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["Lunar Cycle Jitter:  Palmen-McKenna Calendar"]
["http://www.hermetic.ch/cal_stud/palmen/lunar13.htm"]
[{"$f":"\"Each lunar cycle contains \"&MPC&\" months (\"&FMPC&\" full, \"&DMPC&\" deficient) = \"&DPC&\" days = \"&reducefraction(DPC,7,FALSE,FALSE,TRUE)&\" weeks.\"","v":"Each lunar cycle contains 2418 months (1283 full, 1135 deficient) = 71405 days = 10200+5/7 weeks."}]
["Lunar years have 13 lunar months, even-numbered months have 29 days, odd-numbered"]
["months have 30 days, except that one day is removed from the last month of the lunar year if and only if"]
["(19 x year – 1) MOD 186 < 19.  Each calendar cycle contains two 186-year lunar cycles = 372 lunar years."]
[{"$f":"\"Mean month = \"&\"29+\"&reducefraction(FMPC,MPC,FALSE,FALSE,TRUE)&\" days = 29d 12h 44m and \"&reducefraction(240*(360*FMPC-191*MPC),MPC,FALSE,FALSE,TRUE)&\" seconds\"","v":"Mean month = 29+1283/2418 days = 29d 12h 44m and 4+68/403 seconds"}]
[{"$f":"\"or approximately 29\"&MID(FMPC/MPC,2,20)&\" days = 29d 12h 44m and \"&ROUND(240*(360*FMPC-191*MPC)/MPC,6)&\" seconds.\"","v":"or approximately 29.530603804797353 days = 29d 12h 44m and 4.168734 seconds."}]
[{"$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'' = 1/2418 day = 4/403 hour = 240/403 minutes = 35+295/403 seconds;  one hour = 100+3/4 parts."}]
[]
[{"$nulls":16},false]
{"$rows_empty":9}
[{"$nulls":16},13]
[{"$nulls":16},"Selected"]
[{"$nulls":16},"Month"]
[{"$nulls":16},"in Year"]
[{"$nulls":16},"(1 to 13)"]
{"$rows_empty":7}
[{"$nulls":16},2]
[{"$nulls":16},"Selected"]
[{"$nulls":16},"Month"]
[{"$nulls":16},"in Year"]
[{"$nulls":16},"(1 to 13)"]

{"sheet":"Data","index":1,"n_rows":4869,"n_cols":8,"rows_kept":4869}
["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":3293},"maximum",{"$f":"reducefraction(JitterMax*MPC,MPC,FALSE,FALSE,FALSE)","v":"3293"}]
["Months per Cycle (Parts per Day):",2418,"months (parts)",{"$f":"MIN(H:H)","v":-1135},"minimum",{"$f":"reducefraction(JitterMin*MPC,MPC,FALSE,FALSE,FALSE)","v":"–(1135)"}]
["30-day Months per Cycle:",1283,"months",{"$f":"D4-D5","v":4428},"range",{"$f":"reducefraction(JitterRange*MPC,MPC,FALSE,FALSE,FALSE)","v":"4428"}]
["29-day Months per Cycle:",{"$f":"MPC-FMPC","v":1135},"months",{"$f":"\"Jitter range = \"&F6&\" parts = \"&reducefraction(F6*24,MPC,FALSE,FALSE,FALSE)&\" hours\"","v":"Jitter range = 4428 parts = 43 + 383 / 403 hours"}]
["Days per Cycle (Parts per Month):",{"$f":"29*MPC+FMPC","v":71405},"days (parts)"]
[{"$nulls":3},"Limits for Chart:"]
["Mean Month:",{"$f":"\"29 + \"&reducefraction(FMPC,MPC,FALSE,FALSE,FALSE)","v":"29 + 1283 / 2418"},"days","x","y","Hours"]
["Mean Month >29d:",{"$f":"FMPC/MPC","v":{"v":0.5306038047973531,"d":"0.530603804797353"}},"days",{"$f":"A21","v":1},{"$f":"JitterMax","v":3293},{"$f":"E11*24/MPC","v":32.6848635235732}]
