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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. In purely lunar calendars, which do not make use of intercalation, the lunar months cycle through all the seasons of a solar year over the course of a 33 ...
The Islamic calendar is a purely lunar calendar and has a year, whose start drifts through the seasons and so is not a solar calendar. The Maya Tzolkin calendar, which follows a 260-day cycle, has no year, therefore it is not a solar calendar. Also, any calendar synchronized only to the synodic period of Venus would not be solar.
Intercalation of leap months is frequently controlled by the "epact", which is the difference between the lunar and solar years (approximately 11 days). The classic Metonic cycle can be reproduced by assigning an initial epact value of 1 to the last year of the cycle and incrementing by 11 each year.
A candra māna varṣa or lunar year is made up of 12 consecutive candramāsa. [5] These twelve candramāsa are designated by unique names caitra, vaiśākha, etc. [note 2] In some instances an additional candramāsa, known as an adhikamāsa, is added to synchronise the candra māna varṣa with the solar year or saura māna varṣa.
The traditional lunar year of 12 synodic months is about 354 days, approximately eleven days short of the solar year. Thus, every 2 to 3 years there is a discrepancy of 22 to 33 days, or a full synodic month. For example, if the winter solstice and the new moon coincide, it takes 19 tropical years for the coincidence to recur.
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There are 12 synodic months in a lunar year, totaling either 354 or 355 days. The lunar year is about 11 days shorter than the calendar year, which is either 365 or 366 days long. These days by which the solar year exceeds the lunar year are called epacts (Ancient Greek: ἐπακταὶ ἡμέραι, romanized: épaktai hēmérai, lit.
The solar year does not have a whole number of lunar months (it is about 365/29.5 = 12.37 lunations), so a lunisolar calendar must have a variable number of months per year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" or "leap" month or "embolismic" month every second or third year.