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Assyriology
19-Year Cycles in Lunar-Solar Calendars
Data Corroborates the Cairo Sandstone Stele

Explaining the 19-Year Cycle

Both the ancient Hebrew and Babylonian calendars used the moon and the sun to track time. It is easy to ask, "How can the moon and the sun be used to make a simple calendar"

In astronomy, there is a natural 19-year cycle between the sun and the moon. Every 19 years, the month and day of the year will be the same. Here is how the lunar-solar calendar works.

For the lunar calendar, the 19-year cycle requires that 235 months be used in order to equal to the 19-year solar calendar. Since we use 12-months in a year, 19 years of 12 months gives us 228 total months. This is easy to show by using your calculator and multiplying 19 x 12 as follows:

19 x 12 = 228

The 228 months are seven less than the required 235 months. Since we need 235 lunar months, an additional 7 "leap" months must be inserted in any 19-year cycle. (For example, you are familiar with the extra day of February 29 being used every 4 years. Instead, the Hebrew calendar requires 7 extra months be used in a 19-year period of time). By adding 7 additional months to 228 months, we arrive at a value of 235 months.

In the modern Hebrew calendar, the extra seven months are added in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years. It is important that you understand that the modern Hebrew calendar with its calculated dates and predetermined use of 7 intercalary months did not begin to be used until about the year AD 360. Before AD 360, the ancient Hebrew calendar had many errors and there was no certainty as to when to add an intercalary month. This viewpoint is corroborated by the Elephantine papyri and the Cairo Sandstone Stele as shown below.

Finally, it is important that you understand that the 19-year cycle is repeatable. This means that an alignment at 19-years will be repeated at 38-years. Three 19-year cycles are repeatable at 57 years. I found all three alignments in the Elephantine papyri as shown in the paragraphs below.
19-year cycles in the 5th century BC
Corroborates the Cairo Sandstone Stele

I have scientifically dated 18 Elephantine papyri and the Cairo Sandstone Stele, which gives us a total of 19 dates in the 5th century BC to search for and verify the 19-year lunar-solar cycle. I discovered that there are 3 alignments and that 2 of the alignments are to the the Cairo Sandstone Stele. Based on these credible alignments, we can make valid conclusions about the 5th century BC calendar used at Elephantine, Egypt. Below are the three 19-year cycle alignments.
Beginning of
19-Year Cycle		 Cycle
(# of cycles)		 End of
19-Year Cycle		 Intercalary
Months Used
Sandstone Stele
May 15, 459 BC		 19-Years
(1-cycle)		 Kraeling 2
Aug 26, 440 BC		 8 Used
Should be 7
Kraeling 2
Aug 26, 440 BC		 38-Years
(2-cycles)		 Kraeling 10
Mar 9, 402 BC		 13 Used
Should be 14
Sandstone Stele
May 15, 459 BC		 57-Years
(3-cycles)		 Kraeling 10
Mar 9, 402 BC		 21 Used
Natural Cycle

The data above permits several conclusions as follows:

  • The natural cycle of 19-years is verified by the 57-years from the Cairo Sandstone Stele dated May 15, 459 BC to the Kraeling 10 papyrus dated March 9, 402 BC. Twenty-one intercalary months were used in 57 years. This makes the Cairo Sandstone Stele a credible date. In addition, this data verifies that the Hebrew calendar month began 48 hours before the new moon occurred in May, 459 BC (important in supporting that the year AD 32 is viable for the crucifixion date of Jesus).

  • During the 5th century BC, The use of 7 intercalary months in each 19-year cycle was not predetermined as it is in the modern Hebrew calendar. The data shows that the calendar used at Elephantine was not well defined. The Hebrews at Elephantine did not know when to insert an intercalary month as verified by the following data.
  1. For the initial 19-year cycle from 459 to 440 BC, a total of 8 intercalary months were used. If the Hebrew calendar had been predetermined, there would have been only 7 intercalary months used.

  2. For the 38-year cycle from 440 to 402 BC, a total of 13 intercalary months were used. If the Hebrew calendar had been predetermined, there would have been 14 intercalary months used.

  3. Due to the natural 19-year cycle, the 57-year cycle from 459 to 402 BC used a total of 21 intercalary months. Over long periods of time, it would be natural for the Hebrews to have used an average of 7 intercalary months in each 19 year cycle.

On a more appropriate note, this data confirms that the Cairo Sandstone Stele dated May 15, 459 BC was dated correctly. It also confirms that there was a human error in writing the year of king Artaxerxes' reign on the Cairo Sandstone Stele.

Finally, it is important to understand that between the years 465 to 460 BC, the Hebrew calendar did not use a single intercalary month. The Cairo Sandstone Stele verifies that an intercalary month was used in 459 BC. This study also confirms that 9 intercalary months were used in a period of 20 years, which supports the Hebrews at Elephantine were on a learning curve in determining when to insert an intercalary month.

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