L/F/GG/L/F/G/F/L/L/BG/GB/B/BL/FL/FF/GB/17823456162281130811849320 
    B/BL/FB/L/LL/G/FBBF/GG/LL/F/G/FFB/G156782341226152108611147319 
    GB/BFFBF/L/FL/LG/G/F/LL/F/L/B/BG/GB/16782345132876121311153319 
    B/G/FBFB/G/LG/L/FB/L/FBB/G/F/F/L/GGL/17823456142280951013944319 
    BG/FF/G/LG/G/L/FBFLL/B/BB/G/F/F/L/GB/1567823414241201121211246319 
    BL/FL/F/LLL/BG/FBF/L/G/GG/FBFB/GB/16782345113111191412651318 
    LG/LL/BL/G/BFF/G/G/BFFB/G/F/FL/B/G/B/16782345141985108912556318 
    B/B/G/L/FFB/BL/G/F/GL/G/G/B/LG/BFF/LL/1678234515201001041811842318 
    BL/FL/GL/BG/FF/G/B/G/L/F/FF/L/BG/GB/B/167823451534150981111951318 
    LLG/GL/BFL/F/GB/LL/F/GB/BG/G/BFFF1678234510397295411167317 
    GL/BFFBFF/GB/BBF/L/F/G/L/B/LG/GGL/13456782112183105611857317 
    BG/BFFBF/FF/LL/GB/GL/L/F/L/B/LG/BG/13456782122969831012554317 
    F/F/GB/BBBFBL/FL/G/F/L/BL/L/LG/G/GG/15678234132490119149756317 
    BG/FFF/F/L/F/L/GB/L/BFL/BL/G/G/BG/GB/167823451425126108611947317 
    BL/LL/G/G/BFB/G/LL/L/F/G/G/F/F/G/BBFF1567823414258213489762317 
    B/BG/L/L/GL/BG/BG/L/BF/F/FF/F/G/L/BF/G1823456715241231081111840317 
    B/G/GB/BBLLLL/FL/G/GG/FL/G/B/BFFF1567823410268313158364316 
    LLG/GL/BFL/B/GB/LL/F/GB/BG/G/BFFF1678234510387196411167316 
    B/BL/LG/BFFLL/L/FBL/F/GG/FBF/GB/G/178234561124121911011840316 
    BFL/L/BL/BG/BG/FF/FF/GB/G/F/LL/GGL/16782345121872921711859316 
    F/FL/L/GB/GGL/BG/BF/L/B/BL/G/G/FFBF1567823412151001101211229316 
    B/B/BFL/F/GB/LL/F/G/FFFL/G/GB/L/BG/G15678234133914898311165316 
    BG/BF/FB/BG/F/FLL/FL/B/L/G/FL/GB/GL/13456782133015091413260316 
    F/G/GB/LL/GL/LG/BF/L/BFF/F/L/GB/BG/B134567821321441051211848316 
    GB/L/G/G/BL/F/FBL/BG/L/FBFFL/GB/G/F/18234567132542841113955316 
    B/BL/G/L/LG/B/BFF/FL/G/FFFB/GL/G/B/L/1567823414241231051311148316 
    B/LL/BG/F/L/BF/G/G/BG/BL/GL/BG/FL/F/F15678234142890791313945316 
    BG/BFB/LL/LG/BG/F/FFL/L/F/F/L/G/GB/B/18234567142616313049851316Most 56s
    FL/G/FBBL/BL/BF/L/GB/G/L/F/G/F/FL/BG/1567823414188489814646316 
    B/BG/L/L/GL/BG/BG/L/BF/F/FF/F/G/L/FB/G1823456715231231081111840316 
    F/G/BG/FL/BG/BFF/G/L/B/L/FBL/L/BG/L/F/1345678215338291614056316 
    B/BL/F/FL/FFB/L/G/F/LL/FL/G/G/B/G/B/B/G1782345616241401071411836316 
    B/LG/L/FB/G/FF/FL/BFBFL/GG/LL/BG/G/16782345121470941512539315 
    B/LG/L/FB/G/FF/FL/BFBFL/GG/LL/GB/G/16782345121170901513239315 
