{"text_format":"3","workbook":"xlsx","n_sheets":6,"sheets":["Chart","Data","Years","Years2","Zoom","Labels"],"not_rendered":{"charts":1,"macros":1,"external_links":1,"defined_names":19},"read":"whole","date_system":"1900"}

{"sheet":"Chart","index":0,"n_rows":48,"n_cols":17,"rows_kept":48}
["Javanese Lunar Calendar (Windu) Jitter Relative to Mean Month"]
[]
[{"$f":"\"Each lunar year (tahun) has 12 months.  Lunar cycle contains \"&MPC&\" months (\"&FMPC&\" full, \"&DMPC&\" deficient)\"","v":"Each lunar year (tahun) has 12 months.  Lunar cycle contains 1440 months (764 full, 676 deficient)"}]
[{"$f":"\"= \"&DPC&\" days = \"&reducefraction(DPC,7,FALSE,FALSE,TRUE)&\" weeks = \"&MPC/12&\" tahun = \"&MPC/96&\" windu.\"&IF(Reverse,\"  After a common year odd-numbered\",)","v":"= 42524 days = 6074+6/7 weeks = 120 tahun = 15 windu."}]
[{"$f":"IF(Reverse,,\"Odd-numbered \")&\"months have 30 days, even-numbered months have 29 days.\"&IF(Reverse,\"  After a leap year odd-numbered months have 29 days, even-numbered\",)","v":"Odd-numbered months have 30 days, even-numbered months have 29 days."}]
[{"$f":"IF(Reverse,\"months have 30 days.  \",)&\"Year y is a leap year if and only if (3y + \"&Offset&\") MOD 8 < 3, in which case the 12th month has 30 days.\"","v":"Year y is a leap year if and only if (3y + 0) MOD 8 < 3, in which case the 12th month has 30 days."}]
[{"$f":"\"Leap years in each cycle are: \"&javanese_leap_years(Offset)&\".  Common years = FDFDFDFDFDFD\"&IF(Reverse,\" or DFDFDFDFDFDF\",)&\" = 354 days.\"","v":"Leap years in each cycle are: 3, 6, 8.  Common years = FDFDFDFDFDFD = 354 days."}]
[{"$f":"\"Leap years = FDFDFDFDFDFF = 355 days.\"","v":"Leap years = FDFDFDFDFDFF = 355 days."},{"$nulls":5},"In this variant the 120th year of cycle is a common year."]
[{"$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+191/360 days = 29d 12h 44m 0 seconds, or about 29.530555555555556 days or 29d 12h 44m 0 seconds."}]
[{"$f":"\"Duration per ''Part'' = 1/\"&MPC&\" day = \"&reducefraction(24,MPC,FALSE,FALSE,TRUE)&\" hour = \"&reducefraction(1440,MPC,FALSE,FALSE,TRUE)&\" minutes = \"&reducefraction(86400,MPC,FALSE,FALSE,TRUE)&\" seconds.  One hour = \"&reducefraction(MPC,24,FALSE,FALSE,TRUE)&\" parts.\"","v":"Duration per ''Part'' = 1/1440 day = 1/60 hour = 1 minutes = 60 seconds.  One hour = 60 parts."}]
[]
[{"$nulls":16},false]
{"$rows_empty":8}
[{"$nulls":16},9]
[{"$nulls":16},"Selected"]
[{"$nulls":16},"Month"]
[{"$nulls":16},"in Year"]
[{"$nulls":16},"(1 to 12)"]
[]
[]
[]
[]
[]
[]
[{"$nulls":16},6]
[{"$nulls":16},"Selected"]
[{"$nulls":16},"Month 2"]
[{"$nulls":16},"in Year"]
[{"$nulls":16},"(1 to 12)"]
{"$rows_empty":7}
[{"$nulls":16},0]
[{"$nulls":16},"Leap"]
[{"$nulls":16},"Rule"]
[{"$nulls":16},"Offset"]
[{"$nulls":16},"(0 to 7)"]

{"sheet":"Data","index":1,"n_rows":2914,"n_cols":9,"rows_kept":2914}
["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":1640},"maximum",{"$f":"reducefraction(JitterMax*MPC,MPC,FALSE,FALSE,FALSE)","v":"1640"}]
["Months per Cycle (Parts per Day):",{"$f":"12*8*15","v":1440},"months (parts)",{"$f":"MIN(H:H)","v":-2020},"minimum",{"$f":"reducefraction(JitterMin*MPC,MPC,FALSE,FALSE,FALSE)","v":"–(2020)"}]
