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The relationship between the average length of the synodic period of the moon (29.5306 days) and the average length of the solar tropical year (365.2422 days) is not an integer. |
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As long as a lunisolar calendar depends upon the observation of the actual new moon, it is tied to observation by the variation in the moon's orbit and cannot be used to calculate the dates of future events or unrecorded past events. This is a problem, and most calendars with a lunar component solve it by determining an average synodic period. By foregoing the possibility of being exactly correct, the calendar gains a rule that can be used for calculations. |
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The Jewish calendar solved the first problem by using a calculated average of 29 days, 12 hours, and 793 halakim as the length of a lunation. It solved the second problem by using a rule much like the one called Metonic, which equates 235 lunations to 19 years. Several different kinds of additional adjustments are also made. The lengths of the month and year therefore vary. |
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Years occur in a 19-year cycle called the Small Mahzor. In this cycle, 12 years have 12 months and seven years have 13 months (1212 + 713 = 235). Years 3, 6, 8, 11, 14, and 19 are leap years of 13 months, while the remainder are common years of 12 months. |
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Since the average synodic month is about 29 1/2 days, the months alternate between 30 and 29 days in length. The use of unit days, however, omits the 793 halakim, and this omission is further corrected by occasionally adding one day to the month of Heshvan or subtracting a day from the month of Kislev. This practice causes years to be organized as regular, deficient, or excessive, in addition to their classification as common and leap (Tables 9.15 and 9.16). |
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| Table 9.15 Months in a common year. | | Month Number | Month Name | Number of Days | | 1 | Tishri | 30 | | 2 | Heshvan | 29, 30 in excessive years | | 3 | Kislev | 30, 29 in deficient years | | 4 | Tevet | 29 | | 5 | Shevat | 30 | | 6 | Adar | 29 | | 7 | Nisan | 30 | | 8 | Iyar | 29 | | 9 | Sivan | 30 | | 10 | Tammuz | 29 | | 11 | Av | 30 | | 12 | Elul | 29 |
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