    G/FBFL/FF/F/GG/L/L/BL/BG/BF/L/GB/GL/182345671321103871113240315 
    G/L/B/G/F/LL/FFBFL/B/LG/BL/G/G/BFB/G18234567131841891513350315 
    G/L/F/G/B/LL/FFBFL/B/LG/BL/G/G/BFB/G18234567131841891513350315 
    G/L/F/G/F/LL/FFBFL/B/LG/BL/G/G/BFB/G18234567131841891513350315 
    FL/GG/FL/GL/L/BG/F/G/F/L/FB/G/BB/L/BB15678234141746812013235315 
    B/B/G/F/F/G/F/G/BG/L/L/F/FL/L/FL/B/BG/LG/156782341821102131911854315 
    BFLLG/L/FB/BB/G/GGL/BFFL/F/F/L/GB/1823456711201001031310554314 
    BG/FBF/F/FFLL/L/F/GB/LG/L/G/BG/L/GB/14567823133812984611962314 
    F/LL/GG/FBF/F/L/G/L/G/B/BFLL/F/GB/BG/167823451415901111311838314 
    LG/LL/BL/G/BFF/G/G/BFFB/G/F/LL/F/G/B/16782345141985108712556314 
    BL/FFB/G/F/LL/L/L/FFB/L/F/G/BG/G/GB/B/167823451520162122139849314Most 56s
    FL/L/BB/G/G/B/L/FL/BFF/G/FL/BB/LG/G/F/156782341524721191011248314 
    G/L/B/G/F/FL/FFBFL/B/LG/BL/G/G/BFB/G18234567131841891413350313 
    B/BG/L/L/BFB/G/GG/L/F/FF/L/GB/L/BFF/G178234561419132991711136313 
    B/G/BG/F/FLL/FLL/L/FBF/G/B/G/BG/L/GB/178234561426110101712662313 
    BF/GB/G/L/G/BG/FB/L/LG/BFFB/G/F/F/L/L/18234567152062107813256313 
    BL/FF/FB/G/G/BL/L/FB/G/L/G/B/L/FL/G/GB/1678234516191101191011943313 
    BL/FF/FB/G/G/BL/L/FB/G/L/G/F/L/FL/G/GB/1678234516191101191011943313 
    F/G/GB/GL/BBFL/LG/L/G/FBFLL/FFBB145678239174295811844312 
    BL/G/L/G/F/F/L/GB/GB/BLL/BFFFBF/GG/13456782121452842211844312 
    F/FL/BF/GB/GGL/BG/L/L/B/BL/G/G/FFBF1567823412151001101011229312 
    GB/L/G/BG/L/FL/FFF/L/G/BG/BFFBL/GB/16782345121871781213951312 
    GB/L/G/BG/L/FL/FFF/L/G/GB/BFFBL/GB/16782345121871821712551312 
    LG/BL/BL/BG/BG/FFBF/G/F/FLL/LG/G/B/15678234122376100312559312 
    BL/G/LL/LG/BL/FBFF/G/B/G/G/FL/BF/GB/17823456132911484912657312 
    BL/G/LL/LG/BL/FFBF/G/B/G/G/FL/BF/GB/17823456133011483912657312 
    B/BG/B/B/GB/L/FFF/L/GG/LL/F/GB/L/FFL/145678231424112115711162312 
    B/LL/G/BB/L/FL/G/BG/FL/FB/G/F/FFL/BG/1456782314269292813258312 
    B/LL/GB/LG/GB/BL/F/F/L/G/FL/F/G/BFB/G18234567143111291513246312 
    LG/LL/BL/G/BFF/G/G/BFFB/G/F/LL/B/G/B/16782345141985108612556312 
    G/FBF/FBB/BG/FL/F/LLL/BFL/LG/G/GB/156782341116701041510443311 
    L/F/GG/L/FFBFBL/G/LLG/BL/G/FB/BG/B1456782311196086913247311 
    B/L/BG/GB/L/FF/GG/FB/L/G/FBF/G/L/BLL/18234567142375105213252311 
    B/LL/BG/B/L/BF/G/G/BF/F/FFB/LG/LG/LG/17823456143110989612552311 
    B/LL/BG/F/L/BF/G/G/BF/F/FBB/LG/LG/LG/17823456143110991512552311 
