Yerm Era Analysis of Traditional Hebrew Molad Days

Compiled by Dr. Irv Bromberg, University of Toronto, Canada

Based on traditional molad arithmetic analysis at <http://individual.utoronto.ca/kalendis/hebrew/molad.htm#cycle>.

Yerm concept and calendar defined by Karl Palmen at ''Yerm Lunar Calendar'' <http://www.hermetic.ch/cal_stud/palmen/yerm1.htm>.

A yerm is an odd-length sequence of alternating full (F=30 days) and deficient (D=29 days) lunar calendar months that starts and ends with a full month.
The most accurate yerms for traditional molad interval approximation are FDFDFDFDFDFDFDFDF = 17 months and FDFDFDFDFDFDFDF = 15-months.
The traditional molad interval = 29+¹³⁷⁵³/₂₅₉₂₀ days = 29 days 12 hours 44 minutes and 3+¹/₃ seconds.
The 17-month yerm mean month = (9 × 30 + 8 × 29) / 17 = 29+⁹/₁₇ days = 29 days 12 hours 42 minutes and 21+³/₁₇ seconds, shorter than but closest to the traditional molad interval. Any longer yerm has a shorter mean month.
The 15-month yerm mean month = (8 × 30 + 7 × 29) / 15 = 29+⁸/₁₅ days = 29 days 12 hours and 48 minutes, longer than but closest to the traditional molad interval. Any shorter yerm has a longer mean month.

Each molad day starts on FLOOR( traditional molad + ¹/₄ day ).

Era#, Month#, Day# = era number and total elapsed months and days at the start of that era.
JD = era start Julian Day number.
Fixed = era start fixed day number (day 1 = Hebrew calendar epoch = Gregorian Mon, Sep 7, -3760, including year zero).
Gregorian Date = era start Gregorian date.
hYear, hMonth = era start Hebrew year and month.
HCEM = Hebrew calendar elapsed months, relative to zero = Hebrew epoch.
N = number of consecutive 49-month subcycles in era (17+17+15 months). Every era ends with one 17-month yerm.
The 49-month subcycle mean month = (26 × 30 + 23 × 29) / 49 = 29+²⁶/₄₉ days = 29 days 12 hours 44 minutes and 4+⁴⁴/₄₉ seconds,
slightly longer than the traditional molad interval. The number of subcycles together with the final 17-month yerm fine-tunes the era mean month.
Days, Yerms = number of days and yerms in era. Yerm numbers divisible by 3 have 15 months, otherwise 17 months.
n29, n30 = number of deficient 29-day and full 30-day months in era: n29 = (Months - Yerms) / 2, n30 = n29 + Yerms.
Months = number of months in era = (2 × Days - Yerms) / 59 = n29 + n30. Months have 29 + month MOD 2 days.
Excess = mean month as the number of seconds in excess of 29 days 12 hours and 44 minutes (29+¹⁹¹/₃₆₀ days).
Fraction = excess seconds in exact mixed fraction format.
The mean month itself is not shown because for each era it is always exactly n30 / Months + 29 days.

Era#, Month#, and Day# counted from the first era that ended after the traditional Hebrew calendar epoch, for 5 complete molad yerm era cycles.

