{"text_format":"3","workbook":"xlsx","n_sheets":6,"sheets":["Chart","Data","Yerms","Rules","Zoom","Labels"],"not_rendered":{"charts":1,"macros":1,"defined_names":19},"read":"whole","date_system":"1900"}

{"sheet":"Chart","index":0,"n_rows":19,"n_cols":17,"rows_kept":19}
[{"$f":"MPC&\"-Month, \"&Yerms&\"-Yerm Lunar Cycle Jitter\"","v":"49-Month, 3-Yerm Lunar Cycle Jitter"}]
[{"$f":"\"Cycle contains \"&MPC&\" months (\"&FMPC&\" full, \"&DMPC&\" deficient) = \"&DPC&\" days = \"&reducefraction(DPC,7,FALSE,FALSE,TRUE)&\" weeks = \"&Yerms&\" yerms.\"","v":"Cycle contains 49 months (26 full, 23 deficient) = 1447 days = 206+5/7 weeks = 3 yerms."}]
[{"$f":"\"Mean month = \"&\"29+\"&reducefraction(FMPC,MPC,FALSE,FALSE,TRUE)&\" days = 29d 12h 44m \"&reducefraction(240*(360*FMPC-191*MPC),MPC,FALSE,FALSE,TRUE)&\" seconds, or about 29\"&MID(FMPC/MPC,2,20)&\" days or 29d 12h 44m \"&ROUND(240*(360*FMPC-191*MPC)/MPC,6)&\" seconds.\"","v":"Mean month = 29+26/49 days = 29d 12h 44m 4+44/49 seconds, or about 29.530612244897959 days or 29d 12h 44m 4.897959 seconds."}]
[{"$f":"\"Duration per ''Part'' = 1/\"&MPC&\" day = \"&reducefraction(24,MPC,FALSE,FALSE,TRUE)&\" hour = \"&reducefraction(1440,MPC,FALSE,FALSE,TRUE)&\" minutes = \"&reducefraction(86400,MPC,FALSE,FALSE,TRUE)&\" seconds.  One hour = \"&reducefraction(MPC,24,FALSE,FALSE,TRUE)&\" parts.\"","v":"Duration per ''Part'' = 1/49 day = 24/49 hour = 29+19/49 minutes = 1763+13/49 seconds.  One hour = 2+1/24 parts."}]
[]
[]
[]
[]
[{"$nulls":16},false]
[]
[]
[]
[]
[]
[{"$nulls":16},1]
[{"$nulls":16},"Selected"]
[{"$nulls":16},"Month"]
[{"$nulls":16},"in Yerm"]
[{"$nulls":16},"(1 to 17)"]

{"sheet":"Data","index":1,"n_rows":135,"n_cols":8,"rows_kept":135}
["Lunar Cycle Jitter Evaluator"]
["by Dr. Irv Bromberg, University of Toronto, Canada"]
["http://individual.utoronto.ca/intervalmath/jitter/index.html",null,null,"Jitter","(parts)"]
[{"$nulls":3},{"$f":"MAX(H:H)","v":25},"maximum",{"$f":"reducefraction(JitterMax*MPC,MPC,FALSE,FALSE,FALSE)","v":"25"}]
["Months per Cycle (Parts per Day):",49,"months (parts)",{"$f":"MIN(H:H)","v":-23},"minimum",{"$f":"reducefraction(JitterMin*MPC,MPC,FALSE,FALSE,FALSE)","v":"–(23)"}]
["30-day Months per Cycle:",26,"months",{"$f":"D4-D5","v":48},"range",{"$f":"reducefraction(JitterRange*MPC,MPC,FALSE,FALSE,FALSE)","v":"48"}]
["29-day Months per Cycle:",{"$f":"MPC-FMPC","v":23},"months",{"$f":"\"Jitter range = \"&F6&\" parts = \"&reducefraction(F6*24,MPC,FALSE,FALSE,FALSE)&\" hours\"","v":"Jitter range = 48 parts = 23 + 25 / 49 hours"}]
