{"text_format":"3","workbook":"xlsx","n_sheets":16,"sheets":["Setup","Lunar","Yerm1","Yerm2","Yerm3","Yerm4","Lunar_Cycles","Yerm1_Cycles","Yerm2_Cycles","Yerm3_Cycles","Yerm4_Cycles","Lunar_Data","Yerm1_Data","Yerm2_Data","Yerm3_Data","Yerm4_Data"],"not_rendered":{"charts":10,"macros":1,"defined_names":7},"unopened":[{"sheet":"Lunar","index":1,"reason":"not_a_worksheet"},{"sheet":"Yerm1","index":2,"reason":"not_a_worksheet"},{"sheet":"Yerm2","index":3,"reason":"not_a_worksheet"},{"sheet":"Yerm3","index":4,"reason":"not_a_worksheet"},{"sheet":"Yerm4","index":5,"reason":"not_a_worksheet"}],"read":"whole","date_system":"1900"}

{"sheet":"Setup","index":0,"n_rows":32,"n_cols":6,"rows_kept":32}
["Lunar Calendar Drift Calculator and Graphing Spreadsheet"]
["version 2.05(23), revised 2022 Jul 11"]
[]
["by Dr. Irv Bromberg, University of Toronto, Canada"]
["http://individual.utoronto.ca/kalendis/lunar/"]
[]
["Delta T Multiplier: ",1,"1=normal, 0 to <1 = less Earth rotation slowing, >1 to 2 = more Earth rotation slowing"]
["Shift Step Size: ",1000,"years (minimum step size is 500 years)"]
[]
["Chart Sheet Name: ","Lunar","Yerm1","Yerm2","Yerm3","Yerm4"]
["Zero Reference Year: ",0,-1000,2000,6000,10000]
[null,"All cycles have zero drift at the zero reference year, as if it is a calendar epoch."]
[]
[]
[]
["Spreadsheet ","Description"]
["Lunar ","Lunar calendar drift chart"]
["Lunar_Cycles ","Lunar cycles evaluated"]
["Lunar_Data ","Data generated for chart."]
["Yerm# ","Yerm cycles chart (where # is a digit from 1 to 4 from longest to shortest mean month)"]
["Yerm#_Cycles ","Palmen-Meyer yerm cycles, useful for near present era"]
["Yerm#_Data ","Data generated for chart."]
[]
["(Don't rename any sheets, the macros expect them to have the names as assigned.)"]
[]
["Positive drift values correspond to lunar calendar running late relative to the lunar cycle."]
["If a lunar cycle is not wanted then delete its row from the list (don't leave a blank row), and delete its series from its chart."]
["If an additional cycle is wanted then insert it in the list (keep the list sorted descending excess seconds)"]
["and add a series for it to the appropriate chart, pointing to where the new column of data is (or will go)."]
[]
["If desired, change the chart y-axes and x-axes to expand or contract the range displayed."]
["There is no point is making the x-axis wider than the validated limits of the mean astronomical polynomials."]

{"sheet":"Lunar_Cycles","index":6,"n_rows":22,"n_cols":3,"rows_kept":22}
["Description","Seconds *","Comments"]
["Orthodox Easter",{"$f":"1200/47","v":25.53191489361702},"For Julian calendar, mean month = (365+1/4) x 19/235 = 29+499/940 days (very rapid drift)"]
["Gregorian epoch",{"$f":"3+303/779","v":3.3889602053915278},"January 1, 1 AD:  mean month = 29+1240/2337 days = 29d 12h 44m 3+303/779s"]
["Hebrew molad",{"$f":"60/18","v":3.3333333333333335},"1586 yerms with mean month = 29+13753/25920 days = 29d 12h 44m 3+1/3s"]
["Yerm Lunar calendar",{"$f":"2+14/17","v":2.8235294117647056},"52 yerms with mean month = 29+451/850 days = 29d 12h 44m 2+14/17s"]
["Hindu Surya",{"$f":"86400*(7087771/13358334-12/24-44/1440)","v":2.7985405964542465},"Modern Hindu lunisolar, mean month = 29+7087771/13358334 days = 29d 12h 44m 2+1777862/2226389s"]
["Present (2000 AD)",{"$f":"2+7/9","v":2.7777777777777777},"Mean synodic month at J2000 = 2+7/9 seconds in excess, mean month = 29+82517/155520 days"]
["Tibetan Phugpa",{"$f":"86400*(3001/5656-12/24-44/1440)","v":2.71570014144652},"29+3001/5656 days = 29d 12h 44m 2+506/707s"]
["Gregorian Easter",{"$f":"2+49928114/70499183","v":2.70820840576266},"Full cycle = 2,081,882,250 days/70,499,183 months = mean month of 29d 12h 44m 2+49928114/70499183s"]
["Yerms 49",{"$f":"2+62/89","v":2.696629213483146},"49 yerms with mean month = 29+425/801 days = 29d 12h 44m 2+62/89s"]
["Cassidy-Dee Easter",{"$f":"2+616298/1628531","v":2.3784379910483744},"Full cycle = 48091470 days/1628531 months = mean month of 29d 12h 44m 2+616298/1628531s"]
["Saros 25",{"$f":"2+82/223","v":2.367713004484305},"1803/4 northward equinoctial years, mean month = 29+2958/5575 days = 29d 12h 44m 2+82/223s"]
["Hindu Arya",{"$f":"86400*(2362563/4452778-12/24-44/1440)","v":2.2681750583557814},"Old Hindu lunisolar, mean month = 29+2362563/4452778 days = 29d 12h 44m 2+597062/2226389s"]
["Fixed Islamic",{"v":0,"d":"0.0"},"29+191/360 days per lunation, too short until distant future (about 10688 AD)"]
["Progressive molad","P","Progressively shorter**, see <http://individual.utoronto.ca/kalendis/hebrew/rect.htm#msm>."]