Era#	Month#	Day#	JD	Fixed	Gregorian Date	hYear	hMonth	HCEM	N	Days	Yerms	n29	n30	Months	Excess	Fraction
0	0	0	342711	-5285	Sun, Mar 19, -3774	-14	Iyar	-179	23	33783	70	537	607	1144	3.357	3+51/143
1	1144	33783	376494	28498	Mon, Sep 16, -3682	79	Cheshvan	965	22	32336	67	514	581	1095	3.288	3+21/73
2	2239	66119	408830	60834	Thu, Mar 29, -3593	167	Iyar	2060	23	33783	70	537	607	1144	3.357	3+51/143
3	3383	99902	442613	94617	Fri, Sep 25, -3501	260	Cheshvan	3204	23	33783	70	537	607	1144	3.357	3+51/143
4	4527	133685	476396	128400	Sat, Mar 24, -3408	352	Iyar	4348	22	32336	67	514	581	1095	3.288	3+21/73
5	5622	166021	508732	160736	Tue, Oct 5, -3320	441	Cheshvan	5443	23	33783	70	537	607	1144	3.357	3+51/143
6	6766	199804	542515	194519	Wed, Apr 4, -3227	533	Iyar	6587	22	32336	67	514	581	1095	3.288	3+21/73
7	7861	232140	574851	226855	Sat, Oct 15, -3139	622	Kislev	7682	23	33783	70	537	607	1144	3.357	3+51/143
8	9005	265923	608634	260638	Sun, Apr 14, -3046	714	Iyar	8826	23	33783	70	537	607	1144	3.357	3+51/143
9	10149	299706	642417	294421	Mon, Oct 12, -2954	807	Cheshvan	9970	22	32336	67	514	581	1095	3.288	3+21/73
10	11244	332042	674753	326757	Thu, Apr 25, -2865	895	Sivan	11065	23	33783	70	537	607	1144	3.357	3+51/143
11	12388	365825	708536	360540	Fri, Oct 22, -2773	988	Kislev	12209	23	33783	70	537	607	1144	3.357	3+51/143
12	13532	399608	742319	394323	Sat, Apr 20, -2680	1080	Sivan	13353	22	32336	67	514	581	1095	3.288	3+21/73
13	14627	431944	774655	426659	Tue, Nov 1, -2592	1169	Kislev	14448	23	33783	70	537	607	1144	3.357	3+51/143
14	15771	465727	808438	460442	Wed, May 1, -2499	1261	Sivan	15592	23	33783	70	537	607	1144	3.357	3+51/143
15	16915	499510	842221	494225	Thu, Oct 28, -2407	1354	Kislev	16736	22	32336	67	514	581	1095	3.288	3+21/73
16	18010	531846	874557	526561	Sun, May 10, -2318	1442	Sivan	17831	23	33783	70	537	607	1144	3.357	3+51/143
17	19154	565629	908340	560344	Mon, Nov 7, -2226	1535	Kislev	18975	23	33783	70	537	607	1144	3.357	3+51/143
18	20298	599412	942123	594127	Tue, May 7, -2133	1627	Sivan	20119	22	32336	67	514	581	1095	3.288	3+21/73
19	21393	631748	974459	626463	Fri, Nov 18, -2045	1716	Tevet	21214	23	33783	70	537	607	1144	3.357	3+51/143
20	22537	665531	1008242	660246	Sat, May 16, -1952	1808	Sivan	22358	23	33783	70	537	607	1144	3.357	3+51/143
21	23681	699314	1042025	694029	Sun, Nov 13, -1860	1901	Kislev	23502	22	32336	67	514	581	1095	3.288	3+21/73
22	24776	731650	1074361	726365	Wed, May 27, -1771	1989	Tammuz	24597	23	33783	70	537	607	1144	3.357	3+51/143
23	25920	765433	1108144	760148	Thu, Nov 24, -1679	2082	Tevet	25741	23	33783	70	537	607	1144	3.357	3+51/143
24	27064	799216	1141927	793931	Fri, May 23, -1586	2174	Sivan	26885	22	32336	67	514	581	1095	3.288	3+21/73
25	28159	831552	1174263	826267	Mon, Dec 4, -1498	2263	Tevet	27980	23	33783	70	537	607	1144	3.357	3+51/143
26	29303	865335	1208046	860050	Tue, Jun 2, -1405	2355	Tammuz	29124	23	33783	70	537	607	1144	3.357	3+51/143
27	30447	899118	1241829	893833	Wed, Nov 30, -1313	2448	Tevet	30268	22	32336	67	514	581	1095	3.288	3+21/73
28	31542	931454	1274165	926169	Sat, Jun 12, -1224	2536	Tammuz	31363	23	33783	70	537	607	1144	3.357	3+51/143
