Afs I don't know what calendar you have there, but we have something like that as well. It is a lunar calendar and the birthdays are based on a "star" (I guess they are constellations rather, I don't know but we call them stars). There are 27 "stars" and each year the birthday falls on a completely different date, not just a day here or there. It is all very confusing. My father studied astronomy and he is very patient in explaining me the Indian system of stars, lunar cycles, solar cycles etc a million times. I understand it well when he explains, but cannot remember a thing afterwards It is very interesting, but complex at the same time. The western calendar is all I can handle I guess. BTW, not everyone followed lunar cycles traditionally in India, I think the majority followed a solar calendar, but not the western one.
Wow, I had never heard of this kind of calendar before. The simplest way to introduce ours is to say the zodiac months are based on this calendar. For more information check out here:
This calendar has 5 leap years every 33 years observed on March 20th, which explains the confusion between the dates, as the other calendar has one leap year simply every four years. But this calendar is the most accurate when the seasonal swings are concerned.
"Fire cannot kill a dragon." -Daenerys Targaryen, Game of Thrones
It is very interesting, but complex at the same time. The western calendar is all I can handle I guess. BTW, not everyone followed lunar cycles traditionally in India, I think the majority followed a solar calendar, but not the western one. 