["30-day Months per Cycle:",{"$f":"(6*8+3)*15-1","v":764},"months",{"$f":"D4-D5","v":3660},"range",{"$f":"reducefraction(JitterRange*MPC,MPC,FALSE,FALSE,FALSE)","v":"3660"}]
["29-day Months per Cycle:",{"$f":"MPC-FMPC","v":676},"months",{"$f":"\"Jitter range = \"&F6&\" parts = \"&reducefraction(F6*24,MPC,FALSE,FALSE,FALSE)&\" hours\"","v":"Jitter range = 3660 parts = 61 hours"}]
["Days per Cycle (Parts per Month):",{"$f":"29*MPC+FMPC","v":42524},"days (parts)"]
["Yerms per Cycle:",{"$f":"2*DPC-59*MPC","v":88},"yerms","Limits for Chart:"]
["Mean Month:",{"$f":"\"29 + \"&reducefraction(FMPC,MPC,FALSE,FALSE,FALSE)","v":"29 + 191 / 360"},"days","x","y","Hours"]
["Mean Month >29d:",{"$f":"FMPC/MPC","v":{"v":0.5305555555555556,"d":"0.530555555555556"}},"days",{"$f":"B23","v":1},{"$f":"JitterMax","v":1640},{"$f":"E11*24/MPC","v":27.333333333333332}]
["Mean Month >29d 12h 44m:",{"$f":"reducefraction(240*(360*FMPC-191*MPC),MPC,FALSE,FALSE,TRUE)","v":"0"},"seconds",{"$f":"2*MPC+1","v":2881},{"$f":"E11","v":1640},{"$f":"E12*24/MPC","v":27.333333333333332}]
["… or approximately:",{"$f":"240*(360*FMPC-191*MPC)/MPC","v":0},"seconds"]
[{"$nulls":3},{"$f":"D11","v":1},0]
[{"$nulls":3},{"$f":"D12","v":2881},0]
[]
[{"$nulls":3},{"$f":"B23","v":1},{"$f":"JitterMin","v":-2020},{"$f":"E17*24/MPC","v":-33.666666666666664}]
["Duration per Part:",{"$f":"reducefraction(1440,MPC,FALSE,FALSE,FALSE)","v":"1"},"minutes",{"$f":"D12","v":2881},{"$f":"E17","v":-2020},{"$f":"E18*24/MPC","v":-33.666666666666664}]
["Offset:",{"$f":"Offset","v":0}]
["Leap Years:",{"$f":"javanese_leap_years(Offset)","v":"3, 6, 8"},"except last year of 15x8=120 year cycle",{"$nulls":5},"Reverse"]
[{"$nulls":8},false]
["Year","Month #","Month in Year","Leap Month?","Month Length","New Month Moment","Elapsed","Difference","Prior Leap"]
[1,1,1,{"$f":"AND(C23=12,AND(MOD(A23,120)<>0,MOD(A23*3+Offset,8)<3))","v":false},{"$f":"IF(MOD(C23,2)=1,IF(I23,29,30),IF(I23,30,29))+IF(D23,1,0)","v":30},0,0,{"$f":"F23-G23","v":0},{"$f":"IF(Reverse,AND(MOD(A23-1,120)<>0,MOD((A23-1)*3+Offset,8)<3),FALSE)","v":false}]
[{"$f":"IF(C24=1,A23+1,A23)","v":1},{"$f":"B23+1","v":2},{"$f":"IF(C23=12,1,C23+1)","v":2},{"$f":"AND(C24=12,AND(MOD(A24,120)<>0,MOD(A24*3+Offset,8)<3))","v":false},{"$f":"IF(MOD(C24,2)=1,IF(I24,29,30),IF(I24,30,29))+IF(D24,1,0)","v":29},{"$f":"F23+PPM","v":42524},{"$f":"G23+E23*PPD","v":43200},{"$f":"F24-G24","v":-676},{"$f":"IF(Reverse,AND(MOD(A24-1,120)<>0,MOD((A24-1)*3+Offset,8)<3),FALSE)","v":false}]
[{"$f":"IF(C25=1,A24+1,A24)","v":1},{"$f":"B24+1","v":3},{"$f":"IF(C24=12,1,C24+1)","v":3},{"$f":"AND(C25=12,AND(MOD(A25,120)<>0,MOD(A25*3+Offset,8)<3))","v":false},{"$f":"IF(MOD(C25,2)=1,IF(I25,29,30),IF(I25,30,29))+IF(D25,1,0)","v":30},85048,84960,{"$f":"F25-G25","v":88},{"$f":"IF(Reverse,AND(MOD(A25-1,120)<>0,MOD((A25-1)*3+Offset,8)<3),FALSE)","v":false}]
[1,4,4,false,29,127572,128160,-588,false]
[1,5,5,false,30,170096,169920,176,false]
[1,6,6,false,29,212620,213120,-500,false]
[1,7,7,false,30,255144,254880,264,false]
[1,8,8,false,29,297668,298080,-412,false]
[1,9,9,false,30,340192,339840,352,false]
[1,10,10,false,29,382716,383040,-324,false]
