{"text_format":"3","workbook":"xlsx","n_sheets":6,"sheets":["Chart","Data","Solar Cycle","Lunar Cycle","Zoom","Labels"],"not_rendered":{"charts":1,"macros":1,"defined_names":21,"comments":1},"read":"whole","date_system":"1900"}

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["Orthodox Easter Computus Jitter (Easter Sunday 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."}]
[]
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{"$rows_empty":9}
[{"$nulls":16},26]
[{"$nulls":16},"Selected"]
[{"$nulls":16},"Year in"]
[{"$nulls":16},"Solar Cycle"]
[{"$nulls":16},"(1 to 28)"]
{"$rows_empty":9}
[{"$nulls":16},1]
[{"$nulls":16},"Selected"]
[{"$nulls":16},"Year in"]
[{"$nulls":16},"Lunar Cycle"]
[{"$nulls":16},"(1 to 19)"]
{"$rows_empty":9}
[{"$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":6101},"maximum",{"$f":"reducefraction(JitterMax*MPC,MPC,FALSE,FALSE,FALSE)","v":"6101"}]
["Months per Cycle (Parts per Day):",940,"months (parts)",{"$f":"MIN(I:I)","v":-1410},"minimum",{"$f":"reducefraction(JitterMin*MPC,MPC,FALSE,FALSE,FALSE)","v":"–(1410)"}]
["30-day Months per Cycle:",499,"months",{"$f":"D4-D5","v":7511},"range",{"$f":"reducefraction(JitterRange*MPC,MPC,FALSE,FALSE,FALSE)","v":"7511"}]
["29-day Months per Cycle:",{"$f":"MPC-FMPC","v":441},"months",{"$f":"\"Jitter range = \"&F6&\" parts = \"&reducefraction(F6*24,MPC,FALSE,FALSE,FALSE)&\" hours\"","v":"Jitter range = 7511 parts = 191 + 181 / 235 hours"}]
["Days per Cycle (Parts per Month):",{"$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":6101},{"$f":"E11*24/MPC","v":155.77021276595744}]
["Mean Month >29d 12h 44m:",{"$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":6101},{"$f":"E12*24/MPC","v":155.77021276595744}]
["… or approximately:",{"$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":-1410},{"$f":"E17*24/MPC","v":-36}]
["Duration per Part:",{"$f":"reducefraction(1440,MPC,FALSE,FALSE,FALSE)","v":"1 + 25 / 47"},"minutes",{"$f":"D12","v":533},{"$f":"E17","v":-1410},{"$f":"E18*24/MPC","v":-36}]
[{"$nulls":6},"Elapsed","Elapsed"]
[{"$nulls":3},"Easter Sunday","Elapsed","Easter Sunday","Lunar","Mean Month","Difference"]
["Julian Year","isLeapYear","Year Length","(days)","Days","(parts)","Months","Parts","(parts)"]
[1,{"$f":"isJulianLeapYear(A22)","v":false},{"$f":"IF(B22,366,365)","v":365},{"$f":"OrthodoxEaster(A22)","v":84},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},{"$f":"OrthodoxEaster(A23)","v":469},{"$f":"D23-D22","v":385},{"$f":"F22+(D23-D22)*PPD","v":361900},{"$f":"ROUND((D23-D22)/DecMeanMon,0)","v":13},{"$f":"H22+G23*PPM","v":360867},{"$f":"F23-H23","v":1033}]
[{"$f":"A23+1","v":3},false,365,826,357,{"$f":"F23+(D24-D23)*PPD","v":697480},12,{"$f":"H23+G24*PPM","v":693975},3505]
[4,true,366,1176,350,1026480,12,1027083,-603]
[5,false,365,1561,385,1388380,13,1387950,430]
[6,false,365,1918,357,1723960,12,1721058,2902]
[7,false,365,2303,385,2085860,13,2081925,3935]
[8,true,366,2653,350,2414860,12,2415033,-173]
[9,false,365,3010,357,2750440,12,2748141,2299]
[10,false,365,3395,385,3112340,13,3109008,3332]
[11,false,365,3745,350,3441340,12,3442116,-776]
[12,true,366,4102,357,3776920,12,3775224,1696]
[13,false,365,4487,385,4138820,13,4136091,2729]
[14,false,365,4844,357,4474400,12,4469199,5201]
[15,false,365,5194,350,4803400,12,4802307,1093]
[16,true,366,5579,385,5165300,13,5163174,2126]
[17,false,365,5936,357,5500880,12,5496282,4598]