["Days per Cycle (Parts per Month):",{"$f":"29*MPC+FMPC","v":1447},"days (parts)"]
["Yerms per Cycle:",{"$f":"2*DPC-59*MPC","v":3},"yerms","Limits for Chart:"]
["Mean Month:",{"$f":"\"29 + \"&reducefraction(FMPC,MPC,FALSE,FALSE,FALSE)","v":"29 + 26 / 49"},"days","x","y","Hours"]
["Mean Month >29d:",{"$f":"FMPC/MPC","v":{"v":0.5306122448979592,"d":"0.530612244897959"}},"days",{"$f":"C21","v":1},{"$f":"JitterMax","v":25},{"$f":"E11*24/MPC","v":12.244897959183673}]
["Mean Month >29d 12h 44m:",{"$f":"reducefraction(240*(360*FMPC-191*MPC),MPC,FALSE,FALSE,TRUE)","v":"4+44/49"},"seconds",{"$f":"2*MPC+1","v":99},{"$f":"E11","v":25},{"$f":"E12*24/MPC","v":12.244897959183673}]
["… or approximately:",{"$f":"240*(360*FMPC-191*MPC)/MPC","v":4.8979591836734695},"seconds"]
["Has Yerm Zero:",{"$f":"MeanMonth>26/49","v":false},null,{"$f":"D11","v":1},0]
["17-month Yerms per Cycle:",{"$f":"443*MPC-15*DPC","v":2},"yerms",{"$f":"D12","v":99},0]
["15-month Yerms per Cycle:",{"$f":"Yerms-n17my","v":1},"yerms"]
["49-month subcycles:",{"$f":"INT(Yerms/3)","v":1},null,{"$f":"C21","v":1},{"$f":"JitterMin","v":-23},{"$f":"E17*24/MPC","v":-11.26530612244898}]
["Duration per Part:",{"$f":"reducefraction(1440,MPC,FALSE,FALSE,FALSE)","v":"29 + 19 / 49"},"minutes",{"$f":"D12","v":99},{"$f":"E17","v":-23},{"$f":"E18*24/MPC","v":-11.26530612244898}]
[]
["Yerm in Cycle","Months in Yerm","Month #","Month in Yerm","Month Length","New Month Moment","Elapsed","Difference"]
[1,{"$f":"IF(MOD(A21,3)=0,15,17)","v":17},1,1,{"$f":"IF(MOD(D21,2)=1,30,29)","v":30},0,0,{"$f":"F21-G21","v":0}]
[{"$f":"IF(D22=1,IF(A21=Yerms,1,A21+1),A21)","v":1},{"$f":"IF(MOD(A22,3)=0,15,17)","v":17},{"$f":"C21+1","v":2},{"$f":"IF(D21=B21,1,D21+1)","v":2},{"$f":"IF(MOD(D22,2)=1,30,29)","v":29},{"$f":"F21+PPM","v":1447},{"$f":"G21+E21*PPD","v":1470},-23]
[1,17,{"$f":"C22+1","v":3},3,30,{"$f":"F22+PPM","v":2894},2891,3]
[1,17,4,4,29,4341,4361,-20]
[1,17,5,5,30,5788,5782,6]
[1,17,6,6,29,7235,7252,-17]
[1,17,7,7,30,8682,8673,9]
[1,17,8,8,29,10129,10143,-14]
[1,17,9,9,30,11576,11564,12]
[1,17,10,10,29,13023,13034,-11]
[1,17,11,11,30,14470,14455,15]
[1,17,12,12,29,15917,15925,-8]
[1,17,13,13,30,17364,17346,18]
[1,17,14,14,29,18811,18816,-5]
[1,17,15,15,30,20258,20237,21]
[1,17,16,16,29,21705,21707,-2]
[1,{"$f":"IF(MOD(A37,3)=0,15,17)","v":17},17,17,30,23152,23128,24]