["Mean Month >29d 12h 44m:",{"$f":"reducefraction(240*(360*FMPC-191*MPC),MPC,FALSE,FALSE,TRUE)","v":"4+68/403"},"seconds",{"$f":"D11+MPC*2","v":4837},{"$f":"E11","v":3293},{"$f":"E12*24/MPC","v":32.6848635235732}]
["… or approximately:",{"$f":"240*(360*FMPC-191*MPC)/MPC","v":4.168734491315137},"seconds"]
[{"$nulls":3},{"$f":"D11","v":1},0]
[{"$nulls":3},{"$f":"D12","v":4837},0]
[]
[{"$nulls":3},{"$f":"A21","v":1},{"$f":"JitterMin","v":-1135},{"$f":"E17*24/MPC","v":-11.265508684863523}]
["Duration per Part:",{"$f":"reducefraction(1440,MPC,FALSE,FALSE,FALSE)","v":"240 / 403"},"minutes",{"$f":"D12","v":4837},{"$f":"E17","v":-1135},{"$f":"E18*24/MPC","v":-11.265508684863523}]
[]
["Month in Cycle","Lunar Year","Month in Year","Short Month?","Month Length","New Month Moment","Elapsed","Difference"]
[1,1,1,{"$f":"AND(C21=13,MOD(19*B21-1,186)<19)","v":false},{"$f":"IF(MOD(C21,2)=1,30,29)-IF(D21,1,0)","v":30},0,0,{"$f":"F21-G21","v":0}]
[{"$f":"A21+1","v":2},{"$f":"IF(C22=1,B21+1,B21)","v":1},{"$f":"IF(C21=13,1,C21+1)","v":2},{"$f":"AND(C22=13,MOD(19*B22-1,186)<19)","v":false},{"$f":"IF(MOD(C22,2)=1,30,29)-IF(D22,1,0)","v":29},{"$f":"F21+PPM","v":71405},{"$f":"G21+E21*PPD","v":72540},-1135]
[{"$f":"A22+1","v":3},1,{"$f":"IF(C22=13,1,C22+1)","v":3},false,30,{"$f":"F22+PPM","v":142810},142662,148]
[4,1,4,false,29,214215,215202,-987]
[5,1,5,false,30,285620,285324,296]
[6,1,6,false,29,357025,357864,-839]
[7,1,7,false,30,428430,427986,444]
[8,1,8,false,29,499835,500526,-691]
[9,1,9,false,30,571240,570648,592]
[10,1,10,false,29,642645,643188,-543]
[11,1,11,false,30,714050,713310,740]
[12,1,12,false,29,785455,785850,-395]
[13,1,13,true,29,856860,855972,888]
[14,2,1,false,30,928265,926094,2171]
[15,2,2,false,29,999670,998634,1036]
[16,2,3,false,30,1071075,1068756,2319]
[17,2,4,false,29,1142480,1141296,1184]
[18,2,5,false,30,1213885,1211418,2467]
[19,2,6,false,29,1285290,1283958,1332]
[20,2,7,false,30,1356695,1354080,2615]
[21,2,8,false,29,1428100,1426620,1480]
[22,2,9,false,30,1499505,1496742,2763]
[23,2,10,false,29,1570910,1569282,1628]
[24,2,11,false,30,1642315,1639404,2911]
[25,2,12,false,29,1713720,1711944,1776]
[26,2,13,false,30,1785125,1782066,3059]
[27,3,1,false,30,1856530,1854606,1924]
[28,3,2,false,29,1927935,1927146,789]
[29,3,3,false,30,1999340,1997268,2072]
[30,3,4,false,29,2070745,2069808,937]
[31,3,5,false,30,2142150,2139930,2220]
[32,3,6,false,29,2213555,2212470,1085]
[33,3,7,false,30,2284960,2282592,2368]
[34,3,8,false,29,2356365,2355132,1233]
[35,3,9,false,30,2427770,2425254,2516]
[{"$f":"A55+1","v":36},3,10,false,29,2499175,2497794,1381]
[37,3,11,false,30,2570580,2567916,2664]
[38,3,12,false,29,2641985,2640456,1529]
[39,3,13,false,30,2713390,2710578,2812]
[40,4,1,false,30,2784795,2783118,1677]
[41,4,2,false,29,2856200,2855658,542]
