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Since each lunation is approximately 29 + 1 ⁄ 2 days, [1] it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of 12 such lunations, a lunar year, is 354 days, 8 hours, 48 minutes, 34 seconds (354.36707 days), [1] purely lunar calendars are 11 to 12 days shorter than the solar year.
Consequently, at 27 days, 7 hours, 43 minutes and 11.5 seconds, [5] the sidereal month is about 2.2 days shorter than the synodic month. Thus, about 13.37 sidereal months, but about 12.37 synodic months, occur in a Gregorian year .
A month is a unit of time, used with calendars, that is approximately as long as a natural phase cycle of the Moon; the words month and Moon are cognates.The traditional concept of months arose with the cycle of Moon phases; such lunar months ("lunations") are synodic months and last approximately 29.53 days, making for roughly 12.37 such months in one Earth year.
A tropical year is approximately 365.2422 days long and a synodic month is approximately 29.5306 days long, [4] so a tropical year is approximately 365.2422 / 29.5306 ≈ 12.36826 months long. Because 0.36826 is between 1 ⁄ 3 and 1 ⁄ 2 , a typical year of 12 months needs to be supplemented with one intercalary or leap month every 2 to 3 years.
[3] [4] Because a lunar cycle is about 29.5 days long, such months would have varied between 29 and 30 days. [5] Twelve such months would have fallen 10 or 11 days short of the solar year and, without adjustment, such a year would have quickly rotated out of alignment with the seasons [5] in the manner of the Islamic calendar.
Twelve Hindu mas (māsa, lunar month) are equal to approximately 354 days, while the length of a sidereal (solar) year is about 365 days. This creates a difference of about eleven days, which is offset every (29.53/10.63) = 2.71 years, or approximately every 32.5 months. [29]
The actual length of a synodic month varies from about 29 days 6 hours and 30 minutes (29.27 days) to about 29 days and 20 hours (29.83 days), a variation range of about 13 hours and 30 minutes. Accordingly, for convenience, the Hebrew calendar uses a long-term average month length, known as the molad interval , which equals the mean synodic ...
A year was 365.25 days, and a month was 29.5 days. After every 16th month, a half-month was intercalated. According to oracle bone records, the Shang dynasty calendar (c. 1600 – c. 1046 BCE) was a balanced calendar with 12 to 14 months in a year; the month after the winter solstice was Zhēngyuè. [10]