[1,11,11,false,30,425240,424800,440,false]
[1,12,12,false,29,467764,468000,-236,false]
[2,13,1,false,30,510288,509760,528,false]
[2,14,2,false,29,552812,552960,-148,false]
[2,15,3,false,30,595336,594720,616,false]
[2,16,4,false,29,637860,637920,-60,false]
[2,17,5,false,30,680384,679680,704,false]
[2,18,6,false,29,722908,722880,28,false]
[2,19,7,false,30,765432,764640,792,false]
[2,20,8,false,29,807956,807840,116,false]
[2,21,9,false,30,850480,849600,880,false]
[2,22,10,false,29,893004,892800,204,false]
[2,23,11,false,30,935528,934560,968,false]
[2,24,12,false,29,978052,977760,292,false]
[3,25,1,false,30,1020576,1019520,1056,false]
[3,26,2,false,29,1063100,1062720,380,false]
[3,27,3,false,30,1105624,1104480,1144,false]
[3,28,4,false,29,1148148,1147680,468,false]
[3,29,5,false,30,1190672,1189440,1232,false]
[3,30,6,false,29,1233196,1232640,556,false]
[3,31,7,false,30,1275720,1274400,1320,false]
[3,32,8,false,29,1318244,1317600,644,false]
[3,33,9,false,30,1360768,1359360,1408,false]
[3,34,10,false,29,1403292,1402560,732,false]
[3,35,11,false,30,1445816,1444320,1496,false]
[3,36,12,true,30,1488340,1487520,820,false]
[4,37,1,false,30,1530864,1530720,144,false]
[4,38,2,false,29,1573388,1573920,-532,false]
[4,39,3,false,30,1615912,1615680,232,false]
[4,40,4,false,29,1658436,1658880,-444,false]
[4,41,5,false,30,1700960,1700640,320,false]
[4,42,6,false,29,1743484,1743840,-356,false]
[4,43,7,false,30,1786008,1785600,408,false]
[4,44,8,false,29,1828532,1828800,-268,false]
[4,45,9,false,30,1871056,1870560,496,false]
[4,46,10,false,29,1913580,1913760,-180,false]
[4,47,11,false,30,1956104,1955520,584,false]
[4,48,12,false,29,1998628,1998720,-92,false]
[5,49,1,false,30,2041152,2040480,672,false]
[5,50,2,false,29,2083676,2083680,-4,false]
[5,51,3,false,30,2126200,2125440,760,false]
[5,52,4,false,29,2168724,2168640,84,false]
[5,53,5,false,30,2211248,2210400,848,false]
[5,54,6,false,29,2253772,2253600,172,false]
[5,55,7,false,30,2296296,2295360,936,false]
[5,56,8,false,29,2338820,2338560,260,false]
[5,57,9,false,30,2381344,2380320,1024,false]
[5,58,10,false,29,2423868,2423520,348,false]
[5,59,11,false,30,2466392,2465280,1112,false]
[5,60,12,false,29,2508916,2508480,436,false]
[6,61,1,false,30,2551440,2550240,1200,false]
[6,62,2,false,29,2593964,2593440,524,false]
[6,63,3,false,30,2636488,2635200,1288,false]
[6,64,4,false,29,2679012,2678400,612,false]
[6,65,5,false,30,2721536,2720160,1376,false]
[6,66,6,false,29,{"$f":"F87+PPM","v":2764060},{"$f":"G87+E87*PPD","v":2763360},700,false]
[{"$f":"IF(C89=1,A88+1,A88)","v":6},{"$f":"B88+1","v":67},{"$f":"IF(C88=12,1,C88+1)","v":7},{"$f":"AND(C89=12,AND(MOD(A89,120)<>0,MOD(A89*3+Offset,8)<3))","v":false},{"$f":"IF(MOD(C89,2)=1,IF(I89,29,30),IF(I89,30,29))+IF(D89,1,0)","v":30},2806584,2805120,{"$f":"F89-G89","v":1464},{"$f":"IF(Reverse,AND(MOD(A89-1,120)<>0,MOD((A89-1)*3+Offset,8)<3),FALSE)","v":false}]
[6,68,8,false,29,2849108,2848320,788,false]
[6,69,9,false,30,2891632,2890080,1552,false]
[6,70,10,false,29,2934156,2933280,876,false]
[6,71,11,false,30,2976680,2975040,1640,false]
[6,72,12,true,30,3019204,3018240,964,false]
[7,73,1,false,30,3061728,3061440,288,false]
