1) so we all know and love the modern US and European way of calendar generation. 24 hours in a day, 365 +1 on leap year this is called the Gregorian Calendar.
Well It took me by shock when I learned of the other different calendars when trying to create an international holiday calendar that correctly identified holidays that closed the trading markets. So here is a short summary.
2) Julian time is the integer assigned to a whole solar day in the Julian day count starting from noon Greenwich Mean Time, with Julian day number 0 assigned to the day starting at noon on January 1, 4713 BC. (copied from wikipedia) this is used by Astronomers ALOT. And serves as a basis for translating between different calendar systems.
3) The Chinese calendar is a lunisolar calendar, incorporating elements of a lunar calendar with those of a solar calendar. ( from wikipedia ) So basically the days are subject to the sun rising and setting just like the Gregorian calendar.. But the months are tied to the winter equinox. So the winter equinox MUST always fall within a certain month and then the rest of the calendar is built backwards, with a set number of days each, and sometimes you need an extra month to accommodate. It works and is very complex. If you own the book Astronomical Algorithms and know programming you will have enough information to create a calendar as accurate as the Chinese produce.
4) The Hebrew or Jewish calendar ( , ha'luach ha'ivri) is a lunisolar calendar used today predominantly for Jewish religious observances.(taken from wikipedia). The current year of the Jewish calendar (16 September 2012 to 4 September 2013) is AM 5773. The Jewish day is of no fixed length. The Jewish day is modeled on the reference to "...there was evening and there was morning..." in the Creation account in the first chapter of Genesis. The really interesting thing I learned is that every hour is divided into 1080 halakim or parts. A part is 3 seconds or 1/18 minute. This makes predicting the moon extremely accurate to estimation. Also a Metonic cycle equates to 235 lunar months in each 19-year cycle. This gives an average of 6939 days, 16 hours, and 595 parts for each cycle. But due to the Rosh Hashanah postponement rules (preceding section) a cycle of 19 Jewish years can be either 6939, 6940, 6941, or 6942 days in duration. But this calendar is extremely easy to program.
5) Arabic calendar. I never could figure out this calendar system. It is similar to the Jewish calendar but where one allows months to move progressively throughout the year the other is fixed so that months happen around the same time every year. I forget which one does which. Sorry, it been a while. This calendar is supposed to be very computer friendly as well, however I could not figure it out within the time frames of the project I was doing.
6) The Hindi calendar is to my knowledge one of the most complex and complex, and complex ... did I mention complex calenders in existence. I never figured it all out. But it has to do with a month starting depending on where the moon is when the sun rises on a given day. It can be figured out, but because it is based on very complex dimensions like sunrise which varies based on location, and perceived placement of the moon, which varies by location, the calender is fractured into different version for different regions. I am sure it is a good calendar, I just don;t understand how it fits in a 21st century setting. Basically if you have to deal with someone using a Hindu calendar or need to write a contract and guarantee payments that you will get, base it on days, not months or years. Trust me you will save you and your organization brutal misunderstandings. Everyone agrees a day consists of nighttime and daytime.
Those are the 6 calendars I dealt with. They represent the calendars in use by the biggest economies in the world. But there are more. What I learned that impressed me the most was that all of them outside of the Gregorian and Julian are ancient. All the lunisolar calendars basically meant someone went to the same spot day after day and recorded where the moon appeared to be for hundreds of years to create a calendar as accurate as the Chinese and Hebrew calendars. To accommodate what was seen to what was usable took different measures to ensure plants could be planted. A huge undertaking of observation and careful record keeping. And they were created 3-5 thousand years ago and assembled without a computer. I repeat the Chinese and Hebrew calendars are phenomenal when you look into their history and what it takes to construct them by hand.
I hope this sheds light and answers question, and inspires others to seek more knowledge.
be well my friends