Ancient Hebrew Calendar

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Ged
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Re: Ancient Hebrew Calendar

Post by Ged » Mon Mar 06, 2017 5:39 pm

DCHindley wrote: Ged,

I was misunderstanding where you were coming from with the calendar. So, if my take from an initial skim of the paper is correct, you think you have come up with the manner by which a 364 day calendar was kept in tune with the seasons.

The paper has been downloaded & I will take a closer look later.

DCH
No, my reconstructed calendar is still luni-solar, albeit different to modern luni-solar ones. (49 yr cycle rather that 19 yr cycle) I only mentioned the 364-day Qumran solar calendar to make my point that people in those days were trying to find the original system. It was there to be found and they tried, but never got it right. (only my opinion admittedly.) One of the DSS translaters, Jean Carmignac, got an approximate reconciliation with the 364-days plus intercalation, but it never explained the lunar side of things.

Ged

All the best with my download paper.
The science of arranging time in periods and ascertaining the dates and historical order of past events.

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DCHindley
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Re: Ancient Hebrew Calendar

Post by DCHindley » Tue Mar 07, 2017 5:02 am

Ged wrote:
DCHindley wrote: Ged,

I was misunderstanding where you were coming from with the calendar. So, if my take from an initial skim of the paper is correct, you think you have come up with the manner by which a 364 day calendar was kept in tune with the seasons.

The paper has been downloaded & I will take a closer look later.
No, my reconstructed calendar is still luni-solar, albeit different to modern luni-solar ones. (49 yr cycle rather that 19 yr cycle) I only mentioned the 364-day Qumran solar calendar to make my point that people in those days were trying to find the original system. It was there to be found and they tried, but never got it right. (only my opinion admittedly.) One of the DSS translaters, Jean Carmignac, got an approximate reconciliation with the 364-days plus intercalation, but it never explained the lunar side of things.
My interest was actually in how the 364 day calendar might be intercalated, so I was probably misreading your posts here.

Gave your paper a read through and tweaked a spreadsheet I created to analyze the Solar (365.24255 day), Lunar (354.367056 day) & Schematic (364 day) years against average months for the Luni-Solar (29.530588 days) and Schematic 364 day years (30.333333 days).

I have to leave for Physical Therapy for my shoulder now, so I'll take this up again after work when I can create a table to post the results here. It seems that you could do what you proposed (18 intercalated months into the Luni-Solar) but I also noted that the 364 day calendar would also need to intercalate almost exactly 2 months in the same period. If broken down into weeks (8) spread over 49 years would mean an intercalated week every 6 years. The intercalation of weeks or multiples of weeks is necessary to preserve the system where festivals always fell on the same day of the week.

DCH

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DCHindley
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Re: Ancient Hebrew Calendar

Post by DCHindley » Tue Mar 07, 2017 2:46 pm

Below are intercalation schemes for a Luni-Solar calendar (LS), as well as the 364 day Schematic Solar (SS) year of the DSS and Jubilees.