[7,74,2,false,29,3104252,3104640,-388,false]
[7,75,3,false,30,3146776,3146400,376,false]
[7,76,4,false,29,3189300,3189600,-300,false]
[7,77,5,false,30,3231824,3231360,464,false]
[7,78,6,false,29,3274348,3274560,-212,false]
[7,79,7,false,30,3316872,3316320,552,false]
[7,80,8,false,29,3359396,3359520,-124,false]
[7,81,9,false,30,3401920,3401280,640,false]
[7,82,10,false,29,3444444,3444480,-36,false]
[7,83,11,false,30,3486968,3486240,728,false]
[7,84,12,false,29,3529492,3529440,52,false]
[8,85,1,false,30,3572016,3571200,816,false]
[8,86,2,false,29,3614540,3614400,140,false]
[8,87,3,false,30,3657064,3656160,904,false]
[8,88,4,false,29,3699588,3699360,228,false]
[8,89,5,false,30,3742112,3741120,992,false]
[8,90,6,false,29,3784636,3784320,316,false]
[8,91,7,false,30,3827160,3826080,1080,false]
[8,92,8,false,29,3869684,3869280,404,false]
[8,93,9,false,30,3912208,3911040,1168,false]
[8,94,10,false,29,3954732,3954240,492,false]
[8,95,11,false,30,3997256,3996000,1256,false]
[8,96,12,true,30,4039780,4039200,580,false]
[9,97,1,false,30,4082304,4082400,-96,false]
[9,98,2,false,29,4124828,4125600,-772,false]
[9,99,3,false,30,4167352,4167360,-8,false]
[9,100,4,false,29,4209876,4210560,-684,false]
[9,101,5,false,30,4252400,4252320,80,false]
[9,102,6,false,29,4294924,4295520,-596,false]
[9,103,7,false,30,4337448,4337280,168,false]
[9,104,8,false,29,4379972,4380480,-508,false]
[9,105,9,false,30,4422496,4422240,256,false]
[9,106,10,false,29,4465020,4465440,-420,false]
[9,107,11,false,30,4507544,4507200,344,false]
[9,108,12,false,29,4550068,4550400,-332,false]
[10,109,1,false,30,4592592,4592160,432,false]
[10,110,2,false,29,4635116,4635360,-244,false]
[10,111,3,false,30,4677640,4677120,520,false]
[10,112,4,false,29,4720164,4720320,-156,false]
[10,113,5,false,30,4762688,4762080,608,false]
[10,114,6,false,29,4805212,4805280,-68,false]
[10,115,7,false,30,4847736,4847040,696,false]
[10,116,8,false,29,4890260,4890240,20,false]
[10,117,9,false,30,4932784,4932000,784,false]
[10,118,10,false,29,4975308,4975200,108,false]
[10,119,11,false,30,5017832,5016960,872,false]
[10,120,12,false,29,5060356,5060160,196,false]
[11,121,1,false,30,5102880,5101920,960,false]
[11,122,2,false,29,5145404,5145120,284,false]
[11,123,3,false,30,5187928,5186880,1048,false]
[11,124,4,false,29,5230452,5230080,372,false]
[11,125,5,false,30,5272976,5271840,1136,false]
[11,126,6,false,29,5315500,5315040,460,false]
[11,127,7,false,30,5358024,5356800,1224,false]
[11,128,8,false,29,5400548,5400000,548,false]
[11,129,9,false,30,5443072,5441760,1312,false]
[11,130,10,false,29,{"$f":"F151+PPM","v":5485596},{"$f":"G151+E151*PPD","v":5484960},636,false]
[{"$f":"IF(C153=1,A152+1,A152)","v":11},{"$f":"B152+1","v":131},{"$f":"IF(C152=12,1,C152+1)","v":11},{"$f":"AND(C153=12,AND(MOD(A153,120)<>0,MOD(A153*3+Offset,8)<3))","v":false},{"$f":"IF(MOD(C153,2)=1,IF(I153,29,30),IF(I153,30,29))+IF(D153,1,0)","v":30},5528120,5526720,{"$f":"F153-G153","v":1400},{"$f":"IF(Reverse,AND(MOD(A153-1,120)<>0,MOD((A153-1)*3+Offset,8)<3),FALSE)","v":false}]
[11,132,12,true,30,5570644,5569920,724,false]
[12,133,1,false,30,5613168,5613120,48,false]
[12,134,2,false,29,5655692,5656320,-628,false]