29	32686	965237	1307948	959952	Sun, Dec 9, -1132	2629	Tevet	32507	22	32336	67	514	581	1095	3.288	3+21/73
30	33781	997573	1340284	992288	Wed, Jun 22, -1043	2717	Tammuz	33602	23	33783	70	537	607	1144	3.357	3+51/143
31	34925	1031356	1374067	1026071	Thu, Dec 20, -951	2810	Shevat	34746	23	33783	70	537	607	1144	3.357	3+51/143
32	36069	1065139	1407850	1059854	Fri, Jun 19, -858	2902	Tammuz	35890	22	32336	67	514	581	1095	3.288	3+21/73
33	37164	1097475	1440186	1092190	Mon, Dec 30, -770	2991	Shevat	36985	23	33783	70	537	607	1144	3.357	3+51/143
34	38308	1131258	1473969	1125973	Tue, Jun 29, -677	3083	Av	38129	23	33783	70	537	607	1144	3.357	3+51/143
35	39452	1165041	1507752	1159756	Wed, Dec 27, -585	3176	Shevat	39273	22	32336	67	514	581	1095	3.288	3+21/73
36	40547	1197377	1540088	1192092	Sat, Jul 9, -496	3264	Av	40368	23	33783	70	537	607	1144	3.357	3+51/143
37	41691	1231160	1573871	1225875	Sun, Jan 5, -403	3357	Shevat	41512	23	33783	70	537	607	1144	3.357	3+51/143
38	42835	1264943	1607654	1259658	Mon, Jul 4, -311	3449	Av	42656	22	32336	67	514	581	1095	3.288	3+21/73
39	43930	1297279	1639990	1291994	Thu, Jan 15, -222	3538	Shevat	43751	23	33783	70	537	607	1144	3.357	3+51/143
40	45074	1331062	1673773	1325777	Fri, Jul 15, -130	3630	Av	44895	23	33783	70	537	607	1144	3.357	3+51/143
41	46218	1364845	1707556	1359560	Sat, Jan 12, -37	3723	Shevat	46039	22	32336	67	514	581	1095	3.288	3+21/73
42	47313	1397181	1739892	1391896	Tue, Jul 25, 51	3811	Av	47134	23	33783	70	537	607	1144	3.357	3+51/143
43	48457	1430964	1773675	1425679	Wed, Jan 22, 144	3904	Shevat	48278	23	33783	70	537	607	1144	3.357	3+51/143
44	49601	1464747	1807458	1459462	Thu, Jul 21, 236	3996	Av	49422	22	32336	67	514	581	1095	3.288	3+21/73
45	50696	1497083	1839794	1491798	Sun, Feb 1, 325	4085	Adar 1	50517	23	33783	70	537	607	1144	3.357	3+51/143
46	51840	1530866	1873577	1525581	Mon, Jul 31, 417	4177	Elul	51661	23	33783	70	537	607	1144	3.357	3+51/143
47	52984	1564649	1907360	1559364	Tue, Jan 28, 510	4270	Adar 1	52805	22	32336	67	514	581	1095	3.288	3+21/73
48	54079	1596985	1939696	1591700	Fri, Aug 10, 598	4358	Elul	53900	23	33783	70	537	607	1144	3.357	3+51/143
49	55223	1630768	1973479	1625483	Sat, Feb 7, 691	4451	Adar	55044	23	33783	70	537	607	1144	3.357	3+51/143
50	56367	1664551	2007262	1659266	Sun, Aug 7, 783	4543	Elul	56188	22	32336	67	514	581	1095	3.288	3+21/73
51	57462	1696887	2039598	1691602	Wed, Feb 17, 872	4632	Adar	57283	23	33783	70	537	607	1144	3.357	3+51/143
52	58606	1730670	2073381	1725385	Thu, Aug 16, 964	4724	Elul	58427	22	32336	67	514	581	1095	3.288	3+21/73
53	59701	1763006	2105717	1757721	Sun, Feb 27, 1053	4813	Adar 2	59522	23	33783	70	537	607	1144	3.357	3+51/143
54	60845	1796789	2139500	1791504	Mon, Aug 27, 1145	4905	Elul	60666	23	33783	70	537	607	1144	3.357	3+51/143
55	61989	1830572	2173283	1825287	Tue, Feb 23, 1238	4998	Adar	61810	22	32336	67	514	581	1095	3.288	3+21/73
56	63084	1862908	2205619	1857623	Fri, Sep 6, 1326	5087	Tishrei	62905	23	33783	70	537	607	1144	3.357	3+51/143
57	64228	1896691	2239402	1891406	Sat, Mar 6, 1419	5179	Adar 2	64049	23	33783	70	537	607	1144	3.357	3+51/143