[2,17,18,1,30,24599,24598,1]
[2,17,19,2,29,26046,26068,-22]
[2,17,20,3,30,27493,27489,4]
[2,17,21,4,29,28940,28959,-19]
[2,17,22,5,30,30387,30380,7]
[2,17,23,6,29,31834,31850,-16]
[2,17,24,7,30,33281,33271,10]
[2,17,25,8,29,34728,34741,-13]
[2,17,26,9,30,36175,36162,13]
[2,17,27,10,29,37622,37632,-10]
[2,17,28,11,30,39069,39053,16]
[2,17,29,12,29,40516,40523,-7]
[2,17,30,13,30,41963,41944,19]
[2,17,31,14,29,43410,43414,-4]
[2,17,32,15,30,44857,44835,22]
[2,17,33,16,29,46304,46305,-1]
[2,17,34,17,30,47751,47726,25]
[3,15,35,1,30,49198,49196,2]
[3,15,36,2,29,50645,50666,-21]
[3,15,37,3,30,52092,52087,5]
[3,15,38,4,29,53539,53557,-18]
[3,15,39,5,30,54986,54978,8]
[3,15,40,6,29,56433,56448,-15]
[3,15,41,7,30,57880,57869,11]
[3,15,42,8,29,59327,59339,-12]
[3,15,43,9,30,60774,60760,14]
[3,15,44,10,29,62221,62230,-9]
[3,15,45,11,30,63668,63651,17]
[3,15,46,12,29,65115,65121,-6]
[3,15,47,13,30,66562,66542,20]
[3,15,48,14,29,68009,68012,-3]
[3,15,49,15,30,69456,69433,23]
[1,17,50,1,30,70903,70903,0]
[1,17,51,2,29,72350,72373,-23]
[1,17,52,3,30,73797,73794,3]
[1,17,53,4,29,75244,75264,-20]
[1,17,54,5,30,76691,76685,6]
[1,17,55,6,29,78138,78155,-17]
[1,17,56,7,30,79585,79576,9]
[1,17,57,8,29,81032,81046,-14]
[1,17,58,9,30,82479,82467,12]
[1,17,59,10,29,83926,83937,-11]
[1,17,60,11,30,85373,85358,15]
[1,17,61,12,29,86820,86828,-8]
[1,17,62,13,30,88267,88249,18]
[1,17,63,14,29,89714,89719,-5]
[1,17,64,15,30,91161,91140,21]
[1,17,65,16,29,92608,92610,{"$f":"F85-G85","v":-2}]
[{"$f":"IF(D86=1,IF(A85=Yerms,1,A85+1),A85)","v":1},{"$f":"IF(MOD(A86,3)=0,15,17)","v":17},66,{"$f":"IF(D85=B85,1,D85+1)","v":17},{"$f":"IF(MOD(D86,2)=1,30,29)","v":30},94055,{"$f":"G85+E85*PPD","v":94031},24]
[2,17,{"$f":"C86+1","v":67},1,30,{"$f":"F86+PPM","v":95502},95501,1]
[2,17,68,2,29,96949,96971,-22]
[2,17,69,3,30,98396,98392,4]
[2,17,70,4,29,99843,99862,-19]
[2,17,71,5,30,101290,101283,7]
[2,17,72,6,29,102737,102753,-16]
[2,17,73,7,30,104184,104174,10]
[2,17,74,8,29,105631,105644,-13]
[2,17,75,9,30,107078,107065,13]
[2,17,76,10,29,108525,108535,-10]
[2,17,77,11,30,109972,109956,16]
[2,17,78,12,29,111419,111426,-7]
[2,17,79,13,30,112866,112847,19]
[2,17,80,14,29,114313,114317,-4]
[2,17,81,15,30,115760,115738,22]
[2,17,82,16,29,117207,117208,-1]
[2,17,83,17,30,118654,118629,25]
[3,15,84,1,30,120101,120099,2]
[3,15,85,2,29,121548,121569,-21]
[3,15,86,3,30,122995,122990,5]
[3,15,87,4,29,124442,124460,-18]
[3,15,88,5,30,125889,125881,8]