["Experimental molad","E","Like progressive molad**, but doesn't shorten the interval as quickly."]
["RAP molad","R","Rotation-Adjusted Progressive molad handles Delta T outside of molad calculation"]
[]
["The row above must be left blank so that the macro will terminate processing the cycle list."]
["* Seconds are the assumed fixed lunation interval in excess of 29 days 12 hours and 44 minutes."]
["** \"P\" and \"E\" are just special signals to use the Progressive or Experimental molad calculation, respectively."]
["The experimental molad differs from the progressive molad only in its \"InverseRate\" coefficient, see the macro comments."]

{"sheet":"Yerm1_Cycles","index":7,"n_rows":20,"n_cols":7,"rows_kept":20}
["Legend","Seconds *","Fraction","Comments","Days","Weeks","Lunar Years"]
["yerms=3",4.897959183733747,"4 + 44 / 49","n29=23, n30=26, total 49 months in 3 yerms",1447,206.71428571428572,4.083333333333333]
["yerms=115",3.9595529538019036,"3 + 1803 / 1879","n29=882, n30=997, total 1879 months in 115 yerms",55488,7926.857142857143,156.58333333333334]
["yerms=112",3.934426229420751,"3 + 57 / 61","n29=859, n30=971, total 1830 months in 112 yerms",54041,7720.142857142857,152.5]
["yerms=109",3.907916900800501,"3 + 1617 / 1781","n29=836, n30=945, total 1781 months in 109 yerms",52594,7513.428571428572,148.41666666666666]
["yerms=106",3.87990762139907,"3 + 381 / 433","n29=813, n30=919, total 1732 months in 106 yerms",51147,7306.714285714285,144.33333333333334]
["yerms=103",3.8502673796756426,"3 + 159 / 187","n29=790, n30=893, total 1683 months in 103 yerms",49700,7100,140.25]
["yerms=100",3.8188494492487735,"3 + 669 / 817","n29=767, n30=867, total 1634 months in 100 yerms",48253,6893.285714285715,136.16666666666666]
["yerms=97",3.7854889590448693,"3 + 249 / 317","n29=744, n30=841, total 1585 months in 97 yerms",46806,6686.571428571428,132.08333333333334]
["yerms=94",3.7499999999454303,"3 + 3 / 4","n29=721, n30=815, total 1536 months in 94 yerms",45359,6479.857142857143,128]
["yerms=91",3.7121721586572676,"3 + 1059 / 1487","n29=698, n30=789, total 1487 months in 91 yerms",43912,6273.142857142857,123.91666666666667]
["yerms=88",3.671766342210958,"3 + 483 / 719","n29=675, n30=763, total 1438 months in 88 yerms",42465,6066.428571428572,119.83333333333333]
["yerms=85",3.628509719351314,"3 + 291 / 463","n29=652, n30=737, total 1389 months in 85 yerms",41018,5859.714285714285,115.75]
["yerms=82",3.5820895522874707,"3 + 39 / 67","n29=629, n30=711, total 1340 months in 82 yerms",39571,5653,111.66666666666667]
["yerms=79",3.532145623512406,"3 + 687 / 1291","n29=606, n30=685, total 1291 months in 79 yerms",38124,5446.285714285715,107.58333333333333]
["yerms=76",3.478260869701444,"3 + 11 / 23","n29=583, n30=659, total 1242 months in 76 yerms",36677,5239.571428571428,103.5]
["yerms=73",3.419949706699299,"3 + 501 / 1193","n29=560, n30=633, total 1193 months in 73 yerms",35230,5032.857142857143,99.41666666666667]
[]
["The row above must be left blank so that the macro will terminate processing the cycle list."]
