Two pure lunar calendars begin their 'year' with this new moon. The Islamic calendar and my lunar yerm calendar, which begins yerm 19 at noon today. See
I remember this happening for yerm 5 of this cycle, some 19 Islamic years ago. To work out whether a period of yerms has a whole number of lunar years add to the number of yerms twice the number of short (15-month) yerms and if this result is a multiple
of 12, so is the number of months.