[3,15,89,6,29,127336,127351,-15]
[3,15,90,7,30,128783,128772,11]
[3,15,91,8,29,130230,130242,-12]
[3,15,92,9,30,131677,131663,14]
[3,15,93,10,29,133124,133133,-9]
[3,15,94,11,30,134571,134554,17]
[3,15,95,12,29,136018,136024,-6]
[3,15,96,13,30,137465,137445,20]
[3,15,97,14,29,138912,138915,-3]
[3,15,98,15,30,140359,140336,23]
[1,17,99,1,30,141806,141806,0]
[1,17,100,2,29,143253,143276,-23]
[1,17,101,3,30,144700,144697,3]
[1,17,102,4,29,146147,146167,-20]
[1,17,103,5,30,147594,147588,6]
[1,17,104,6,29,149041,149058,-17]
[1,17,105,7,30,150488,150479,9]
[1,17,106,8,29,151935,151949,-14]
[1,17,107,9,30,153382,153370,12]
[1,17,108,10,29,154829,154840,-11]
[1,17,109,11,30,156276,156261,15]
[1,17,110,12,29,157723,157731,-8]
[1,17,111,13,30,159170,159152,18]
[1,17,112,14,29,160617,160622,-5]
[1,17,113,15,30,162064,162043,21]
[1,17,114,16,29,163511,163513,-2]
[1,17,115,17,30,164958,164934,24]

{"sheet":"Yerms","index":2,"n_rows":46,"n_cols":7,"rows_kept":46}
["Month in Cycle","Yerm","New Yerm Moment","Elapsed","Difference","Top","Yerm Start"]
[{"$f":"StartMonth","v":1},1,{"$f":"(A2-1)*PPM","v":0},{"$f":"LOOKUP(A2,Data!C$21:C$135,Data!G$21:G$135)","v":0},{"$f":"IF(AND(StartMonth>15,MOD(B2,3)=0),NA(),C2-D2)","v":0},100,{"$f":"A2-StartMonth+1","v":1}]
[{"$f":"A2+IF(MOD(B2,3)=0,15,17)","v":18},{"$f":"MOD(B2,Yerms)+1","v":2},{"$f":"(A3-1)*PPM","v":24599},{"$f":"LOOKUP(A3,Data!C$21:C$135,Data!G$21:G$135)","v":24598},1,{"$f":"F2","v":100},18]
[{"$f":"A3+IF(MOD(B3,3)=0,15,17)","v":35},{"$f":"MOD(B3,Yerms)+1","v":3},{"$f":"(A4-1)*PPM","v":49198},{"$f":"LOOKUP(A4,Data!C$21:C$135,Data!G$21:G$135)","v":49196},2,{"$f":"F3","v":100},35]
[50,1,70903,{"$f":"LOOKUP(A5,Data!C$21:C$135,Data!G$21:G$135)","v":70903},0,100,50]
[67,2,95502,{"$f":"LOOKUP(A6,Data!C$21:C$135,Data!G$21:G$135)","v":95501},1,100,67]
[84,3,120101,{"$f":"LOOKUP(A7,Data!C$21:C$135,Data!G$21:G$135)","v":120099},2,100,84]
[99,1,141806,{"$f":"LOOKUP(A8,Data!C$21:C$135,Data!G$21:G$135)","v":141806},0,100,99]
[116,2,166405,{"$f":"LOOKUP(A9,Data!C$21:C$135,Data!G$21:G$135)","v":164934},1471,100,116]
[133,3,191004,{"$f":"LOOKUP(A10,Data!C$21:C$135,Data!G$21:G$135)","v":164934},26070,100,133]
[148,1,212709,{"$f":"LOOKUP(A11,Data!C$21:C$135,Data!G$21:G$135)","v":164934},47775,100,148]
[165,2,237308,{"$f":"LOOKUP(A12,Data!C$21:C$135,Data!G$21:G$135)","v":164934},72374,100,165]
[182,3,261907,{"$f":"LOOKUP(A13,Data!C$21:C$135,Data!G$21:G$135)","v":164934},96973,100,182]
