The 12 or 13 Lunations Calendar is a calendar made up in school one day which has 12 or 13 lunations per year. The calendar, in normal years, has 353, 354 or 355 days or approximately 12 lunations. In leap years, there are 382, 383 or 384 days, resulting from a leap month.

## Months and lunations

1. January: 29 days
2. February: 30 days
3. March: 29 days
4. April: 30 days
5. May: 29 days
6. June: 30 days
7. July: 29 days
8. August: 30 days
9. September: 29 days
10. October: 30 days
11. November: 29 days
12. December: 29, 30 or 31 days
13. intercalary month: 32 days

Instead of 383, 384 and 385 days for 13 lunations, there are 382, 383 and 384 days for 13 lunations, for fixed calendar length.

For example: 353 days could equal to 12 months in one year, and 385 could equal to 13. This intercalary month has 32 days. So, for fixed calendar length, there are 382, 383 or 384 days in 13 lunations.

2 months is also always equal to 59 days, since in a cycle of 2 months, there is one month with 29 days and one with 30 days.

For example, in a normal year with 353, 354 or 355 days, it would be:

• 2 months - 59 days
• 4 months - 118 days
• 6 months - 177 days
• 8 months - 236 days
• 10 months - 295 days
• 12 months - 353, 354 or 355 days

## Leap rule

If a year is normal, it will stay like that for 6 years. And after those 6 years, there will be a leap year. After 6 years of having leap years, we will go back to normal years. And after 6 years of normal years, we will go back to 6 years of leap years and so on.

In the 6 year cycle of normal years, 2 years have 353 days, 2 years have 354 days, and 2 years have 355 days. This equals to 706+708+710. This is equal to 2124 days.

In the 6 year cycle of leap years, 2 years have 382 days, 2 years have 383 days, and 2 years have 384 days. This equals to 764+766+768. This is equal to 2298 days.

This means that 12 lunations have an approximate length of 354 days (2124/6), and that 13 lunations have an approximate length of 383 days (2298/6).

The actual length is 383.8978 days, or 29.5306 times 13.

13 lunations ≈ 384 days

Like said earlier, normal years and leap years can only be repeated 6 times. Hence, you cannot have 383x7, 2681 days, or a more accurate length, 383.8978. You also cannot have 354x7, 2478 days as that is over the limit.

In a 6 year cycle, each year has 353, 354 or 355 days. Every 2 years we get one more day. This means, there are 2 years with 353 days, 2 years with 354 days, 2 years with 355 days. This is so that it is equal, and also that it has an approximate length (354 for normal years, 383 for leap years). So, in a 6 year cycle, 1/3 have 353 days, 1/3 have 354 days, and 1/3 have 355 days.

This 12-year or 150-lunation cycle contains 4422 days, which makes the average year 368.5 days and the average month 29.48 days.