58	65372	1930474	2273185	1925189	Sun, Sep 3, 1511	5271	Elul	65193	22	32336	67	514	581	1095	3.288	3+21/73
59	66467	1962810	2305521	1957525	Wed, Mar 15, 1600	5360	Nisan	66288	23	33783	70	537	607	1144	3.357	3+51/143
60	67611	1996593	2339304	1991308	Thu, Sep 11, 1692	5453	Tishrei	67432	23	33783	70	537	607	1144	3.357	3+51/143
61	68755	2030376	2373087	2025091	Fri, Mar 11, 1785	5545	Nisan	68576	22	32336	67	514	581	1095	3.288	3+21/73
62	69850	2062712	2405423	2057427	Mon, Sep 22, 1873	5634	Tishrei	69671	23	33783	70	537	607	1144	3.357	3+51/143
63	70994	2096495	2439206	2091210	Tue, Mar 22, 1966	5726	Nisan	70815	23	33783	70	537	607	1144	3.357	3+51/143
64	72138	2130278	2472989	2124993	Wed, Sep 18, 2058	5819	Tishrei	71959	22	32336	67	514	581	1095	3.288	3+21/73
65	73233	2162614	2505325	2157329	Sat, Apr 1, 2147	5907	Nisan	73054	23	33783	70	537	607	1144	3.357	3+51/143
66	74377	2196397	2539108	2191112	Sun, Sep 29, 2239	6000	Tishrei	74198	23	33783	70	537	607	1144	3.357	3+51/143
67	75521	2230180	2572891	2224895	Mon, Mar 28, 2332	6092	Nisan	75342	22	32336	67	514	581	1095	3.288	3+21/73
68	76616	2262516	2605227	2257231	Thu, Oct 8, 2420	6181	Cheshvan	76437	23	33783	70	537	607	1144	3.357	3+51/143
69	77760	2296299	2639010	2291014	Fri, Apr 7, 2513	6273	Nisan	77581	23	33783	70	537	607	1144	3.357	3+51/143
70	78904	2330082	2672793	2324797	Sat, Oct 5, 2605	6366	Tishrei	78725	22	32336	67	514	581	1095	3.288	3+21/73
71	79999	2362418	2705129	2357133	Tue, Apr 17, 2694	6454	Iyar	79820	23	33783	70	537	607	1144	3.357	3+51/143
72	81143	2396201	2738912	2390916	Wed, Oct 15, 2786	6547	Cheshvan	80964	23	33783	70	537	607	1144	3.357	3+51/143
73	82287	2429984	2772695	2424699	Thu, Apr 13, 2879	6639	Nisan	82108	22	32336	67	514	581	1095	3.288	3+21/73
74	83382	2462320	2805031	2457035	Sun, Oct 25, 2967	6728	Cheshvan	83203	23	33783	70	537	607	1144	3.357	3+51/143
75	84526	2496103	2838814	2490818	Mon, Apr 23, 3060	6820	Iyar	84347	22	32336	67	514	581	1095	3.288	3+21/73
76	85621	2528439	2871150	2523154	Thu, Nov 4, 3148	6909	Cheshvan	85442	23	33783	70	537	607	1144	3.357	3+51/143
77	86765	2562222	2904933	2556937	Fri, May 3, 3241	7001	Iyar	86586	23	33783	70	537	607	1144	3.357	3+51/143
78	87909	2596005	2938716	2590720	Sat, Oct 31, 3333	7094	Cheshvan	87730	22	32336	67	514	581	1095	3.288	3+21/73
79	89004	2628341	2971052	2623056	Tue, May 14, 3422	7182	Iyar	88825	23	33783	70	537	607	1144	3.357	3+51/143
80	90148	2662124	3004835	2656839	Wed, Nov 11, 3514	7275	Kislev	89969	23	33783	70	537	607	1144	3.357	3+51/143
81	91292	2695907	3038618	2690622	Thu, May 10, 3607	7367	Iyar	91113	22	32336	67	514	581	1095	3.288	3+21/73
82	92387	2728243	3070954	2722958	Sun, Nov 20, 3695	7456	Kislev	92208	23	33783	70	537	607	1144	3.357	3+51/143
83	93531	2762026	3104737	2756741	Mon, May 19, 3788	7548	Sivan	93352	23	33783	70	537	607	1144	3.357	3+51/143
84	94675	2795809	3138520	2790524	Tue, Nov 16, 3880	7641	Kislev	94496	22	32336	67	514	581	1095	3.288	3+21/73
85	95770	2828145	3170856	2822860	Fri, May 30, 3969	7729	Sivan	95591	23	33783	70	537	607	1144	3.357	3+51/143
86	96914	2861928	3204639	2856643	Sat, Nov 26, 4061	7822	Kislev	96735	23	33783	70	537	607	1144	3.357	3+51/143