[18,false,365,6321,385,5862780,13,5857149,5631]
[19,false,365,6671,350,6191780,12,6190257,1523]
[20,true,366,7028,357,6527360,12,6523365,3995]
[21,false,365,7413,385,6889260,13,6884232,5028]
[22,false,365,7763,350,7218260,12,7217340,920]
[23,false,365,8120,357,7553840,12,7550448,3392]
[24,true,366,8505,385,7915740,13,7911315,4425]
[25,false,365,8855,350,8244740,12,8244423,317]
[26,false,365,9240,385,8606640,13,8605290,1350]
[27,false,365,9597,357,8942220,12,8938398,3822]
[28,true,366,9947,350,9271220,12,9271506,-286]
[29,false,365,10332,385,9633120,13,9632373,747]
[30,false,365,10689,357,9968700,12,9965481,3219]
[31,false,365,11039,350,10297700,12,10298589,-889]
[32,true,366,11424,385,10659600,13,10659456,144]
[33,false,365,11781,357,10995180,12,10992564,2616]
[34,false,365,12138,{"$f":"D55-D54","v":357},11330760,12,11325672,5088]
[35,false,365,12516,378,11686080,13,11686539,-459]
[36,true,366,12873,357,12021660,12,12019647,2013]
[37,false,365,13258,385,12383560,13,12380514,3046]
[38,false,365,13608,350,12712560,12,12713622,-1062]
[39,false,365,13965,357,13048140,12,13046730,1410]
[40,true,366,14350,385,13410040,13,13407597,2443]
[41,false,365,14707,357,13745620,12,13740705,4915]
[42,false,365,15057,350,14074620,12,14073813,807]
[43,false,365,15442,385,14436520,13,14434680,1840]
[44,true,366,15799,357,14772100,12,14767788,4312]
[45,false,365,16184,385,15134000,13,15128655,5345]
[46,false,365,16534,350,15463000,12,15461763,1237]
[47,false,365,16891,357,15798580,12,15794871,3709]
[48,true,366,17276,385,16160480,13,16155738,4742]
[49,false,365,17626,350,16489480,12,16488846,634]
[50,false,365,17983,357,16825060,12,16821954,3106]
[51,false,365,18368,385,17186960,13,17182821,4139]
[52,true,366,18718,350,17515960,12,17515929,31]
[53,false,365,19075,357,17851540,12,17849037,2503]
[54,false,365,19460,385,18213440,13,18209904,3536]
[55,false,365,19810,350,18542440,12,18543012,-572]
[56,true,366,20195,385,18904340,13,18903879,461]
[57,false,365,20552,357,19239920,12,19236987,2933]
[58,false,365,20902,350,19568920,12,19570095,-1175]
[59,false,365,21287,385,19930820,13,19930962,-142]
[60,true,366,21644,357,20266400,12,20264070,2330]
[61,false,365,22001,357,20601980,12,20597178,4802]
[62,false,365,22379,378,20957300,13,20958045,-745]
[63,false,365,22736,357,21292880,12,21291153,1727]
[64,true,366,23121,385,21654780,13,21652020,2760]
[65,false,365,23478,357,21990360,12,21985128,5232]
[66,{"$f":"isJulianLeapYear(A87)","v":false},{"$f":"IF(B87,366,365)","v":365},{"$f":"OrthodoxEaster(A87)","v":23828},{"$f":"D87-D86","v":350},22319360,{"$f":"ROUND((D87-D86)/DecMeanMon,0)","v":12},22318236,{"$f":"F87-H87","v":1124}]
[{"$f":"A87+1","v":67},false,365,24213,{"$f":"D88-D87","v":385},{"$f":"F87+(D88-D87)*PPD","v":22681260},13,{"$f":"H87+G88*PPM","v":22679103},{"$f":"F88-H88","v":2157}]
[{"$f":"A88+1","v":68},true,366,24570,{"$f":"D89-D88","v":357},{"$f":"F88+(D89-D88)*PPD","v":23016840},12,{"$f":"H88+G89*PPM","v":23012211},{"$f":"F89-H89","v":4629}]
[{"$f":"A89+1","v":69},false,365,24920,{"$f":"D90-D89","v":350},{"$f":"F89+(D90-D89)*PPD","v":23345840},12,{"$f":"H89+G90*PPM","v":23345319},{"$f":"F90-H90","v":521}]
[{"$f":"A90+1","v":70},false,365,25305,{"$f":"D91-D90","v":385},{"$f":"F90+(D91-D90)*PPD","v":23707740},13,{"$f":"H90+G91*PPM","v":23706186},{"$f":"F91-H91","v":1554}]
[71,false,365,25662,357,24043320,12,24039294,4026]
[72,true,366,26012,350,24372320,12,24372402,-82]