[42,4,3,false,30,2927605,2925780,1825]
[43,4,4,false,29,2999010,2998320,690]
[44,4,5,false,30,3070415,3068442,1973]
[45,4,6,false,29,3141820,3140982,838]
[46,4,7,false,30,3213225,3211104,2121]
[47,4,8,false,29,3284630,3283644,986]
[48,4,9,false,30,3356035,3353766,2269]
[49,4,10,false,29,3427440,3426306,1134]
[50,4,11,false,30,3498845,3496428,2417]
[51,4,12,false,29,3570250,3568968,1282]
[52,4,13,false,30,3641655,3639090,2565]
[53,5,1,false,30,3713060,3711630,1430]
[54,5,2,false,29,3784465,3784170,295]
[55,5,3,false,30,3855870,3854292,1578]
[56,5,4,false,29,3927275,3926832,443]
[57,5,5,false,30,3998680,3996954,1726]
[58,5,6,false,29,4070085,4069494,591]
[59,5,7,false,30,4141490,4139616,1874]
[60,5,8,false,29,4212895,4212156,739]
[61,5,9,false,30,4284300,4282278,2022]
[62,5,10,false,29,4355705,4354818,887]
[63,5,11,false,30,4427110,4424940,2170]
[64,5,12,false,29,4498515,4497480,1035]
[65,5,13,false,30,4569920,4567602,{"$f":"F85-G85","v":2318}]
[66,{"$f":"IF(C86=1,B85+1,B85)","v":6},1,{"$f":"AND(C86=13,MOD(19*B86-1,186)<19)","v":false},{"$f":"IF(MOD(C86,2)=1,30,29)-IF(D86,1,0)","v":30},4641325,{"$f":"G85+E85*PPD","v":4640142},1183]
[67,6,{"$f":"IF(C86=13,1,C86+1)","v":2},false,29,{"$f":"F86+PPM","v":4712730},4712682,48]
[68,6,3,false,30,4784135,4782804,1331]
[69,6,4,false,29,4855540,4855344,196]
[70,6,5,false,30,4926945,4925466,1479]
[71,6,6,false,29,4998350,4998006,344]
[72,6,7,false,30,5069755,5068128,1627]
[73,6,8,false,29,5141160,5140668,492]
[74,6,9,false,30,5212565,5210790,1775]
[75,6,10,false,29,5283970,5283330,640]
[76,6,11,false,30,5355375,5353452,1923]
[77,6,12,false,29,5426780,5425992,788]
[78,6,13,false,30,5498185,5496114,2071]
[79,7,1,false,30,5569590,5568654,936]
[80,7,2,false,29,5640995,5641194,-199]
[81,7,3,false,30,5712400,5711316,1084]
[82,7,4,false,29,5783805,5783856,-51]
[83,7,5,false,30,5855210,5853978,1232]
[84,7,6,false,29,5926615,5926518,97]
[85,7,7,false,30,5998020,5996640,1380]
[86,7,8,false,29,6069425,6069180,245]
[87,7,9,false,30,6140830,6139302,1528]
[88,7,10,false,29,6212235,6211842,393]
[89,7,11,false,30,6283640,6281964,1676]
[90,7,12,false,29,6355045,6354504,541]
[91,7,13,false,30,6426450,6424626,1824]
[92,8,1,false,30,6497855,6497166,689]
[93,8,2,false,29,6569260,6569706,-446]
[94,8,3,false,30,6640665,6639828,837]
[95,8,4,false,29,6712070,6712368,-298]
[96,8,5,false,30,6783475,6782490,985]
[97,8,6,false,29,6854880,6855030,-150]
[98,8,7,false,30,6926285,6925152,1133]
[99,8,8,false,29,6997690,6997692,-2]
[{"$f":"A119+1","v":100},8,9,false,30,7069095,7067814,1281]
[101,8,10,false,29,7140500,7140354,146]
[102,8,11,false,30,7211905,7210476,1429]
[103,8,12,false,29,7283310,7283016,294]
[104,8,13,false,30,7354715,7353138,1577]
[105,9,1,false,30,7426120,7425678,442]
[106,9,2,false,29,7497525,7498218,-693]
[107,9,3,false,30,7568930,7568340,590]
