{"text_format":"3","workbook":"xlsx","n_sheets":6,"sheets":["Chart","Data","Solar Cycle","Lunar Cycle","Zoom","Labels"],"not_rendered":{"charts":1,"macros":1,"external_links":1,"defined_names":23,"comments":1},"read":"whole","date_system":"1900"}

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["Orthodox Easter Computus Jitter (Paschal Moon relative to Mean Elapsed Months)"]
[{"$f":"\"Solar cycle contains 28 years (common = 365 days, every 4th year leap = 366 days) = \"&(28*365+7)&\" days per cycle = \"&reducefraction(28*365+7,7,FALSE,FALSE,TRUE)&\" weeks per cycle.\"","v":"Solar cycle contains 28 years (common = 365 days, every 4th year leap = 366 days) = 10227 days per cycle = 1461 weeks per cycle."}]
[{"$f":"\"Lunar cycle contains \"&MPC&\" months (\"&FMPC&\" full, \"&DMPC&\" deficient) = \"&DPC&\" days = \"&reducefraction(DPC,7,FALSE,FALSE,TRUE)&\" weeks = \"&Yerms&\" yerms. Lunisolar cycle = 28 x 19 = \"&(28*19)&\" years.\"","v":"Lunar cycle contains 940 months (499 full, 441 deficient) = 27759 days = 3965+4/7 weeks = 58 yerms. Lunisolar cycle = 28 x 19 = 532 years."}]
[{"$f":"\"Mean month = \"&\"29+\"&reducefraction(FMPC,MPC,FALSE,FALSE,TRUE)&\" days = 29d 12h 44m \"&reducefraction(240*(360*FMPC-191*MPC),MPC,FALSE,FALSE,TRUE)&\" seconds, or about 29\"&MID(FMPC/MPC,2,20)&\" days or 29d 12h 44m \"&ROUND(240*(360*FMPC-191*MPC)/MPC,6)&\" seconds.\"","v":"Mean month = 29+499/940 days = 29d 12h 44m 25+25/47 seconds, or about 29.530851063829787 days or 29d 12h 44m 25.531915 seconds."}]
[{"$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'' = 1/940 day = 6/235 hour = 1+25/47 minutes = 91+43/47 seconds.  One hour = 39+1/6 parts."}]
[]
[]
[{"$nulls":16},true]
{"$rows_empty":10}
[{"$nulls":16},3]
[{"$nulls":16},"Selected"]
[{"$nulls":16},"Year in"]
[{"$nulls":16},"Solar Cycle"]
[{"$nulls":16},"(1 to 28)"]
{"$rows_empty":8}
[{"$nulls":16},18]
[{"$nulls":16},"Selected"]
[{"$nulls":16},"Year in"]
[{"$nulls":16},"Lunar Cycle"]
[{"$nulls":16},"(1 to 19)"]
{"$rows_empty":8}
[{"$nulls":8},{"$f":"ZoomLevel","v":1}]

{"sheet":"Data","index":1,"n_rows":591,"n_cols":9,"rows_kept":591}
["Lunar Cycle Jitter Evaluator"]
["by Dr. Irv Bromberg, University of Toronto, Canada"]
["http://individual.utoronto.ca/intervalmath/jitter/index.html",null,null,"Jitter","(parts)"]
["Decimal Mean Month:",{"$f":"29+FMPC/MPC","v":29.530851063829786},null,{"$f":"MAX(I:I)","v":1401},"maximum",{"$f":"reducefraction(JitterMax*MPC,MPC,FALSE,FALSE,FALSE)","v":"1401"}]
["Months per Cycle (Parts per Day):",940,"months (parts)",{"$f":"MIN(I:I)","v":-470},"minimum",{"$f":"reducefraction(JitterMin*MPC,MPC,FALSE,FALSE,FALSE)","v":"–(470)"}]
["30-day Months per Cycle:",499,"months",{"$f":"D4-D5","v":1871},"range",{"$f":"reducefraction(JitterRange*MPC,MPC,FALSE,FALSE,FALSE)","v":"1871"}]
["29-day Months per Cycle:",{"$f":"MPC-FMPC","v":441},"months",{"$f":"\"Jitter range = \"&F6&\" parts = \"&reducefraction(F6*24,MPC,FALSE,FALSE,FALSE)&\" hours\"","v":"Jitter range = 1871 parts = 47 + 181 / 235 hours"}]
["Days per Cycle (Parts per Month):",{"$f":"29*MPC+FMPC","v":27759},"days (parts)",null,"Years Per Cycle:",{"$f":"4*19","v":76}]
["Yerms per Cycle:",{"$f":"2*DPC-59*MPC","v":58},"yerms","Limits for Chart:"]