365.242550
Total
364.000000
Part of SS
Total
354.367056
Part of
Total
Avs SS Mo.
Avg LS Mo.
Notes
Year # Days Solar Diff Month Days Solar Diff Lunar Mo. Days weeks weeks
1 354.367056 1.242550 0.040963 354.367056 10.875494 0.368279 354.367056 30.333333 29.530588 average days in a month
2 708.734112 2.485100 0.081926 708.734112 21.750988 0.736558 708.734112 4.333333 4.218655429 weeks in average length month
3 1063.101168 3.727650 0.122890 1063.101168 32.626482 1.104837 1063.101168
4 1417.468224 4.970200 0.163853 1417.468224 43.501976 1.473116 1417.468224
5 1771.835280 6.212750 0.204816 1771.835280 54.377470 1.841395 1771.835280
6 2126.202336 7.455300 0.245779 2126.202336 65.252964 2.209674 2126.202336
7 2480.569392 8.697850 0.286742 2480.569392 76.128458 2.577953 2480.569392
8 2834.936448 9.940400 0.327705 2834.936448 87.003952 2.946232 2834.936448 octaetris 3 intercalated LS mos in 8 year cycle
9 3189.303504 11.182950 0.368669 3189.303504 97.879446 3.314511 3189.303504
10 3543.670560 12.425500 0.409632 3543.670560 108.754940 3.682790 3543.670560
11 3898.037616 13.668050 0.450595 3898.037616 119.630434 4.051068 3898.037616
12 4252.404672 14.910600 0.491558 4252.404672 130.505928 4.419347 4252.404672
13 4606.771728 16.153150 0.532521 4606.771728 141.381422 4.787626 4606.771728
14 4961.138784 17.395700 0.573485 4961.138784 152.256916 5.155905 4961.138784
15 5315.505840 18.638250 0.614448 5315.505840 163.132410 5.524184 5315.505840
16 5669.872896 19.880800 0.655411 5669.872896 174.007904 5.892463 5669.872896
17 6024.239952 21.123350 0.696374 6024.239952 184.883398 6.260742 6024.239952
18 6378.607008 22.365900 0.737337 6378.607008 195.758892 6.629021 6378.607008
19 6732.974064 23.608450 0.778301 6732.974064 206.634386 6.997300 6732.974064 Metonic 7 intercalated LS mos in 19 year cycle
20 7087.341120 24.851000 0.819264 7087.341120 217.509880 7.365579 7087.341120
21 7441.708176 26.093550 0.860227 7441.708176 228.385374 7.733858 7441.708176
22 7796.075232 27.336100 0.901190 7796.075232 239.260868 8.102137 7796.075232
23 8150.442288 28.578650 0.942153 8150.442288 250.136362 8.470416 8150.442288
24 8504.809344 29.821200 0.983116 8504.809344 261.011856 8.838695 8504.809344
25 8859.176400 31.063750 1.024080 8859.176400 271.887350 9.206974 8859.176400
26 9213.543456 32.306300 1.065043 9213.543456 282.762844 9.575253 9213.543456
27 9567.910512 33.548850 1.106006 9567.910512 293.638338 9.943532 9567.910512
28 9922.277568 34.791400 1.146969 9922.277568 304.513832 10.311811 9922.277568
29 10276.644624 36.033950 1.187932 10276.644624 315.389326 10.680090 10276.644624
30 10631.011680 37.276500 1.228896 10631.011680 326.264820 11.048369 10631.011680
31 10985.378736 38.519050 1.269859 10985.378736 337.140314 11.416648 10985.378736
32 11339.745792 39.761600 1.310822 11339.745792 348.015808 11.784926 11339.745792
33 11694.112848 41.004150 1.351785 11694.112848 358.891302 12.153205 11694.112848
34 12048.479904 42.246700 1.392748 12048.479904 369.766796 12.521484 12048.479904
35 12402.846960 43.489250 1.433712 12402.846960 380.642290 12.889763 12402.846960
36 12757.214016 44.731800 1.474675 12757.214016 391.517784 13.258042 12757.214016
37 13111.581072 45.974350 1.515638 13111.581072 402.393278 13.626321 13111.581072
38 13465.948128 47.216900 1.556601 13465.948128 413.268772 13.994600 13465.948128
39 13820.315184 48.459450 1.597564 13820.315184 424.144266 14.362879 13820.315184
40 14174.682240 49.702000 1.638527 14174.682240 435.019760 14.731158 14174.682240
41 14529.049296 50.944550 1.679491 14529.049296 445.895254 15.099437 14529.049296
42 14883.416352 52.187100 1.720454 14883.416352 456.770748 15.467716 14883.416352
43 15237.783408 53.429650 1.761417 15237.783408 467.646242 15.835995 15237.783408
44 15592.150464 54.672200 1.802380 15592.150464 478.521736 16.204274 15592.150464
45 15946.517520 55.914750 1.843343 15946.517520 489.397230 16.572553 15946.517520
46 16300.884576 57.157300 1.884307 16300.884576 500.272724 16.940832 16300.884576
47 16655.251632 58.399850 1.925270 16655.251632 511.148218 17.309111 16655.251632
48 17009.618688 59.642400 1.966233 17009.618688 522.023712 17.677390 17009.618688 DCH 2 intercalated SS mos in 48 or 49 years
49 17363.985744 60.884950 2.007196 17363.985744 532.899206 18.045669 17363.985744 Ged 18 intercalated LS month in 49 year Jubilee cycle

Hopefully, that all makes things clear as mud.

DCH

Edit 3/8/17: Don't know why, but the table I originally inserted did not have the first column. Fixed. I really *really* need a new laptop.
Last edited by DCHindley on Wed Mar 08, 2017 2:25 pm, edited 1 time in total.