[12,135,3,false,30,5698216,5698080,136,false]
[12,136,4,false,29,5740740,5741280,-540,false]
[12,137,5,false,30,5783264,5783040,224,false]
[12,138,6,false,29,5825788,5826240,-452,false]
[12,139,7,false,30,5868312,5868000,312,false]
[12,140,8,false,29,5910836,5911200,-364,false]
[12,141,9,false,30,5953360,5952960,400,false]
[12,142,10,false,29,5995884,5996160,-276,false]
[12,143,11,false,30,6038408,6037920,488,false]
[12,144,12,false,29,6080932,6081120,-188,false]
[13,145,1,false,30,6123456,6122880,576,false]
[13,146,2,false,29,6165980,6166080,-100,false]
[13,147,3,false,30,6208504,6207840,664,false]
[13,148,4,false,29,6251028,6251040,-12,false]
[13,149,5,false,30,6293552,6292800,752,false]
[13,150,6,false,29,6336076,6336000,76,false]
[13,151,7,false,30,6378600,6377760,840,false]
[13,152,8,false,29,6421124,6420960,164,false]
[13,153,9,false,30,6463648,6462720,928,false]
[13,154,10,false,29,6506172,6505920,252,false]
[13,155,11,false,30,6548696,6547680,1016,false]
[13,156,12,false,29,6591220,6590880,340,false]
[14,157,1,false,30,6633744,6632640,1104,false]
[14,158,2,false,29,6676268,6675840,428,false]
[14,159,3,false,30,6718792,6717600,1192,false]
[14,160,4,false,29,6761316,6760800,516,false]
[14,161,5,false,30,6803840,6802560,1280,false]
[14,162,6,false,29,6846364,6845760,604,false]
[14,163,7,false,30,6888888,6887520,1368,false]
[14,164,8,false,29,6931412,6930720,692,false]
[14,165,9,false,30,6973936,6972480,1456,false]
[14,166,10,false,29,7016460,7015680,780,false]
[14,167,11,false,30,7058984,7057440,1544,false]
[14,168,12,true,30,7101508,7100640,868,false]
[15,169,1,false,30,7144032,7143840,192,false]
[15,170,2,false,29,7186556,7187040,-484,false]
[15,171,3,false,30,7229080,7228800,280,false]
[15,172,4,false,29,7271604,7272000,-396,false]
[15,173,5,false,30,7314128,7313760,368,false]
[15,174,6,false,29,7356652,7356960,-308,false]
[15,175,7,false,30,7399176,7398720,456,false]
[15,176,8,false,29,7441700,7441920,-220,false]
[15,177,9,false,30,7484224,7483680,544,false]
[15,178,10,false,29,7526748,7526880,-132,false]
[15,179,11,false,30,7569272,7568640,632,false]
[15,180,12,false,29,7611796,7611840,-44,false]
[16,181,1,false,30,7654320,7653600,720,false]
[16,182,2,false,29,7696844,7696800,44,false]
[16,183,3,false,30,7739368,7738560,808,false]
[16,184,4,false,29,7781892,7781760,132,false]
[16,185,5,false,30,7824416,7823520,896,false]
[16,186,6,false,29,7866940,7866720,220,false]
[16,187,7,false,30,7909464,7908480,984,false]
[16,188,8,false,29,7951988,7951680,308,false]
[16,189,9,false,30,7994512,7993440,1072,false]
[16,190,10,false,29,8037036,8036640,396,false]
[16,191,11,false,30,8079560,8078400,1160,false]
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[0,"= Current Zoom Level"]
["Level","Months","MajorTick","MinorTick","Shift","Connect","Years","YearsMajor","YearsMinor"]
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[3,{"$f":"B5/2","v":360},24,6,180,false,30,2,1]
[4,{"$f":"B6/2","v":180},12,3,96,true,15,1,1]
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[7,{"$f":"B9/2","v":24},2,1,12,true,2,1,1]
[8,{"$f":"B10/2","v":12},1,1,12,true,1,1,1]

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