Most lunar years have 384 days, which is achieved by alternating months of 30 and 29 days, but just over one in ten years have one day less (383 days) to keep the mean month accurate to the phases of the moon.
Each date in the lunar calendar has a solar date assigned to it. The rules for assigning the solar date can be applied to any lunar calendar with lunar years of 13 months, not just the Palmen-McKenna Calendar. In the Palmen McKenna Calendar the Solar Dates determine whether a given lunar year has a day taken away from it.
Determining the Solar Date of a Lunar Date
The solar date assigned to a lunar date is determined by the following rules:
- The solar year has 12 solar months each with 31 solar dates.
- A solar date is skipped at the end of each lunar month of only 29 days.
- In addition, a solar date is skipped at the end of each lunar year
- Lunar year 1 begins close to a northern spring equinox and its first day has the first date of a solar year.
This ensures that there are exactly 391 solar years every 372 lunar years, 403 lunar years of 12 months or 4836 lunar months. This cycle is also an eclipse cycle called the Grattan-Guinness cycle.
The Short Year Rule
A lunar year has one day removed from it, if it contains two occurrences of either the first date of a solar year or the first date of the seventh solar month of a solar year. If any of these dates are skipped it is counted in the year, if the previous day belongs to the year.
This results in the following 186-year cycle of short lunar years:
1, 10, 20, 30, 40, 49, 59, 69, 79, 89, 98, 108, 118, 128, 138, 147, 157, 167, 177.
Each such cycle is half a Grattan-Guinness cycle of 372 lunar years equated to 391 solar years.
The mean lunar month is 29.5306038 days and the mean solar year is 365.242967 days.
No epoch has been chosen for this calendar. Year 1 must begin close to a northern spring equinox and a new moon.