[108,9,4,false,29,7640335,7640880,-545]
[109,9,5,false,30,7711740,7711002,738]
[110,9,6,false,29,7783145,7783542,-397]
[111,9,7,false,30,7854550,7853664,886]
[112,9,8,false,29,7925955,7926204,-249]
[113,9,9,false,30,7997360,7996326,1034]
[114,9,10,false,29,8068765,8068866,-101]
[115,9,11,false,30,8140170,8138988,1182]
[116,9,12,false,29,8211575,8211528,47]
[117,9,13,false,30,8282980,8281650,1330]
[118,10,1,false,30,8354385,8354190,195]
[119,10,2,false,29,8425790,8426730,-940]
[120,10,3,false,30,8497195,8496852,343]
[121,10,4,false,29,8568600,8569392,-792]
[122,10,5,false,30,8640005,8639514,491]
[123,10,6,false,29,8711410,8712054,-644]
[124,10,7,false,30,8782815,8782176,639]
[125,10,8,false,29,8854220,8854716,-496]
[126,10,9,false,30,8925625,8924838,787]
[127,10,10,false,29,8997030,8997378,-348]
[128,10,11,false,30,9068435,9067500,935]
[129,10,12,false,29,9139840,9140040,{"$f":"F149-G149","v":-200}]
[130,{"$f":"IF(C150=1,B149+1,B149)","v":10},13,{"$f":"AND(C150=13,MOD(19*B150-1,186)<19)","v":true},{"$f":"IF(MOD(C150,2)=1,30,29)-IF(D150,1,0)","v":29},9211245,{"$f":"G149+E149*PPD","v":9210162},1083]
[131,11,{"$f":"IF(C150=13,1,C150+1)","v":1},false,30,{"$f":"F150+PPM","v":9282650},9280284,2366]
[132,11,2,false,29,9354055,9352824,1231]
[133,11,3,false,30,9425460,9422946,2514]
[134,11,4,false,29,9496865,9495486,1379]
[135,11,5,false,30,9568270,9565608,2662]
[136,11,6,false,29,9639675,9638148,1527]
[137,11,7,false,30,9711080,9708270,2810]
[138,11,8,false,29,9782485,9780810,1675]
[139,11,9,false,30,9853890,9850932,2958]
[140,11,10,false,29,9925295,9923472,1823]
[141,11,11,false,30,9996700,9993594,3106]
[142,11,12,false,29,10068105,10066134,1971]
[143,11,13,false,30,10139510,10136256,3254]
[144,12,1,false,30,10210915,10208796,2119]
[145,12,2,false,29,10282320,10281336,984]
[146,12,3,false,30,10353725,10351458,2267]
[147,12,4,false,29,10425130,10423998,1132]
[148,12,5,false,30,10496535,10494120,2415]
[149,12,6,false,29,10567940,10566660,1280]
[150,12,7,false,30,10639345,10636782,2563]
[151,12,8,false,29,10710750,10709322,1428]
[152,12,9,false,30,10782155,10779444,2711]
[153,12,10,false,29,10853560,10851984,1576]
[154,12,11,false,30,10924965,10922106,2859]
[155,12,12,false,29,10996370,10994646,1724]
[156,12,13,false,30,11067775,11064768,3007]
[157,13,1,false,30,11139180,11137308,1872]
[158,13,2,false,29,11210585,11209848,737]
[159,13,3,false,30,11281990,11279970,2020]
[160,13,4,false,29,11353395,11352510,885]
[161,13,5,false,30,11424800,11422632,2168]
[162,13,6,false,29,11496205,11495172,1033]
[163,13,7,false,30,11567610,11565294,2316]
[{"$f":"A183+1","v":164},13,8,false,29,11639015,11637834,1181]
[165,13,9,false,30,11710420,11707956,2464]
[166,13,10,false,29,11781825,11780496,1329]
[167,13,11,false,30,11853230,11850618,2612]
[168,13,12,false,29,11924635,11923158,1477]