87	98058	2895711	3238422	2890426	Sun, May 26, 4154	7914	Sivan	97879	22	32336	67	514	581	1095	3.288	3+21/73
88	99153	2928047	3270758	2922762	Wed, Dec 7, 4242	8003	Kislev	98974	23	33783	70	537	607	1144	3.357	3+51/143
89	100297	2961830	3304541	2956545	Thu, Jun 6, 4335	8095	Sivan	100118	23	33783	70	537	607	1144	3.357	3+51/143
90	101441	2995613	3338324	2990328	Fri, Dec 3, 4427	8188	Kislev	101262	22	32336	67	514	581	1095	3.288	3+21/73
91	102536	3027949	3370660	3022664	Mon, Jun 15, 4516	8276	Sivan	102357	23	33783	70	537	607	1144	3.357	3+51/143
92	103680	3061732	3404443	3056447	Tue, Dec 13, 4608	8369	Kislev	103501	23	33783	70	537	607	1144	3.357	3+51/143
93	104824	3095515	3438226	3090230	Wed, Jun 12, 4701	8461	Sivan	104645	22	32336	67	514	581	1095	3.288	3+21/73
94	105919	3127851	3470562	3122566	Sat, Dec 23, 4789	8550	Tevet	105740	23	33783	70	537	607	1144	3.357	3+51/143
95	107063	3161634	3504345	3156349	Sun, Jun 21, 4882	8642	Tammuz	106884	23	33783	70	537	607	1144	3.357	3+51/143
96	108207	3195417	3538128	3190132	Mon, Dec 19, 4974	8735	Tevet	108028	22	32336	67	514	581	1095	3.288	3+21/73
97	109302	3227753	3570464	3222468	Thu, Jul 2, 5063	8823	Tammuz	109123	23	33783	70	537	607	1144	3.357	3+51/143
98	110446	3261536	3604247	3256251	Fri, Dec 30, 5155	8916	Tevet	110267	22	32336	67	514	581	1095	3.288	3+21/73
99	111541	3293872	3636583	3288587	Mon, Jul 11, 5244	9004	Tammuz	111362	23	33783	70	537	607	1144	3.357	3+51/143
100	112685	3327655	3670366	3322370	Tue, Jan 8, 5337	9097	Tevet	112506	23	33783	70	537	607	1144	3.357	3+51/143
101	113829	3361438	3704149	3356153	Wed, Jul 8, 5429	9189	Tammuz	113650	22	32336	67	514	581	1095	3.288	3+21/73
102	114924	3393774	3736485	3388489	Sat, Jan 19, 5518	9278	Shevat	114745	23	33783	70	537	607	1144	3.357	3+51/143
103	116068	3427557	3770268	3422272	Sun, Jul 18, 5610	9370	Tammuz	115889	23	33783	70	537	607	1144	3.357	3+51/143
104	117212	3461340	3804051	3456055	Mon, Jan 15, 5703	9463	Tevet	117033	22	32336	67	514	581	1095	3.288	3+21/73
105	118307	3493676	3836387	3488391	Thu, Jul 28, 5791	9551	Av	118128	23	33783	70	537	607	1144	3.357	3+51/143
106	119451	3527459	3870170	3522174	Fri, Jan 25, 5884	9644	Shevat	119272	23	33783	70	537	607	1144	3.357	3+51/143
107	120595	3561242	3903953	3555957	Sat, Jul 24, 5976	9736	Tammuz	120416	22	32336	67	514	581	1095	3.288	3+21/73
108	121690	3593578	3936289	3588293	Tue, Feb 3, 6065	9825	Shevat	121511	23	33783	70	537	607	1144	3.357	3+51/143
109	122834	3627361	3970072	3622076	Wed, Aug 3, 6157	9917	Av	122655	23	33783	70	537	607	1144	3.357	3+51/143
110	123978	3661144	4003855	3655859	Thu, Jan 31, 6250	10010	Shevat	123799	22	32336	67	514	581	1095	3.288	3+21/73
111	125073	3693480	4036191	3688195	Sun, Aug 14, 6338	10098	Av	124894	23	33783	70	537	607	1144	3.357	3+51/143
112	126217	3727263	4069974	3721978	Mon, Feb 10, 6431	10191	Shevat	126038	23	33783	70	537	607	1144	3.357	3+51/143
113	127361	3761046	4103757	3755761	Tue, Aug 10, 6523	10283	Av	127182	22	32336	67	514	581	1095	3.288	3+21/73
114	128456	3793382	4136093	3788097	Fri, Feb 21, 6612	10372	Adar 1	128277	23	33783	70	537	607	1144	3.357	3+51/143

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