[197,1,283612,{"$f":"LOOKUP(A14,Data!C$21:C$135,Data!G$21:G$135)","v":164934},118678,100,197]
[214,2,308211,{"$f":"LOOKUP(A15,Data!C$21:C$135,Data!G$21:G$135)","v":164934},143277,100,214]
[231,3,332810,{"$f":"LOOKUP(A16,Data!C$21:C$135,Data!G$21:G$135)","v":164934},167876,100,231]
[246,1,354515,{"$f":"LOOKUP(A17,Data!C$21:C$135,Data!G$21:G$135)","v":164934},189581,100,246]
[263,2,379114,{"$f":"LOOKUP(A18,Data!C$21:C$135,Data!G$21:G$135)","v":164934},214180,100,263]
[280,3,403713,{"$f":"LOOKUP(A19,Data!C$21:C$135,Data!G$21:G$135)","v":164934},238779,100,280]
[295,1,425418,{"$f":"LOOKUP(A20,Data!C$21:C$135,Data!G$21:G$135)","v":164934},260484,100,295]
[312,2,450017,{"$f":"LOOKUP(A21,Data!C$21:C$135,Data!G$21:G$135)","v":164934},285083,100,312]
[329,3,474616,{"$f":"LOOKUP(A22,Data!C$21:C$135,Data!G$21:G$135)","v":164934},309682,100,329]
[344,1,496321,{"$f":"LOOKUP(A23,Data!C$21:C$135,Data!G$21:G$135)","v":164934},331387,100,344]
[{"$f":"A23+IF(MOD(B23,3)=0,15,17)","v":361},{"$f":"MOD(B23,Yerms)+1","v":2},{"$f":"(A24-1)*PPM","v":520920},{"$f":"LOOKUP(A24,Data!C$21:C$135,Data!G$21:G$135)","v":164934},355986,{"$f":"F23","v":100},{"$f":"A24-StartMonth+1","v":361}]
[378,3,545519,{"$f":"LOOKUP(A25,Data!C$21:C$135,Data!G$21:G$135)","v":164934},380585,100,378]
[393,1,567224,{"$f":"LOOKUP(A26,Data!C$21:C$135,Data!G$21:G$135)","v":164934},402290,100,393]
[410,2,591823,{"$f":"LOOKUP(A27,Data!C$21:C$135,Data!G$21:G$135)","v":164934},426889,100,410]
[427,3,616422,{"$f":"LOOKUP(A28,Data!C$21:C$135,Data!G$21:G$135)","v":164934},451488,100,427]
[442,1,638127,{"$f":"LOOKUP(A29,Data!C$21:C$135,Data!G$21:G$135)","v":164934},473193,100,442]
[459,2,662726,{"$f":"LOOKUP(A30,Data!C$21:C$135,Data!G$21:G$135)","v":164934},497792,100,459]
[476,3,687325,{"$f":"LOOKUP(A31,Data!C$21:C$135,Data!G$21:G$135)","v":164934},522391,100,476]
[491,1,709030,{"$f":"LOOKUP(A32,Data!C$21:C$135,Data!G$21:G$135)","v":164934},544096,100,491]
[508,2,733629,{"$f":"LOOKUP(A33,Data!C$21:C$135,Data!G$21:G$135)","v":164934},568695,100,508]
[525,3,758228,{"$f":"LOOKUP(A34,Data!C$21:C$135,Data!G$21:G$135)","v":164934},{"$f":"IF(AND(StartMonth>15,MOD(B34,3)=0),NA(),C34-D34)","v":593294},100,525]
[540,1,779933,{"$f":"LOOKUP(A35,Data!C$21:C$135,Data!G$21:G$135)","v":164934},614999,100,540]
[557,2,804532,{"$f":"LOOKUP(A36,Data!C$21:C$135,Data!G$21:G$135)","v":164934},639598,100,557]
[574,3,829131,{"$f":"LOOKUP(A37,Data!C$21:C$135,Data!G$21:G$135)","v":164934},664197,100,574]