    B/LL/BG/F/L/BF/G/G/BF/F/FFB/LG/LG/LG/17823456143110989612552311 
    BL/FL/F/FL/L/GL/BFFB/L/F/G/BG/G/GB/B/145678231428150951311245311 
    BL/LL/G/G/BFF/G/LL/L/F/G/G/B/B/G/BBFF1567823414268213489062311 
    G/F/F/G/BG/L/L/L/FFB/BG/BG/FL/FB/LG/B13456782142645108412550311 
    GB/LL/FL/G/F/FL/FB/G/L/L/GG/FFB/GB/B/145678231427124109311859311 
    BL/L/FB/L/GB/G/F/LL/F/G/G/L/F/FBFB/GB/134567821525111961112650311 
    L/GB/G/FL/B/GB/BG/BFBFF/FL/LLG/LG/16782345113333721212564310 
    B/BL/G/GB/G/G/BG/FB/LLL/BF/G/F/FF/LL/156782341425145951610441310 
    F/L/BG/GB/L/BF/GG/FB/L/G/FBF/G/L/BLL/1823456714226599213952310 
    FL/L/GB/L/B/GG/L/B/G/BL/F/FFBL/BG/FF/16782345142576108511964310 
    GB/LL/BL/G/F/FL/FB/G/L/L/GG/FFB/GB/B/145678231427124108311859310 
    L/B/G/FF/G/BL/L/L/FL/BG/BL/G/G/BFF/GB/13456782151982112712551310 
    L/B/G/L/G/BL/L/L/FL/BG/BFF/G/G/BFF/GB/13456782152182112612550310 
    L/F/G/F/G/B/LG/L/L/FB/BFB/G/BG/F/LL/GB/16782345161872105713959310 
    FL/BB/GB/GL/GGL/BBL/BFL/GL/G/F/FF/13456782111773891211953309 
    B/BF/G/F/FLLG/BBFLL/G/B/BF/F/L/GGL/178234561235124103310460309 
    B/LG/L/FB/G/FF/FL/BBBFL/GG/FL/BG/G/16782345121670931511839309 
    B/LG/L/FB/G/FF/FL/BBBFL/GG/FL/GB/G/16782345121370891512539309 
    BG/FL/FFB/LG/BG/FF/L/L/FBLL/BG/G/B/134567821224103100411957309 
    F/FL/G/BBFB/GB/LG/BG/LL/G/FFB/GL/L/182345671219100881112545309 
    FL/FL/LG/G/B/G/B/LG/BL/GL/BG/BF/FFB15678234122352761313256309 
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    FL/B/B/L/F/L/BG/L/F/F/L/GG/B/BG/LG/BG/F/13456782171473891912643297 
    BFFL/G/B/LG/GB/BBFLL/FF/FL/GG/GB/14567823102511310159164296 
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    G/F/F/G/LG/L/L/L/FBB/BG/BG/FL/FB/LG/B1345678214294588512550296 
    G/F/GL/G/B/GB/BFBL/G/FB/L/L/FFF/L/LG/14567823141763104611945296 
    G/FL/L/BG/L/G/BF/FB/L/G/F/G/BG/FBBLL/17823456141721791513242296 
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    B/G/L/FFB/L/GGL/G/BL/BG/BF/F/FF/G/B/L/16782345151852921212559296 
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    F/L/G/F/L/G/L/B/LG/BF/G/BFBF/G/B/G/L/BF/18234567172570631315440295Most changes of method
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    L/GB/G/FL/BL/BG/FF/F/FB/LG/B/BF/G/LL/17823456141631682611946294 
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