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Ged
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Re: Ancient Hebrew Calendar

Post by Ged » Tue Mar 07, 2017 9:08 pm

Im following down your 'Solar Diff' column, and I can see how the Metonic adds 7 months over 19 years, and how I add 18 months over 49 years. However Im a bit lost at your "2 intercalated SS mos in 48 or 49 years"
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Re: Ancient Hebrew Calendar

Post by DCHindley » Wed Mar 08, 2017 2:07 pm

Ged wrote:Im following down your 'Solar Diff' column, and I can see how the Metonic adds 7 months over 19 years, and how I add 18 months over 49 years. However Im a bit lost at your "2 intercalated SS mos in 48 or 49 years"
That must be the "mud" part. :cheeky:

The second column states the number of days difference between 365.24... day calendar and the 364 day calendar, and for the mathematically challenged among us (me) the 3rd column states the same thing as the number of mean solar months (30.333333 days). So, anything close to 2.00 is "two" of said average 364 day year months. In actuality the months were ordered as two 30 day months followed by one 31 day month, or alternatively, they were all 30 day months with four single day adjustments every 3 months. This is kind of like the Egyptian year, which was 12 30 day months, but with five adjustment days at the end of the year.

I just realized that the table has cut off the first column. I must fix now ...

Edit 3/8/17: Well, "the fix is in." Something is odd about my laptop, and it may have hiccupped when I copied the range for the table to input into jsfiddle.net "Excel to BBCode" page. The laptop is now about 10 years old, no HDMI port, and while it has a lot of HDD memory available, it seems to have trouble with IE 11 and managing image files, so I suspect RAM memory problems, maybe just not enough. On the other hand, we had water quality issues at the local water department that made the water rust colored, and when I drank some before I realized it was bad I started to feel really fatigued. Maybe I was not running on all cylinders that evening. FWIW, the jsfiddle.net webpage also converts Word tables. For those who still use MS DOS/Win 98, the old ASCII WordPad or some Open Office type CSV spreadsheet program, none of that will convert. Go to: http://jsfiddle.net/agKTg/6/embedded/result/

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Re: Ancient Hebrew Calendar

Post by DCHindley » Thu Mar 09, 2017 5:33 pm

Just out of curiosity, Ged, why did you use the Anno Mundi dating scheme? Was it imported from the Jewish Calendar website you mention or is t something to do with a Christian POV.

The book of Jubilees uses AM but once you get past Abraham , Isaac & Jacob, the means to interconnect datable events falls apart. There is no way to continue it into the times of the Judges, Kings and such. The Rabbis may think they have it figured out, but I am skeptical. Jack Finnegan has a section on it in his Handbook of Biblical Chronology.

DCH

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Re: Ancient Hebrew Calendar

Post by Ged » Thu Mar 09, 2017 10:32 pm

I used the BC and AM side by side out of deference to Jewish readers. I am conscious that Jews may get annoyed with Christians who come across as thinking they know more about pre-Christian history of Israel than they do. If I was a Jew it would irritate me, so by using their calendar I hope at least to be seen as respectful.

Funnily enough, I do get hits from the middle east, but its hard to know what people are thinking. I thought of sending my paper to Tel Aviv University, but Im scared that I'll be given the flick because of a perception that this subject is the domain of crackpots.

I like what Ive seen of Jack Finnegan. Do you have his chronology?
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Re: Ancient Hebrew Calendar

Post by Ged » Fri Mar 10, 2017 11:34 am

DCHindley wrote:
The second column states the number of days difference between 365.24... day calendar and the 364 day calendar, and for the mathematically challenged among us (me) the 3rd column states the same thing as the number of mean solar months (30.333333 days). So, anything close to 2.00 is "two" of said average 364 day year months. In actuality the months were ordered as two 30 day months followed by one 31 day month, or alternatively, they were all 30 day months with four single day adjustments every 3 months. This is kind of like the Egyptian year, which was 12 30 day months, but with five adjustment days at the end of the year.
I see what you're getting at now. There is a deficit of 59 - 60 days over any jubilee period, so two months would have to be added to a 364-day calendar. Presumably, one would be added after 24 years, and the other after 49? It would work as a solar calendar, I think, but I can't see it fitting with 'New Moons' etc. Also, the Qumran community were fanatical Sabbatarians. I doubt that they would have been happy about making an adjustment on the 24th year. (21st year maybe. Either that or they waited 49 years before adding 2 months.)
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Re: Ancient Hebrew Calendar