["Mean Month:",{"$f":"\"29 + \"&reducefraction(FMPC,MPC,FALSE,FALSE,FALSE)","v":"29 + 499 / 940"},"days","x","y","Hours"]
["Mean Month >29d:",{"$f":"FMPC/MPC","v":{"v":0.5308510638297872,"d":"0.530851063829787"}},"days",{"$f":"A22","v":1},{"$f":"JitterMax","v":1401},{"$f":"E11*24/MPC","v":35.770212765957446}]
["Mean Month >29d 12h 44m:",{"$f":"reducefraction(240*(360*FMPC-191*MPC),MPC,FALSE,FALSE,TRUE)","v":"25+25/47"},"seconds",{"$f":"7*YPC+1","v":533},{"$f":"E11","v":1401},{"$f":"E12*24/MPC","v":35.770212765957446}]
["… or approximately:",{"$f":"240*(360*FMPC-191*MPC)/MPC","v":25.53191489361702},"seconds"]
["Has Yerm Zero:",{"$f":"MeanMonth>26/49","v":true},null,{"$f":"D11","v":1},0]
["17-month Yerms per Cycle:",{"$f":"443*MPC-15*DPC","v":35},"yerms",{"$f":"D12","v":533},0]
["15-month Yerms per Cycle:",{"$f":"Yerms-n17my","v":23},"yerms"]
["49-month subcycles:",{"$f":"INT(Yerms/3)","v":19},null,{"$f":"A22","v":1},{"$f":"JitterMin","v":-470},{"$f":"E17*24/MPC","v":-12}]
["Duration per Part:",{"$f":"reducefraction(1440,MPC,FALSE,FALSE,FALSE)","v":"1 + 25 / 47"},"minutes",{"$f":"D12","v":533},{"$f":"E17","v":-470},{"$f":"E18*24/MPC","v":-12}]
[{"$nulls":6},"Elapsed","Elapsed"]
[{"$nulls":3},"Paschal Moon","Elapsed","Paschal Moon","Lunar","Mean Month","Difference"]
["Julian Year","isLeapYear","Year Length","(days)","Days","(parts)","Months","Parts","(parts)"]
[1,{"$f":"isJulianLeapYear(A22)","v":false},{"$f":"IF(B22,366,365)","v":365},{"$f":"PaschalMoon(A22)","v":82},null,0,null,0,{"$f":"F22-H22","v":0}]
[{"$f":"A22+1","v":2},{"$f":"isJulianLeapYear(A23)","v":false},{"$f":"IF(B23,366,365)","v":365},{"$f":"PaschalMoon(A23)","v":466},{"$f":"D23-D22","v":384},{"$f":"F22+(D23-D22)*PPD","v":360960},{"$f":"ROUND((D23-D22)/DecMeanMon,1)","v":13},{"$f":"H22+G23*PPM","v":360867},{"$f":"F23-H23","v":93}]
[{"$f":"A23+1","v":3},false,365,820,354,{"$f":"F23+(D24-D23)*PPD","v":693720},{"$f":"ROUND((D24-D23)/DecMeanMon,1)","v":12},{"$f":"H23+G24*PPM","v":693975},-255]
[4,true,366,1175,355,1027420,{"$f":"ROUND((D25-D24)/DecMeanMon,1)","v":12},1027083,337]
[5,false,365,1559,384,1388380,{"$f":"ROUND((D26-D25)/DecMeanMon,1)","v":13},1387950,430]
[6,false,365,1913,354,1721140,12,1721058,82]
[7,false,365,2297,384,2082100,13,2081925,175]
[8,true,366,2652,355,2415800,12,2415033,767]
[9,false,365,3006,354,2748560,12,2748141,419]
[10,false,365,3390,384,3109520,13,3109008,512]
[11,false,365,3744,354,3442280,12,3442116,164]
[12,true,366,4099,355,3775980,12,3775224,756]
[13,false,365,4483,384,4136940,13,4136091,849]
[14,false,365,4837,354,4469700,12,4469199,501]
[15,false,365,5191,354,4802460,12,4802307,153]
[16,true,366,5576,385,5164360,13,5163174,1186]
[17,false,365,5930,354,5497120,12,5496282,838]
[18,false,365,6314,384,5858080,13,5857149,931]
[19,false,365,6667,353,6189900,12,6190257,-357]
[20,true,366,7022,355,6523600,12,6523365,235]
[21,false,365,7406,384,6884560,13,6884232,328]
[22,false,365,7760,354,7217320,12,7217340,-20]
[23,false,365,8114,354,7550080,12,7550448,-368]
[24,true,366,8499,385,7911980,13,7911315,665]
[25,false,365,8853,354,8244740,12,8244423,317]
[26,false,365,9237,384,8605700,13,8605290,410]
[27,false,365,9591,354,8938460,12,8938398,62]
