AFAIK, there are only two purely lunar calendars in historical use. The #LunarHijriCalendar (AKA #MuslimCalendar, #ArabCalendar) is a straightforward cycle of 12 months; it is adapted from an older lunisolar calendar which dropped leap months when #Muhammad ruled you can't add extra months.
The traditional calendar of the Kazakh nomads is also purely lunar. Months directly match the lunar cycle, and the year begins when the new moon aligns with Polaris and the Pleiades.
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Somebody was talking to me about the #MuslimCalendar, and it occurred to me that knowing the #JewishCalendar means I can calculate how the former cycles through the year.
The lunisolar Jewish Calendar has 7 leap months every 19 years, or 7 extra months every 235 months. It thus falls behind the pure-lunar Muslim Calendar at a unitless rate of 7/235 (on average). Thus, it takes 235/7 ≈ 33.6 years for the Muslim holidays to cycle through the solar year.
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JDushoff @jdushoff.bsky.social