Hebrew Calendar Science and Myths
The Ben Meir Years

by Remy Landau

In the year 920g (4681H) Aaron Ben Meir of Palestine proposed that the rule known as Dehiyyah Molad Zakein be relaxed by 642 parts. Hence, instead of limiting the time of postonement to 18 hours, Ben Meir suggested that it be increased to 18 hours and 642 parts. That set off a storm of controversy which saw Saadia Ben Yosef (Saadia Gaon) enter into the battle.

Some of the details of this incredible battle came to light with the discovery of the Cairo Geniza in the late part of the 19th century.

In English, the most authoritative reference to the calendar controversy of 920g (4681H) appears to be found in the book Saadia Gaon: His Life and His Works by Henry Malter (1926).

The calendar controvery is described in Chapter 4, pages 69-89. The first 10 pages appear to be devoted to a description of the calendar rules. Unfortunately, Henry Malter failed to realize that the way to calculate the dates under the Ben Meir rules necessarily requires that the rules which eliminate the 356 and 382 day years also have to be adjusted by an additional 642 parts.

In order to maintain the existing keviyyot, those 642p must also be added to the "356 Rule" and the "382 Rule". Hence, their limiting times become 3d;9h;846p and 2d;16h;151p.
(See The Keviyyot in the additional notes).

Once all of these adjustments are made, the dates for the Ben Meir years can be found through arithmetic computation.

The Malter decription also omits any explanation as to why Ben Meir settled to limit the additional number of parts to 642. In order to ensure that the time of the molad for any month never exceed the first day of that month Ben Meir could have chosen a number as high as 657 parts.
(See The Overpost Problem in the additional notes).

The modification to the calendar rules as proposed by Ben Meir would have first taken effect in the year 922g (4683H) because the time of the molad of Tishrei was Tuesday at 9h;441p.

The classic rules required a postponement of Rosh Hashannah for that year because the time of the molad of Tishrei was past the limit of Tuesday 9h;204p. However, this was less than the 9h;846p required by the Ben Meir rules, and so under his proposal, no postponement would be required for Rosh Hashannah in that year.

Similarly, the Ben Meir rules did not require postponement for the year 4684H (923g) because its molad of Tishrei occurred on Saturday at 18h;237p and for the year 4688H (927g) because its molad of Tishrei occurred on Thursday at 18h;214p.

Rosh Hashannah Dates Under the Ben Meir Rules

                    Comparison of RH Dates 900g-2300g
                    Current RH Dates| Meir's RH Dates
                    ================| ===============
                    Thu  922 Oct  1 | Tue  922 Sep 29
                    Mon  923 Sep 20 | Sat  923 Sep 18
                    Sat  927 Sep  6 | Thu  927 Sep  4
                    Tue 1108 Sep 15 | Mon 1108 Sep 14
                    Sat 1330 Sep 23 | Thu 1330 Sep 21
                    Thu 1334 Sep  9 | Tue 1334 Sep  7
                    Tue 1335 Sep 27 | Mon 1335 Sep 26
                    Thu 1514 Oct  1 | Tue 1514 Sep 29
                    Mon 1515 Sep 20 | Sat 1515 Sep 18
                    Sat 1519 Sep  6 | Thu 1519 Sep  4
                    Sat 1655 Oct  2 | Thu 1655 Sep 30
                    Tue 1700 Sep 14 | Mon 1700 Sep 13
                    Mon 1840 Sep 28 | Sat 1840 Sep 26
                    Sat 1844 Sep 14 | Thu 1844 Sep 12
                    Tue 2025 Sep 23 | Mon 2025 Sep 22
                    Thu 2028 Sep 21 | Tue 2028 Sep 19
                    Mon 2029 Sep 10 | Sat 2029 Sep  8
                    Sat 2247 Oct  2 | Thu 2247 Sep 30
                    Thu 2251 Sep 18 | Tue 2251 Sep 16
                    Tue 2252 Oct  5 | Mon 2252 Oct  4

Note that the Ben Meir modification would have required only 19 changes to the dates of Rosh Hashannah in this 1400 year period.

Properties of the Year 4683H (922g)

The year 922g (4683H) was followed by two more years within a 5 year period which were also affected by Ben Meir's rules. These were 923g (4684H) and 927g (4688H).

The molad of Tishrei for 923g was 18 hours and 237 parts, while the molad for 927g was 18 hours and 214 parts.

It is interesting to note that the years 4779g (8540H), 12246g (16007H), and 16103g (19864H) also are followed, within a five year period, by two more years which each are affected by the Ben Meir proposal.

These years would normally have Rosh Hasannah begin as follows

                            Thu 4779g Oct 18
                            Mon 4780g Oct  6
                            Sat 4784g Sep 22
                            Thu 12246g Nov 19
                            Mon 12247g Nov  8
                            Sat 12251g Oct 25
                            Thu 16103g Dec  6
                            Mon 16104g Nov 24
                            Sat 16108g Nov 10

Surprisingly, the next time that the Ben Meir rule could be applied after each of the third years in these groups is 181 years later, just as was the case following the year 927g.

One of the most intriguing coincidences in the years 4683H, 4684H, and 4688H is that each of these years began the shortest 247 year period possible. The shortest possible period of 247 years is 90,214 days long.

The year 4683H (922g) had a number of other properties which were quite interesting under the existing calendar rules.

- It ended one of the longest possible periods of 19 years
- It ended one of the longest possible periods of 120 Hebrew years
- Rosh Hashannah had never before started that late in the solar year.

The next few times that any Hebrew year can be affected by Ben Meir's rule and in addition have the other 3 properties is

                     Thu 18 Oct  4779g ( 8540H)
                     Thu 19 Nov 12246g (16007H)
                     Thu  6 Dec 16103g (19864H) ...

To return to the top click here.
For other Additional Notes click here.
To continue the reading click here.

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Remy Landau

First  Paged  3 Aug 1997
Next Revised 16 Nov 2004