[169,13,13,false,30,11996040,11993280,2760]
[170,14,1,false,30,12067445,12065820,1625]
[171,14,2,false,29,12138850,12138360,490]
[172,14,3,false,30,12210255,12208482,1773]
[173,14,4,false,29,12281660,12281022,638]
[174,14,5,false,30,12353065,12351144,1921]
[175,14,6,false,29,12424470,12423684,786]
[176,14,7,false,30,12495875,12493806,2069]
[177,14,8,false,29,12567280,12566346,934]
[178,14,9,false,30,12638685,12636468,2217]
[179,14,10,false,29,12710090,12709008,1082]
[180,14,11,false,30,12781495,12779130,2365]
[181,14,12,false,29,12852900,12851670,1230]
[182,14,13,false,30,12924305,12921792,2513]
[183,15,1,false,30,12995710,12994332,1378]
[184,15,2,false,29,13067115,13066872,243]
[185,15,3,false,30,13138520,13136994,1526]
[186,15,4,false,29,13209925,13209534,391]
[187,15,5,false,30,13281330,13279656,1674]
[188,15,6,false,29,13352735,13352196,539]
[189,15,7,false,30,13424140,13422318,1822]
[190,15,8,false,29,13495545,13494858,687]
[191,15,9,false,30,13566950,13564980,1970]
[192,15,10,false,29,13638355,13637520,835]
[193,15,11,false,30,13709760,13707642,{"$f":"F213-G213","v":2118}]
[194,{"$f":"IF(C214=1,B213+1,B213)","v":15},12,{"$f":"AND(C214=13,MOD(19*B214-1,186)<19)","v":false},{"$f":"IF(MOD(C214,2)=1,30,29)-IF(D214,1,0)","v":29},13781165,{"$f":"G213+E213*PPD","v":13780182},983]
[195,15,{"$f":"IF(C214=13,1,C214+1)","v":13},false,30,{"$f":"F214+PPM","v":13852570},13850304,2266]
[196,16,1,false,30,13923975,13922844,1131]
[197,16,2,false,29,13995380,13995384,-4]
[198,16,3,false,30,14066785,14065506,1279]
[199,16,4,false,29,14138190,14138046,144]
[200,16,5,false,30,14209595,14208168,1427]
[201,16,6,false,29,14281000,14280708,292]
[202,16,7,false,30,14352405,14350830,1575]
[203,16,8,false,29,14423810,14423370,440]
[204,16,9,false,30,14495215,14493492,1723]
[205,16,10,false,29,14566620,14566032,588]
[206,16,11,false,30,14638025,14636154,1871]
[207,16,12,false,29,14709430,14708694,736]
[208,16,13,false,30,14780835,14778816,2019]
[209,17,1,false,30,14852240,14851356,884]
[210,17,2,false,29,14923645,14923896,-251]
[211,17,3,false,30,14995050,14994018,1032]
[212,17,4,false,29,15066455,15066558,-103]
[213,17,5,false,30,15137860,15136680,1180]
[214,17,6,false,29,15209265,15209220,45]
[215,17,7,false,30,15280670,15279342,1328]
[216,17,8,false,29,15352075,15351882,193]
[217,17,9,false,30,15423480,15422004,1476]
[218,17,10,false,29,15494885,15494544,341]
[219,17,11,false,30,15566290,15564666,1624]
[220,17,12,false,29,15637695,15637206,489]
[221,17,13,false,30,15709100,15707328,1772]
[222,18,1,false,30,15780505,15779868,637]
[223,18,2,false,29,15851910,15852408,-498]
[224,18,3,false,30,15923315,15922530,785]
[225,18,4,false,29,15994720,15995070,-350]
[226,18,5,false,30,16066125,16065192,933]
[227,18,6,false,29,16137530,16137732,-202]
[{"$f":"A247+1","v":228},18,7,false,30,16208935,16207854,1081]
