The moon cycles are important to navigators and fishermen because of the effect they have on tides.
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Calendars do not always have Moon cycles on them. I've been buying Lang calendars for more than 10 years - no moon cycles, and the religious holidays are based on a British/U.K. almanac database, so sometimes they are a day "off " from the U.S.A. holidays. The Moon was full today on Uiversal Time Coordinate time - cesium atomic clock time.
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I don't know, just because...probably has to do with the fact that the moon cycle is about 30 days (the length of a month), the months are based on the moon cycle.