# Double Blue Moons

In four or five years per century, there are two Blue Moons.

The first Blue Moon always occurs in January. The second occurs predominantly in March. In the 10,000 years starting with 1600, this is true in 343 out of 400 cases, or 86 per cent of the time. In 37 cases (or 9 per cent), the second Blue Moon is in April. In the remaining 20 cases (5 per cent) it is in May.

In order for a second Blue Moon to take place in March, there can be no Full Moon in February, and so non-leap years will inevitably be favoured. However, it is possible to have a double Blue Moon in a leap year. Clearly, the second Full Moon in January takes place near the very end of the 31st, and the first Full Moon in March is early on the 1st. The extremes of the lengths of the lunar month are 29 days 6 hours and 29 days 20 hours, so it is possible to skip February altogether in this way.

It is also possible for December and the following March both to have Blue Moons. This happened, for example, in December 1933 and March 1934. Since the practice of beginning the year on January 1st is just a convention (and quite a recent one), we can regard December/March pairs as double Blue Moons. When a December/March pair occurs, then February has no Full Moon, just as in January/March or January/April or January/May pairs.

There is a pattern to double Blue Moons. If you make a list of every year between 1600 and 9999 in which two Blue Moons occur, then take the year modulo 19 and assign a letter to it so that zero maps to A, 1 to B and so forth, up to S, then you find that there are sequences of successive double Blue Moon years which have the same letter. Eventually, another letter appears to herald the start of a new sequence. This is always 8 letters earlier in the sequence.

For example, the E sequence, which runs from 1771 to 2113, gives way to the P sequence which begins in 1915 and ends in 2485. The sequences almost always overlap in this way, but there are never more than two parallel sequences at any one time.

Each sequence runs for between 17 and 31 Metonic cycles, i.e. between 323 years and 589 years. A given sequence letter recurs after about 6700 years, but the sequence is not repeated exactly.

## How many double Blue Moons per century?

We counted the number of double Blue Moons in each 100-year period in our list which covers the 84 centuries from 1600 to 9999. Here are the results:

Double Blue Moons
in a century
Number of centuries Percentage
3 4 4.8
4 46 54.8
5 25 29.8
6 8 9.5
7 1 1.1
TOTAL 84 100.0

We thank Ronald Dodge for the question which prompted us to create this table.