[229,18,8,false,29,16280340,16280394,-54]
[230,18,9,false,30,16351745,16350516,1229]
[231,18,10,false,29,16423150,16423056,94]
[232,18,11,false,30,16494555,16493178,1377]
[233,18,12,false,29,16565960,16565718,242]
[234,18,13,false,30,16637365,16635840,1525]
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[4805,370,8,false,29,343029620,343029570,50]
[4806,370,9,false,30,343101025,343099692,1333]
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[4818,371,8,false,29,343957885,343958082,-197]
[4819,371,9,false,30,344029290,344028204,1086]
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[4821,371,11,false,30,344172100,344170866,1234]
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{"sheet":"Rules","index":2,"n_rows":9,"n_cols":3,"rows_kept":9}
["lunar year has 13 months"]
["odd-numbered months have 30 days, even numbered months have 29 days"]
["so common years have 7 full months and 6 deficient months"]
["length of common year =",{"$f":"6*29+7*30","v":384},"days"]
["in short years remove one day from 13th month = 383 days"]
["A lunar year is short if it has two occurrences of either of:"]
["-- Solar date Month 1 Date 1 (new solar year)  OR"]
["-- Solar date Month 7 Date 1 (half solar year) "]
["A lunar year y is short if and only if (19*y-1) mod 186 < 19"]

{"sheet":"Years","index":3,"n_rows":374,"n_cols":5,"rows_kept":374}
["Month in Cycle","Lunar Year","New Year Moment","Elapsed","Difference"]
[{"$f":"StartMonth","v":13},1,{"$f":"(A2-1)*PPM","v":856860},{"$f":"LOOKUP(A2,Data!A$21:A$4869,Data!G$21:G$4869)","v":855972},{"$f":"C2-D2","v":888}]
[{"$f":"A2+13","v":26},{"$f":"B2+1","v":2},{"$f":"(A3-1)*PPM","v":1785125},{"$f":"LOOKUP(A3,Data!A$21:A$4869,Data!G$21:G$4869)","v":1782066},{"$f":"C3-D3","v":3059}]
[{"$f":"A3+13","v":39},{"$f":"B3+1","v":3},2713390,{"$f":"LOOKUP(A4,Data!A$21:A$4869,Data!G$21:G$4869)","v":2710578},2812]
[52,4,3641655,{"$f":"LOOKUP(A5,Data!A$21:A$4869,Data!G$21:G$4869)","v":3639090},2565]
[65,5,4569920,{"$f":"LOOKUP(A6,Data!A$21:A$4869,Data!G$21:G$4869)","v":4567602},2318]
[78,6,5498185,{"$f":"LOOKUP(A7,Data!A$21:A$4869,Data!G$21:G$4869)","v":5496114},2071]
[91,7,6426450,{"$f":"LOOKUP(A8,Data!A$21:A$4869,Data!G$21:G$4869)","v":6424626},1824]
[104,8,7354715,{"$f":"LOOKUP(A9,Data!A$21:A$4869,Data!G$21:G$4869)","v":7353138},1577]
[117,9,8282980,{"$f":"LOOKUP(A10,Data!A$21:A$4869,Data!G$21:G$4869)","v":8281650},1330]
[130,10,9211245,{"$f":"LOOKUP(A11,Data!A$21:A$4869,Data!G$21:G$4869)","v":9210162},1083]
[143,11,10139510,{"$f":"LOOKUP(A12,Data!A$21:A$4869,Data!G$21:G$4869)","v":10136256},3254]
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{"sheet":"Years2","index":4,"n_rows":374,"n_cols":5,"rows_kept":374}
["Month in Cycle","Lunar Year","New Year Moment","Elapsed","Difference"]
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