[28,true,366,9946,355,9272160,12,9271506,654]
[29,false,365,10330,384,9633120,13,9632373,747]
[30,false,365,10684,354,9965880,12,9965481,399]
[31,false,365,11038,354,10298640,12,10298589,51]
[32,true,366,11423,385,10660540,13,10659456,1084]
[33,false,365,11777,354,10993300,12,10992564,736]
[34,false,365,12131,{"$f":"D55-D54","v":354},11326060,12,11325672,388]
[35,false,365,12515,384,11687020,13,11686539,481]
[36,true,366,12870,355,12020720,12,12019647,1073]
[37,false,365,13254,384,12381680,13,12380514,1166]
[38,false,365,13607,353,12713500,12,12713622,-122]
[39,false,365,13961,354,13046260,12,13046730,-470]
[40,true,366,14346,385,13408160,13,13407597,563]
[41,false,365,14700,354,13740920,12,13740705,215]
[42,false,365,15054,354,14073680,12,14073813,-133]
[43,false,365,15438,384,14434640,13,14434680,-40]
[44,true,366,15793,355,14768340,12,14767788,552]
[45,false,365,16177,384,15129300,13,15128655,645]
[46,false,365,16531,354,15462060,12,15461763,297]
[47,false,365,16885,354,15794820,12,15794871,-51]
[48,true,366,17270,385,16156720,13,16155738,982]
[49,false,365,17624,354,16489480,12,16488846,634]
[50,false,365,17978,354,16822240,12,16821954,286]
[51,false,365,18362,384,17183200,13,17182821,379]
[52,true,366,18717,355,17516900,12,17515929,971]
[53,false,365,19071,354,17849660,12,17849037,623]
[54,false,365,19455,384,18210620,13,18209904,716]
[55,false,365,19809,354,18543380,12,18543012,368]
[56,true,366,20194,385,18905280,13,18903879,1401]
[57,false,365,20547,353,19237100,12,19236987,113]
[58,false,365,20901,354,19569860,12,19570095,-235]
[59,false,365,21285,384,19930820,13,19930962,-142]
[60,true,366,21640,355,20264520,12,20264070,450]
[61,false,365,21994,354,20597280,12,20597178,102]
[62,false,365,22378,384,20958240,13,20958045,195]
[63,false,365,22732,354,21291000,12,21291153,-153]
[64,true,366,23117,385,21652900,13,21652020,880]
[65,false,365,23471,354,21985660,12,21985128,532]
[66,{"$f":"isJulianLeapYear(A87)","v":false},{"$f":"IF(B87,366,365)","v":365},{"$f":"PaschalMoon(A87)","v":23825},{"$f":"D87-D86","v":354},22318420,12,22318236,{"$f":"F87-H87","v":184}]
[{"$f":"A87+1","v":67},false,365,{"$f":"PaschalMoon(A88)","v":24209},{"$f":"D88-D87","v":384},{"$f":"F87+(D88-D87)*PPD","v":22679380},{"$f":"ROUND((D88-D87)/DecMeanMon,1)","v":13},{"$f":"H87+G88*PPM","v":22679103},{"$f":"F88-H88","v":277}]
[{"$f":"A88+1","v":68},true,366,{"$f":"PaschalMoon(A89)","v":24564},{"$f":"D89-D88","v":355},{"$f":"F88+(D89-D88)*PPD","v":23013080},{"$f":"ROUND((D89-D88)/DecMeanMon,1)","v":12},{"$f":"H88+G89*PPM","v":23012211},{"$f":"F89-H89","v":869}]
[{"$f":"A89+1","v":69},false,365,{"$f":"PaschalMoon(A90)","v":24918},{"$f":"D90-D89","v":354},{"$f":"F89+(D90-D89)*PPD","v":23345840},{"$f":"ROUND((D90-D89)/DecMeanMon,1)","v":12},{"$f":"H89+G90*PPM","v":23345319},{"$f":"F90-H90","v":521}]
[{"$f":"A90+1","v":70},false,365,{"$f":"PaschalMoon(A91)","v":25302},{"$f":"D91-D90","v":384},{"$f":"F90+(D91-D90)*PPD","v":23706800},{"$f":"ROUND((D91-D90)/DecMeanMon,1)","v":13},{"$f":"H90+G91*PPM","v":23706186},{"$f":"F91-H91","v":614}]
[71,false,365,25656,354,24039560,12,24039294,266]
[72,true,366,26011,355,24373260,12,24372402,858]
