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Lunar calendar and Moon’s phases

Lunar calendar, any dating system based on a year consisting of synodic months

lunar calendar is a calendar based upon the monthly cycles of the Moon’s phases (synodic months), in contrast to solar calendars, whose annual cycles are based only directly upon the solar year. 
The Sumerians were probably the first to develop a calendar based entirely on the recurrence of lunar phases. Each Sumero-Babylonian month began on the first day of visibility of the new Moon.
The most commonly used calendar, the Gregorian calendar, is a solar calendar system that originally evolved out of a lunar calendar system. 
Chinese calendar, a lunisolar calendar, is formed on the movement of the moon. It defines Chinese 24 solar terms, traditional holidays and helps to choose a lucky day before important activities such as marriage proposal, wedding, praying for pregnancy, traveling.
Hourglass 261, post card
Hourglass 261, post card
A purely lunar calendar is also distinguished from a lunisolar calendar, whose lunar months are brought into alignment with the solar year through some process of intercalation. 
The details of when months begin varies from calendar to calendar, with some using new, full, or crescent moons and others employing detailed calculations.

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