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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#SaudiArabia used the #LunarHijriCalendar for all official purposes until the 1950s. At some point, it was decided to switch to a #SolarCalendar to reduce the frequency of monthly salary payments, thus saving the government money.

Arabia adopted the Gregorian calendar, which is used throughout the world, partly because it would make #commerce easier. #OmarKhayyam had invented better calendars, but money talks and Arabians are apparently OK with Christians than the wrong type of Muslims.