[73,false,365,26395,384,24734220,13,24733269,951]
[74,false,365,26749,354,25066980,12,25066377,603]
[75,false,365,27133,384,25427940,13,25427244,696]
[76,true,366,27487,354,25760700,12,25760352,348]
[77,false,365,27841,354,26093460,12,26093460,0]
[78,false,365,28225,384,26454420,13,26454327,93]
[79,false,365,28579,354,26787180,12,26787435,-255]
[80,true,366,28934,355,27120880,12,27120543,337]
[81,false,365,29318,384,27481840,13,27481410,430]
[82,false,365,29672,354,27814600,12,27814518,82]
[83,false,365,30056,384,28175560,13,28175385,175]
[84,true,366,30411,355,28509260,12,28508493,767]
[85,false,365,30765,354,28842020,12,28841601,419]
[86,false,365,31149,384,29202980,13,29202468,512]
[87,false,365,31503,354,29535740,12,29535576,164]
[88,true,366,31858,355,29869440,12,29868684,756]
[89,false,365,32242,384,30230400,13,30229551,849]
[90,false,365,32596,354,30563160,12,30562659,501]
[91,false,365,32950,354,30895920,12,30895767,153]
[92,true,366,33335,385,31257820,13,31256634,1186]
[93,false,365,33689,354,31590580,12,31589742,838]
[94,false,365,34073,384,31951540,13,31950609,931]
[95,false,365,34426,353,32283360,12,32283717,-357]
[96,true,366,34781,355,32617060,12,32616825,235]
[97,false,365,35165,384,32978020,13,32977692,328]
[98,{"$f":"isJulianLeapYear(A119)","v":false},{"$f":"IF(B119,366,365)","v":365},35519,354,33310780,12,33310800,-20]
[99,false,365,35873,354,33643540,12,33643908,-368]
[100,true,366,36258,385,34005440,13,34004775,665]
[101,false,365,36612,354,34338200,12,34337883,317]
[102,false,365,36996,384,34699160,13,34698750,410]
[103,false,365,37350,354,35031920,12,35031858,62]
[104,true,366,37705,355,35365620,12,35364966,654]
[105,false,365,38089,384,35726580,13,35725833,747]
[106,false,365,38443,354,36059340,12,36058941,399]
[107,false,365,38797,354,36392100,12,36392049,51]
[108,true,366,39182,385,36754000,13,36752916,1084]
[109,false,365,39536,354,37086760,12,37086024,736]
[110,false,365,39890,354,37419520,12,37419132,388]
[111,false,365,40274,384,37780480,13,37779999,481]
[112,true,366,40629,355,38114180,12,38113107,1073]
[113,false,365,41013,384,38475140,13,38473974,1166]
[114,false,365,41366,353,38806960,12,38807082,-122]
[115,false,365,41720,354,39139720,12,39140190,-470]
[116,true,366,42105,385,39501620,13,39501057,563]
[117,false,365,42459,354,39834380,12,39834165,215]
[118,false,365,42813,354,40167140,12,40167273,-133]
[119,false,365,43197,384,40528100,13,40528140,-40]
[120,true,366,43552,355,40861800,12,40861248,552]
[121,false,365,43936,384,41222760,13,41222115,645]
[122,false,365,44290,354,41555520,12,41555223,297]
[123,false,365,44644,354,41888280,12,41888331,-51]
[124,true,366,45029,385,42250180,13,42249198,982]
[125,false,365,45383,354,42582940,12,42582306,634]
[126,false,365,45737,354,42915700,12,42915414,286]
[127,false,365,46121,384,43276660,13,43276281,379]
[128,true,366,46476,355,43610360,12,43609389,971]
[129,false,365,46830,354,43943120,12,43942497,623]
[130,{"$f":"isJulianLeapYear(A151)","v":false},{"$f":"IF(B151,366,365)","v":365},47214,384,44304080,13,44303364,716]
[131,false,365,47568,354,44636840,12,44636472,368]
[132,true,366,47953,385,44998740,13,44997339,1401]
[133,false,365,48306,353,45330560,12,45330447,113]