[73,false,365,26397,385,24734220,13,24733269,951]
[74,false,365,26754,357,25069800,12,25066377,3423]
[75,false,365,27139,385,25431700,13,25427244,4456]
[76,true,366,27489,350,25760700,12,25760352,348]
[77,false,365,27846,357,26096280,12,26093460,2820]
[78,false,365,28231,385,26458180,13,26454327,3853]
[79,false,365,28581,350,26787180,12,26787435,-255]
[80,true,366,28938,357,27122760,12,27120543,2217]
[81,false,365,29323,385,27484660,13,27481410,3250]
[82,false,365,29673,350,27813660,12,27814518,-858]
[83,false,365,30058,385,28175560,13,28175385,175]
[84,true,366,30415,357,28511140,12,28508493,2647]
[85,false,365,30772,357,28846720,12,28841601,5119]
[86,false,365,31150,378,29202040,13,29202468,-428]
[87,false,365,31507,357,29537620,12,29535576,2044]
[88,true,366,31864,357,29873200,12,29868684,4516]
[89,false,365,32249,385,30235100,13,30229551,5549]
[90,false,365,32599,350,30564100,12,30562659,1441]
[91,false,365,32956,357,30899680,12,30895767,3913]
[92,true,366,33341,385,31261580,13,31256634,4946]
[93,false,365,33691,350,31590580,12,31589742,838]
[94,false,365,34076,385,31952480,13,31950609,1871]
[95,false,365,34433,357,32288060,12,32283717,4343]
[96,true,366,34783,350,32617060,12,32616825,235]
[97,false,365,35168,385,32978960,13,32977692,1268]
[98,{"$f":"isJulianLeapYear(A119)","v":false},{"$f":"IF(B119,366,365)","v":365},35525,357,33314540,12,33310800,3740]
[99,false,365,35875,350,33643540,12,33643908,-368]
[100,true,366,36260,385,34005440,13,34004775,665]
[101,false,365,36617,357,34341020,12,34337883,3137]
[102,false,365,37002,385,34702920,13,34698750,4170]
[103,false,365,37352,350,35031920,12,35031858,62]
[104,true,366,37709,357,35367500,12,35364966,2534]
[105,false,365,38094,385,35729400,13,35725833,3567]
[106,false,365,38444,350,36058400,12,36058941,-541]
[107,false,365,38801,357,36393980,12,36392049,1931]
[108,true,366,39186,385,36755880,13,36752916,2964]
[109,false,365,39543,357,37091460,12,37086024,5436]
[110,false,365,39893,350,37420460,12,37419132,1328]
[111,false,365,40278,385,37782360,13,37779999,2361]
[112,true,366,40635,357,38117940,12,38113107,4833]
[113,false,365,41020,385,38479840,13,38473974,5866]
[114,false,365,41370,350,38808840,12,38807082,1758]
[115,false,365,41727,357,39144420,12,39140190,4230]
[116,true,366,42112,385,39506320,13,39501057,5263]
[117,false,365,42462,350,39835320,12,39834165,1155]
[118,false,365,42819,357,40170900,12,40167273,3627]
[119,false,365,43204,385,40532800,13,40528140,4660]
[120,true,366,43554,350,40861800,12,40861248,552]
[121,false,365,43939,385,41223700,13,41222115,1585]
[122,false,365,44296,357,41559280,12,41555223,4057]
[123,false,365,44646,350,41888280,12,41888331,-51]
[124,true,366,45031,385,42250180,13,42249198,982]
[125,false,365,45388,357,42585760,12,42582306,3454]
[126,false,365,45738,350,42914760,12,42915414,-654]
[127,false,365,46123,385,43276660,13,43276281,379]
[128,true,366,46480,357,43612240,12,43609389,2851]
[129,false,365,46837,357,43947820,12,43942497,5323]
[130,{"$f":"isJulianLeapYear(A151)","v":false},{"$f":"IF(B151,366,365)","v":365},{"$f":"OrthodoxEaster(A151)","v":47215},378,44303140,{"$f":"ROUND((D151-D150)/DecMeanMon,0)","v":13},44303364,-224]
[131,false,365,47572,357,44638720,12,44636472,2248]
[132,true,366,47957,385,45000620,13,44997339,3281]
[133,false,365,48307,350,45329620,12,45330447,-827]