["* Seconds are the assumed fixed lunation interval in excess of 29 days 12 hours and 44 minutes."]

{"sheet":"Yerm2_Cycles","index":8,"n_rows":20,"n_cols":7,"rows_kept":20}
["Legend","Seconds *","Fraction","Comments","Days","Weeks","Lunar Years"]
["yerms=70",3.3566433567898457,"3 + 51 / 143","n29=537, n30=607, total 1144 months in 70 yerms",33783,4826.142857142857,95.33333333333333]
["yerms=67",3.2876712328288704,"3 + 21 / 73","n29=514, n30=581, total 1095 months in 67 yerms",32336,4619.428571428572,91.25]
["yerms=64",3.2122370937145206,"3 + 111 / 523","n29=491, n30=555, total 1046 months in 64 yerms",30889,4412.714285714285,87.16666666666667]
["yerms=61",3.1293881644614885,"3 + 129 / 997","n29=468, n30=529, total 997 months in 61 yerms",29442,4206,83.08333333333333]
["yerms=58",3.0379746835933474,"3 + 3 / 79","n29=445, n30=503, total 948 months in 58 yerms",27995,3999.285714285714,79]
["yerms=113",2.988630211098098,"2 + 1826 / 1847","n29=867, n30=980, total 1847 months in 113 yerms",54543,7791.857142857143,153.91666666666666]
["yerms=55",2.9365962180349925,"2 + 842 / 899","n29=422, n30=477, total 899 months in 55 yerms",26548,3792.5714285714284,74.91666666666667]
["yerms=107",2.8816466551575104,"2 + 514 / 583","n29=821, n30=928, total 1749 months in 107 yerms",51649,7378.428571428572,145.75]
["yerms=52",2.823529411864456,"2 + 14 / 17","n29=399, n30=451, total 850 months in 52 yerms",25101,3585.8571428571427,70.83333333333333]
["yerms=101",2.761962447038968,"2 + 1258 / 1651","n29=775, n30=876, total 1651 months in 101 yerms",48755,6965,137.58333333333334]
["yerms=49",2.696629213585311,"2 + 62 / 89","n29=376, n30=425, total 801 months in 49 yerms",23654,3379.1428571428573,66.75]
["yerms=95",2.6271732130567216,"2 + 974 / 1553","n29=729, n30=824, total 1553 months in 95 yerms",45861,6551.571428571428,129.41666666666666]
["yerms=46",2.5531914894486363,"2 + 26 / 47","n29=353, n30=399, total 752 months in 46 yerms",22207,3172.4285714285716,62.666666666666664]
["yerms=89",2.474226804315549,"2 + 46 / 97","n29=683, n30=772, total 1455 months in 89 yerms",42967,6138.142857142857,121.25]
["yerms=43",2.389758179197088,"2 + 274 / 703","n29=330, n30=373, total 703 months in 43 yerms",20760,2965.714285714286,58.583333333333336]
["yerms=83",2.2991893885091486,"2 + 406 / 1357","n29=637, n30=720, total 1357 months in 83 yerms",40073,5724.714285714285,113.08333333333333]
[]
["The row above must be left blank so that the macro will terminate processing the cycle list."]
["* Seconds are the assumed fixed lunation interval in excess of 29 days 12 hours and 44 minutes."]

