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Epact
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===19-year cycle=== The [[tropical year|solar calendar year]] is slightly shorter than {{sfrac|365|β―1β―β―|4}} days, while the [[synodic month]], on average, is slightly longer than {{sfrac|29|β―1β―|2}} days meaning both are non-integers. This gets corrected in the following way. Nineteen tropical years are deemed to be as long as 235 synodic months ([[Metonic cycle]]). A cycle can last 6939 or 6940 full days, depending on whether there are 4 or 5 leap days in this 19-year period. After 19 years the lunations should fall the same way in the solar years, so the epact should repeat after 19 years. However, {{nobr|19 Γ 11 {{=}} 209,}} and this is not an integer multiple of the full cycle of 30 epact numbers ({{nobr|209 [[modular arithmetic|modulo]] 30 {{=}} 29,}} not 0). So after 19 years the epact must be corrected by +1 in order for the cycle to repeat over 19 years. This is the {{lang|la|saltus lunae}} ("leap of the moon"). The sequence number of the year in the 19-year cycle is called the [[golden number (time)|golden number]]. The extra 209 days fill 7 embolismic months, for a total of {{nobr|19 Γ 12 + 7 {{=}} 235 lunations.}}
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