[{"$f":"A154+1","v":134},false,365,{"$f":"PaschalMoon(A155)","v":48660},{"$f":"D155-D154","v":354},{"$f":"F154+(D155-D154)*PPD","v":45663320},{"$f":"ROUND((D155-D154)/DecMeanMon,1)","v":12},{"$f":"H154+G155*PPM","v":45663555},{"$f":"F155-H155","v":-235}]
[135,false,365,49044,384,46024280,13,46024422,-142]
[136,true,366,49399,355,46357980,12,46357530,450]
[137,false,365,49753,354,46690740,12,46690638,102]
[138,false,365,50137,384,47051700,13,47051505,195]
[139,false,365,50491,354,47384460,12,47384613,-153]
[140,true,366,50876,385,47746360,13,47745480,880]
[141,false,365,51230,354,48079120,12,48078588,532]
[142,false,365,51584,354,48411880,12,48411696,184]
[143,false,365,51968,384,48772840,13,48772563,277]
[144,true,366,52323,355,49106540,12,49105671,869]
[145,false,365,52677,354,49439300,12,49438779,521]
[146,false,365,53061,384,49800260,13,49799646,614]
[147,false,365,53415,354,50133020,12,50132754,266]
[148,true,366,53770,355,50466720,12,50465862,858]
[149,false,365,54154,384,50827680,13,50826729,951]
[150,false,365,54508,354,51160440,12,51159837,603]
[151,false,365,54892,384,51521400,13,51520704,696]
[152,true,366,55246,354,51854160,12,51853812,348]
[153,false,365,55600,354,52186920,12,52186920,0]
[154,false,365,55984,384,52547880,13,52547787,93]
[155,false,365,56338,354,52880640,12,52880895,-255]
[156,true,366,56693,355,53214340,12,53214003,337]
[157,false,365,57077,384,53575300,13,53574870,430]
[158,false,365,57431,354,53908060,12,53907978,82]
[159,false,365,57815,384,54269020,13,54268845,175]
[160,true,366,58170,355,54602720,12,54601953,767]
[161,false,365,58524,354,54935480,12,54935061,419]
[162,{"$f":"isJulianLeapYear(A183)","v":false},{"$f":"IF(B183,366,365)","v":365},58908,384,55296440,13,55295928,512]
[163,false,365,59262,354,55629200,12,55629036,164]
[164,true,366,59617,355,55962900,12,55962144,756]
[165,false,365,60001,384,56323860,13,56323011,849]
[166,false,365,60355,354,56656620,12,56656119,501]
[167,false,365,60709,354,56989380,12,56989227,153]
[168,true,366,61094,385,57351280,13,57350094,1186]
[169,false,365,61448,354,57684040,12,57683202,838]
[170,false,365,61832,384,58045000,13,58044069,931]
[171,false,365,62185,353,58376820,12,58377177,-357]
[172,true,366,62540,355,58710520,12,58710285,235]
[173,false,365,62924,384,59071480,13,59071152,328]
[174,false,365,63278,354,59404240,12,59404260,-20]
[175,false,365,63632,354,59737000,12,59737368,-368]
[176,true,366,64017,385,60098900,13,60098235,665]
[177,false,365,64371,354,60431660,12,60431343,317]
[178,false,365,64755,384,60792620,13,60792210,410]
[179,false,365,65109,354,61125380,12,61125318,62]
[180,true,366,65464,355,61459080,12,61458426,654]
[181,false,365,65848,384,61820040,13,61819293,747]
[182,false,365,66202,354,62152800,12,62152401,399]
[183,false,365,66556,354,62485560,12,62485509,51]
[184,true,366,66941,385,62847460,13,62846376,1084]
[185,false,365,67295,354,63180220,12,63179484,736]
[186,false,365,67649,354,63512980,12,63512592,388]
[187,false,365,68033,384,63873940,13,63873459,481]
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[1,"= Current Zoom Level"]
["Level","Years","MajorTick","MinorTick","Shift","Connect"]
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