[{"$f":"A154+1","v":134},false,365,48664,{"$f":"D155-D154","v":357},{"$f":"F154+(D155-D154)*PPD","v":45665200},12,{"$f":"H154+G155*PPM","v":45663555},{"$f":"F155-H155","v":1645}]
[135,false,365,49049,385,46027100,13,46024422,2678]
[136,true,366,49406,357,46362680,12,46357530,5150]
[137,false,365,49756,350,46691680,12,46690638,1042]
[138,false,365,50141,385,47053580,13,47051505,2075]
[139,false,365,50498,357,47389160,12,47384613,4547]
[140,true,366,50883,385,47751060,13,47745480,5580]
[141,false,365,51233,350,48080060,12,48078588,1472]
[142,false,365,51590,357,48415640,12,48411696,3944]
[143,false,365,51975,385,48777540,13,48772563,4977]
[144,true,366,52325,350,49106540,12,49105671,869]
[145,false,365,52682,357,49442120,12,49438779,3341]
[146,false,365,53067,385,49804020,13,49799646,4374]
[147,false,365,53417,350,50133020,12,50132754,266]
[148,true,366,53774,357,50468600,12,50465862,2738]
[149,false,365,54159,385,50830500,13,50826729,3771]
[150,false,365,54509,350,51159500,12,51159837,-337]
[151,false,365,54894,385,51521400,13,51520704,696]
[152,true,366,55251,357,51856980,12,51853812,3168]
[153,false,365,55601,350,52185980,12,52186920,-940]
[154,false,365,55986,385,52547880,13,52547787,93]
[155,false,365,56343,357,52883460,12,52880895,2565]
[156,true,366,56700,357,53219040,12,53214003,5037]
[157,false,365,57078,378,53574360,13,53574870,-510]
[158,false,365,57435,357,53909940,12,53907978,1962]
[159,false,365,57820,385,54271840,13,54268845,2995]
[160,true,366,58177,357,54607420,12,54601953,5467]
[161,false,365,58527,350,54936420,12,54935061,1359]
[162,{"$f":"isJulianLeapYear(A183)","v":false},{"$f":"IF(B183,366,365)","v":365},58912,385,55298320,13,55295928,2392]
[163,false,365,59269,357,55633900,12,55629036,4864]
[164,true,366,59619,350,55962900,12,55962144,756]
[165,false,365,60004,385,56324800,13,56323011,1789]
[166,false,365,60361,357,56660380,12,56656119,4261]
[167,false,365,60711,350,56989380,12,56989227,153]
[168,true,366,61096,385,57351280,13,57350094,1186]
[169,false,365,61453,357,57686860,12,57683202,3658]
[170,false,365,61838,385,58048760,13,58044069,4691]
[171,false,365,62188,350,58377760,12,58377177,583]
[172,true,366,62545,357,58713340,12,58710285,3055]
[173,false,365,62930,385,59075240,13,59071152,4088]
[174,false,365,63280,350,59404240,12,59404260,-20]
[175,false,365,63637,357,59739820,12,59737368,2452]
[176,true,366,64022,385,60101720,13,60098235,3485]
[177,false,365,64372,350,60430720,12,60431343,-623]
[178,false,365,64757,385,60792620,13,60792210,410]
[179,false,365,65114,357,61128200,12,61125318,2882]
[180,true,366,65471,357,61463780,12,61458426,5354]
[181,false,365,65849,378,61819100,13,61819293,-193]
[182,false,365,66206,357,62154680,12,62152401,2279]
[183,false,365,66563,357,62490260,12,62485509,4751]
[184,true,366,66948,385,62852160,13,62846376,5784]
[185,false,365,67298,350,63181160,12,63179484,1676]
[186,false,365,67655,357,63516740,12,63512592,4148]
[187,false,365,68040,385,63878640,13,63873459,5181]
[188,true,366,68390,350,64207640,12,64206567,1073]
[189,false,365,68775,385,64569540,13,64567434,2106]
[190,false,365,69132,357,64905120,12,64900542,4578]
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{"sheet":"Zoom","index":4,"n_rows":9,"n_cols":6,"rows_kept":9}
[1,"= Current Zoom Level"]
["Level","Years","MajorTick","MinorTick","Shift","Connect"]
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[4,152,4,1,76,true]
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