{"sheet":"Yerm3_Cycles","index":9,"n_rows":20,"n_cols":7,"rows_kept":20}
["Legend","Seconds *","Fraction","Comments","Days","Weeks","Lunar Years"]
["yerms=40",2.20183486235328,"2 + 22 / 109","n29=307, n30=347, total 654 months in 40 yerms",19313,2759,54.5]
["yerms=77",2.096902303378556,"2 + 122 / 1259","n29=591, n30=668, total 1259 months in 77 yerms",37179,5311.285714285715,104.91666666666667]
["yerms=114",2.060085836831149,"2 + 14 / 233","n29=875, n30=989, total 1864 months in 114 yerms",55045,7863.571428571428,155.33333333333334]
["yerms=37",1.9834710744248696,"1 + 119 / 121","n29=284, n30=321, total 605 months in 37 yerms",17866,2552.285714285714,50.416666666666664]
["yerms=108",1.902604756674009,"1 + 797 / 883","n29=829, n30=937, total 1766 months in 108 yerms",52151,7450.142857142857,147.16666666666666]
["yerms=71",1.8604651162377195,"1 + 37 / 43","n29=545, n30=616, total 1161 months in 71 yerms",34285,4897.857142857143,96.75]
["yerms=105",1.817122888689937,"1 + 1403 / 1717","n29=806, n30=911, total 1717 months in 105 yerms",50704,7243.428571428572,143.08333333333334]
["yerms=34",1.7266187051632187,"1 + 101 / 139","n29=261, n30=295, total 556 months in 34 yerms",16419,2345.5714285714284,46.333333333333336]
["yerms=99",1.6306361951592407,"1 + 1021 / 1619","n29=760, n30=859, total 1619 months in 99 yerms",47810,6830,134.91666666666666]
["yerms=65",1.580432737614501,"1 + 617 / 1063","n29=499, n30=564, total 1063 months in 65 yerms",31391,4484.428571428572,88.58333333333333]
["yerms=96",1.5286624205828048,"1 + 83 / 157","n29=737, n30=833, total 1570 months in 96 yerms",46363,6623.285714285715,130.83333333333334]
["yerms=31",1.420118343150989,"1 + 71 / 169","n29=238, n30=269, total 507 months in 31 yerms",14972,2138.8571428571427,42.25]
["yerms=90",1.30434782621478,"1 + 7 / 23","n29=691, n30=781, total 1472 months in 90 yerms",43469,6209.857142857143,122.66666666666667]
["yerms=59",1.2435233160886128,"1 + 47 / 193","n29=453, n30=512, total 965 months in 59 yerms",28497,4071,80.41666666666667]
["yerms=87",1.1806043571368718,"1 + 257 / 1423","n29=668, n30=755, total 1423 months in 87 yerms",42022,6003.142857142857,118.58333333333333]
["yerms=115",1.148325358974489,"1 + 31 / 209","n29=883, n30=998, total 1881 months in 115 yerms",55547,7935.285714285715,156.75]
[]
["The row above must be left blank so that the macro will terminate processing the cycle list."]
["* Seconds are the assumed fixed lunation interval in excess of 29 days 12 hours and 44 minutes."]

{"sheet":"Yerm4_Cycles","index":10,"n_rows":20,"n_cols":7,"rows_kept":20}
["Legend","Seconds *","Fraction","Comments","Days","Weeks","Lunar Years"]
["yerms=28",1.0480349346380535,"1 + 11 / 229","n29=215, n30=243, total 458 months in 28 yerms",13525,1932.142857142857,38.166666666666664]
["yerms=109",0.9422321929150712,"1680 / 1783","n29=837, n30=946, total 1783 months in 109 yerms",52653,7521.857142857143,148.58333333333334]
["yerms=81",0.9056603773615279,"48 / 53","n29=622, n30=703, total 1325 months in 81 yerms",39128,5589.714285714285,110.41666666666667]
["yerms=53",0.8304498269467331,"240 / 289","n29=407, n30=460, total 867 months in 53 yerms",25603,3657.5714285714284,72.25]
["yerms=78",0.7523510971850556,"240 / 319","n29=599, n30=677, total 1276 months in 78 yerms",37681,5383,106.33333333333333]
["yerms=103",0.7121661722294448,"240 / 337","n29=791, n30=894, total 1685 months in 103 yerms",49759,7108.428571428572,140.41666666666666]
["yerms=25",0.5867970661824984,"240 / 409","n29=192, n30=217, total 409 months in 25 yerms",12078,1725.4285714285713,34.083333333333336]
["yerms=97",0.4536862005693365,"240 / 529","n29=745, n30=842, total 1587 months in 97 yerms",46865,6695,132.25]
["yerms=72",0.40747028867826884,"240 / 589","n29=553, n30=625, total 1178 months in 72 yerms",34787,4969.571428571428,98.16666666666667]
["yerms=47",0.31209362820163733,"240 / 769","n29=361, n30=408, total 769 months in 47 yerms",22709,3244.1428571428573,64.08333333333333]
["yerms=69",0.21257750232734907,"240 / 1129","n29=530, n30=599, total 1129 months in 69 yerms",33340,4762.857142857143,94.08333333333333]
["yerms=91",0.16118200124992654,"240 / 1489","n29=699, n30=790, total 1489 months in 91 yerms",43971,6281.571428571428,124.08333333333333]
["yerms=113",0.1297998917948462,"240 / 1849","n29=868, n30=981, total 1849 months in 113 yerms",54602,7800.285714285715,154.08333333333334]
["yerms=22",0,"0","n29=169, n30=191, total 360 months in 22 yerms",10631,1518.7142857142858,30]
["yerms=107",-0.13706453454460643,"-240 / 1751","n29=822, n30=929, total 1751 months in 107 yerms",51708,7386.857142857143,145.91666666666666]
["yerms=85",-0.1725377425827901,"-240 / 1391","n29=653, n30=738, total 1391 months in 85 yerms",41077,5868.142857142857,115.91666666666667]
[]
["The row above must be left blank so that the macro will terminate processing the cycle list."]