[589,1,850836,{"$f":"LOOKUP(A38,Data!C$21:C$135,Data!G$21:G$135)","v":164934},685902,100,589]
[606,2,875435,{"$f":"LOOKUP(A39,Data!C$21:C$135,Data!G$21:G$135)","v":164934},710501,100,606]
[623,3,900034,{"$f":"LOOKUP(A40,Data!C$21:C$135,Data!G$21:G$135)","v":164934},735100,100,623]
[638,1,921739,{"$f":"LOOKUP(A41,Data!C$21:C$135,Data!G$21:G$135)","v":164934},756805,100,638]
[655,2,946338,{"$f":"LOOKUP(A42,Data!C$21:C$135,Data!G$21:G$135)","v":164934},781404,100,655]
[672,3,970937,{"$f":"LOOKUP(A43,Data!C$21:C$135,Data!G$21:G$135)","v":164934},806003,100,672]
[687,1,992642,{"$f":"LOOKUP(A44,Data!C$21:C$135,Data!G$21:G$135)","v":164934},827708,100,687]
[704,2,1017241,{"$f":"LOOKUP(A45,Data!C$21:C$135,Data!G$21:G$135)","v":164934},852307,100,704]
[721,3,1041840,{"$f":"LOOKUP(A46,Data!C$21:C$135,Data!G$21:G$135)","v":164934},876906,100,721]

{"sheet":"Rules","index":3,"n_rows":11,"n_cols":3,"rows_kept":11}
["odd-numbered months have 30 days, even numbered months have 29 days"]
["yerms have 17 months (9 full, 8 deficient) or 15 months (8 full, 7 deficient)"]
["length of 17-month yerm =",{"$f":"(9*30)+(8*29)","v":502},"days"]
["length of 15-month yerm =",{"$f":"(8*30)+(7*29)","v":443},"days"]
["yerms are numbered from yerm #1"]
["if yerm# is divisible by 3 then it has 15 months, otherwise it has 17 months"]
["repeating pattern = 17+17+15 = ",{"$f":"17+17+15","v":49},"months"]
["which is repeated",{"$f":"INT(MPC/B7)","v":1},"times"]
["to make a subtotal of",{"$f":"3*B8","v":3},"yerms"]
["full cycle has",{"$f":"Yerms","v":3},"yerms"]
[{"$f":"\"The last yerm #\"&Yerms&\" has 17 months.\"","v":"The last yerm #3 has 17 months."}]

{"sheet":"Zoom","index":4,"n_rows":6,"n_cols":6,"rows_kept":6}
[0,"= Current Zoom Level"]
["Level","Months","MajorTick","MinorTick","Shift","Connect"]
[{"$f":"ROW()-3","v":0},98,14,2,null,true]
[1,49,7,1,{"$f":"B5","v":17},true]
[2,17,17,2,{"$f":"B6","v":15},true]
[3,15,15,3,3,true]

{"sheet":"Labels","index":5,"n_rows":34,"n_cols":3,"rows_kept":34}
["Month","Hours",{"$f":"\"Span \"&B2-B34&\"h\"","v":"Span 96h"}]
[99,48]
[{"$f":"A2","v":99},{"$f":"B2-3","v":45}]
[{"$f":"A3","v":99},{"$f":"B3-3","v":42}]
[{"$f":"A4","v":99},39]
[{"$f":"A5","v":99},36]
[99,33]
[99,30]
[99,27]
[99,24]
[99,21]
[99,18]
[99,15]
[99,12]
[99,9]
[99,6]
[99,3]
[99,0]
[99,-3]
[99,-6]
[99,-9]
[99,-12]
[99,-15]
[99,-18]
[99,-21]
[99,-24]
[99,-27]
[99,-30]
[99,-33]
[99,-36]
[99,-39]
[99,-42]
[99,-45]
[99,-48]