Hi. As part of a religious studies project, I'm trying to create a calendar that aligns lunar months with solar years. I've been working on it for a couple of days and I'm having a lot of problems with the maths, so I wondered if you could help. Here are the specs I've come up with for one concept:

-a year has 365.25 days

-a month has 29.5 days

-each month has 29 or 30 days alternately to correct the half day anomaly every two months, thus keeping the lunar cycle in sync with the months

-the format I've worked with is having twelve months, plus one month spanning the new year with a variable number of days before and after the new year, to keep the lunar cycle in with the solar year

-the number of days in the first month of the year is dependent on the number of days in the last month of the last year, in that if the twelfth month (not including the first month except where this equals 29 days) equals 29, the number of days in the month spanning the new year should equal 30, and if the twelfth month has 30 days, the span month should have 29 days, with enough in the old year to make the total (of the sum of days in all months, including the first/last months within that year) equal 365, or 366 in a leap year

-the number of days in a year must equal 365, except every fourth year which must equal 366 to correct the anomaly and bring the solar cycle in sync with the solar year...

(unless another solution can be offered)

-as it is, the years could come around in a cycle, eventually coming back to the year beginning with 29 day month 1 and being three away from a leap year. The cycle just never seems to get there. I'd appreciate some kind of equation to speed up working out the lengths of the first and last months.

-phew.

Here are the results I've come up with so far on my latest try: (days in old year half of last month, days in new year, etc.)

11,18,22,7,4,26,16,14,27,2,9,21

come up with a formula for that sequence and you might have something..

mind you, I may not have worked out the sequence correctly. And my maths and explanatory skills are generally bad. Apologies.