["* Seconds are the assumed fixed lunation interval in excess of 29 days 12 hours and 44 minutes."]

{"sheet":"Lunar_Data","index":11,"n_rows":202,"n_cols":18,"rows_kept":202}
["Lunation","Year","25.53191 Orthodox Easter","3.38896 Gregorian epoch","3.33333 Hebrew molad","2.82353 Yerm Lunar calendar","2.79854 Hindu Surya","2.77778 Present (2000 AD)","2.7157 Tibetan Phugpa","2.70821 Gregorian Easter","2.69663 Yerms 49","2.37844 Cassidy-Dee Easter","2.36771 Saros 25","2.26818 Hindu Arya","0.0 Fixed Islamic","Progressive molad","Experimental molad","RAP molad"]
[-123683,-8000,-580.840207714131,27.758901891746,29.2878064702656,43.2997672545792,43.9865848433871,44.5572509147099,46.2634547492746,46.4693651045455,46.7876192043478,55.5331049529678,55.8278812086809,58.5636816580236,120.904473136932,11.3210995607078,8.90628474578261,{"v":0.00531115382909775,"d":"5.31E-03"}]
[-122446,-7900,-573.873779329202,27.1167650129711,28.6265555801752,42.4633420725497,43.1415732267635,43.7051049628911,45.3899782318608,45.5933143435093,45.9075897041866,54.54374141332,54.8348324444832,57.5364305495589,119.097851876471,11.0193874910474,8.6619800850749,{"v":0.00508122146129608,"d":"5.08E-03"}]
[-121209,-7800,-566.901431018404,26.4805480600647,27.9712246159533,41.6328368163888,42.3024815360084,42.8588789369408,44.5224216403156,44.7231835083415,45.033480129894,53.5602977995407,53.847703606154,56.5150993669628,117.297150541879,10.7228666134179,8.4228666163981,{"v":0.00485684350132942,"d":"4.86E-03"}]
[-119972,-7700,-559.923093748383,25.8503200663814,27.3218826109544,40.8083205194509,41.4693788044763,42.0186418702135,43.6608540079933,43.8590416323968,44.1653595148243,52.5828431449844,52.8665637270478,55.4997571435896,115.50243816651,10.4323938041925,8.18794935196638,{"v":0.00463793054223061,"d":"4.64E-03"}]
[-118736,-7600,-552.944347677275,25.2266516945322,26.6791156796985,39.9905209084565,40.6429997002254,41.1851341982169,42.8060330141897,43.0016484760084,43.3039908357533,51.6122288128774,51.8922671495538,54.4912858712582,113.71522679081,10.1473829448223,7.9584940597415,{"v":0.0044245719909668,"d":"4.42E-03"}]
[-117499,-7500,-545.95383232896,24.6086017791426,26.0419517529934,39.1781826898124,39.8220750469871,40.3570752097834,41.9566434601613,42.1496846783574,42.4480482989774,50.6469522366149,50.9233053487414,53.4881217261788,111.932692493734,9.86695428192616,7.73362095281482,{"v":0.00421639904379845,"d":"4.22E-03"}]
[-116262,-7400,-538.957123905317,23.9967449390822,25.4109809016174,38.3720375464974,39.0073434690779,39.535209296679,41.1134469814619,41.3039139560356,41.5982988375306,49.6878687356815,49.9605366232581,52.4911506564286,110.156351271988,9.59329550340772,7.51273994520307,{"v":0.00401347875595093,"d":"4.01E-03"}]
[-115025,-7300,-531.954155339943,23.391148240752,24.7862701919717,37.5721525449126,38.198872032899,38.7196035253048,40.2765106444928,40.4644033754441,40.7548095178142,48.7350453764785,49.0040280395051,51.5004397284086,108.386270191972,9.32448768988252,7.29763584583998,{"v":0.00381577759981155,"d":"3.82E-03"}]
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