Post by DCHindley » Fri Mar 10, 2017 8:00 pm

Ged wrote:
DCHindley wrote:
The second column states the number of days difference between 365.24... day calendar and the 364 day calendar, and for the mathematically challenged among us (me) the 3rd column states the same thing as the number of mean solar months (30.333333 days). So, anything close to 2.00 is "two" of said average 364 day year months. In actuality the months were ordered as two 30 day months followed by one 31 day month, or alternatively, they were all 30 day months with four single day adjustments every 3 months. This is kind of like the Egyptian year, which was 12 30 day months, but with five adjustment days at the end of the year.
I see what you're getting at now. There is a deficit of 59 - 60 days over any jubilee period, so two months would have to be added to a 364-day calendar. Presumably, one would be added after 24 years, and the other after 49? It would work as a solar calendar, I think, but I can't see it fitting with 'New Moons' etc. Also, the Qumran community were fanatical Sabbatarians. I doubt that they would have been happy about making an adjustment on the 24th year. (21st year maybe. Either that or they waited 49 years before adding 2 months.)
What I am thinking they did was add an extra week every few years to get things on track, maybe tacking it at the end of a year as a special festival week. It has been some while since I have read anything about it (although I have a bunch of books and articles that touch on the subject of DSS calendars) but I seem to recall that the calendric writings refer to festivals that are not otherwise known from the Luni-Solar calendar of Babylon or modern Judaism. They were fanatical about having each specific festival day fall on the same day of the week each year.

The thing is, despite their fascination with multiples of seven, their basic month is 30 days, which is not a multiple of seven. To add 30 days (or 31 days) will not yield a multiple of 30 and the day of the week of the festival would shift, which is a no-no. So I suppose they could have some other scheme to intercalate. Thirty is a multiple of 5 or 6 (6 x 5 = 30). To harmonize, the solution would have to be some factorial of 5 x 7 = 35 or 6 x 7 = 42. Thirty five days variance happens between the 28th or 29th year and forty two days happens in the 34th year, so that means either 5 weeks in 28.5 years or six weeks in forty two years. The former is hard to get a smooth result from but adding a week every 6 years might work.

Basically, an extra week is added every 6 years, and another week was added two years after the 8th intercalation (year 48), that is, the 50th year. The start of the next intercalation 50 year intercalation scheme (apparently not same as the system for measuring years of time) varies from a true solar by just -0.370050 day at the start of the next cycle (the 51st year). Then an extra week would only need be added every 19 of those fifty-year cycles (i.e., every 950 years). That's a lot of time before you would have to introduce a secondary intercalation! You can't wave a sheaf on the designated date if that falls in mid winter. The dates of festivals, etc., need to keep in track with the seasons. This intercalation system is never more than one week off. That is pretty damn close.

On the other hand, the years-of-time counting scheme seems to have been based on multiples of 49 years, not 50, but those years still need to be intercalated, so the two systems, one for counting time and the other to intercalate with the seasonal years, must have been maintained at the same time. Then years of this entirely calculated time tracking scheme can be synchronized with other calculated cycles, like the luni-solar Babylonian and the Syro-Macedonian calendars, or the priestly rotation for service in the temple. The common denominator for synchronizations like this is that they are calculated schemes. On the other hand, annalists (recorders of events) probably used synchronizations like these to correlate events in history with fixed cycles. "This or that priestly family was in service in the temple when king so-and-so attacked a certain town or city," etc.

I'd love to claim credit for this idea, but I believe I have read it proposed before.

DCH

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Re: Ancient Hebrew Calendar

Post by Ged » Fri Mar 10, 2017 9:08 pm

One of the things I have to admit is that the Essenes (or Essenic sect) were using a 364-day calendar from about 200 BC to 70 AD. They would have had to intercalate during that time span somehow! So, they may well have done something like you are proposing. Ive got a book called, 'Calendar and Chronology, Jewish and Christian' by Roger Beckwith. He explains the theories of various writers on the subject, but none of them fit exactly.

My conclusion, is that the original calendar formulas were lost during the tumultuous times arising from the invasions of Babylon, Persia and Greece. The book of Daniel speaks of certain individuals who had insight in scientific matters (Daniel 1:17) but this knowledge (astronomical understandings?) was lost sometime after then. The Qumran people knew something was lost, and they knew it had to be sabbatical. So, they created the 364-day calendar, and said (a ridiculous claim) that it came from Enoch.

I like my calendar better. (lol) :mrgreen: but admitedly, Im biased.
The science of arranging time in periods and ascertaining the dates and historical order of past events.

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