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Re: Ancient Hebrew Calendar
Posted: Mon Mar 06, 2017 5:39 pm
by Ged
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.
Re: Ancient Hebrew Calendar
Posted: Tue Mar 07, 2017 5:02 am
by DCHindley
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
Re: Ancient Hebrew Calendar
Posted: Tue Mar 07, 2017 2:46 pm
by DCHindley
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.
Re: Ancient Hebrew Calendar
Posted: Tue Mar 07, 2017 9:08 pm
by Ged
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"
Re: Ancient Hebrew Calendar
Posted: Wed Mar 08, 2017 2:07 pm
by DCHindley
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.
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/
Re: Ancient Hebrew Calendar
Posted: Thu Mar 09, 2017 5:33 pm
by DCHindley
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
Re: Ancient Hebrew Calendar
Posted: Thu Mar 09, 2017 10:32 pm
by Ged
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?
Re: Ancient Hebrew Calendar
Posted: Fri Mar 10, 2017 11:34 am
by Ged
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.)
Re: Ancient Hebrew Calendar
Posted: Fri Mar 10, 2017 8:00 pm
by DCHindley
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
Re: Ancient Hebrew Calendar
Posted: Fri Mar 10, 2017 9:08 pm
by Ged
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)
but admitedly, Im biased.