Rules for determining Blue Moons

Last updated 3 Apr 1999

Note: The explanation that follows has been superseded by an article in the May 1999 issue of Sky & Telescope . Click here for details. The following may still be of interest, but the proposed rule for blue moons must be modified slightly by re-defining the terms "equinox" and "solstice" to indicate the mean position of the sun (i.e., that it would have if the earth's orbit were circular), rather than the apparent position (which includes the effects of an elliptical orbit, perturbations by other planets, and so on).

The March 1999 issue of Sky & Telescope contains an article, "Once in a Blue Moon", concerning different "folk etymologies" for the expression "blue moon". A total of eight different meanings were given. (The commonly used meaning today is the second full moon in a given calendar month, but this appears to be a recent innovation.)

The earliest reference cited was from the Maine Farmers' Almanac for 1937. This states that:

   The Moon usually comes full twelve times in a year,  three times in each
season.  These moons were named by our early English ancestors as follows:

 Yule 
Winter Moons:
   0 Moon after Yule
   1 Wolf Moon
   2 Lenten Moon
 First Day of Spring 
Spring Moons:
   3 Egg Moon
   4 Milk Moon
   5 Flower Moon
 The Long Day 
Summer Moons:
   6 Hay Moon
   7 Grain Moon
   8 Fruit Moon
 Summer's End 
Fall Moons:
   9 Harvest Moon
  10 Hunter's Moon
  12 Moon before Yule

   However,  occasionally the moon comes full thirteen times in a year.
This was considered a very unfortunate circumstance,  especially by the
monks who had charge of the calendar.  It became necessary for them
to make a calendar of thirteen months,  and it upset the regular arrangement
of church festivals.  For this reason thirteen came to be considered an
unlucky number.  Also,  this extra moon had a way of coming in each of
the seasons so that it could not be given a name appropriate to the time
of year like the other moons.  It was usually called the Blue Moon.  There
are seven Blue Moons in a lunar cycle of nineteen years.  This year (1937)
has a Blue Moon in August,  the same as 1918.  In 1934 and 1915 Blue Moons
came in November.  The next Blue Moon will occur in May 1940 as it did in
1921.  There was a Blue Moon in February 1924.  In olden times the almanac
makers had much difficulty calculating the occurrence of the Blue Moon
and this uncertainty gave rise to the expression "Once in a Blue Moon".

Calendars which follow both the solar and lunar cycles are common; these are called lunisolar calendars. Examples are the Chinese and Hebrew calendars, but it seems unlikely that either corresponds to the Maine Farmers' Almanac definition. (The Hebrew "leap month" is always inserted in the spring.)

In such a calendar, one does indeed average out very close to seven "leap months" or "Blue Moons" in a 19-year cycle (the "Metonic" cycle). Exactly what calendar is being referred to in the above is a mystery to me. The old (pre-Christian) Roman calendar did insert a thirteenth month, Intercalus, at odd intervals. And it was considered to be unlucky; the priests maintaining the calendar were sometimes bribed to not insert this month. But this still seems far-fetched; presumably, some other lunisolar calendar is meant.

The Blue Moons mentioned in the above excerpt occur on 21 Nov 1915, 22 Aug 1918, 21 May 1921, 20 Feb 1924, 21 Nov 1934, 22 Aug 1937, and 21 May 1940. These dates, combined with the above text, are a strong hint that blue moons have something to do with there being four full moons in one season of the year.

It also occurred to me that it might have something to do with the sun's motion along the zodiac. The present-day Old Farmers' Almanac does include some astrological information, and I wondered if perhaps a "blue moon" might be the second full moon while the sun was in a given zodiacal sign; that is, while the sun was in a given 30-degree range of ecliptical longitude. (The Chinese calendar follows a similar rule; its "thirteenth month" usually happens when there are two new moons while the sun is in a given zodiacal sign.) I had to junk that theory, though, because most of the cases mentioned in the excerpt don't fit any such rule.

I built the following table. For each Blue Moon mentioned in the above excerpt, I found the times when that season began and ended, and the dates of the full moons during that season. The times are in Universal Time. The Blue Moons are marked with a 'B'.

   Full moons              Solar 30 degrees

  23 Sep 1915  9:34     24 Sep 1915  3:28:37 (autumnal equinox)
  23 Oct 1915  0:15
B 21 Nov 1915 17:36
  21 Dec 1915 12:51     22 Dec 1915 22:20:50 (winter solstice)

  24 Jun 1918 10:37     22 Jun 1918  6:06:49 (summer solstice)
  23 Jul 1918 20:34
B 22 Aug 1918  5:01
  20 Sep 1918 13:00     23 Sep 1918 20:52:25 (autumnal equinox)

  23 Mar 1921 20:18     21 Mar 1921  3:54:36 (spring equinox)
  22 Apr 1921  7:49
B 21 May 1921 20:14
  20 Jun 1921  9:40     21 Jun 1921 23:38:51 (summer solstice)

  23 Dec 1923  7:32     22 Dec 1923 20:50:24 (winter solstice)
  22 Jan 1924  0:56
B 20 Feb 1924 16:07
  21 Mar 1924  4:29     20 Mar 1924 21:16:55 (spring equinox)

  23 Sep 1934  4:18     23 Sep 1934 17:50:33 (autumnal equinox)
  22 Oct 1934 15:01
B 21 Nov 1934  4:26
  20 Dec 1934 20:53     22 Dec 1934 12:55:08 (winter solstice)

  23 Jun 1937 22:59     21 Jun 1937 20:19:02 (summer solstice)
  23 Jul 1937 12:45
B 22 Aug 1937  0:47
  20 Sep 1937 11:32     23 Sep 1937 11:19:23 (autumnal equinox)

  23 Mar 1940 19:33     20 Mar 1940 18:26:29 (spring equinox)
  22 Apr 1940  4:36
B 21 May 1940 13:32
  19 Jun 1940 23:01     21 Jun 1940 13:38:34 (summer solstice)

A few patterns are readily apparent. The Blue Moon is always the third of the season. In most cases, all four moons "fit" into the season in question. The exceptions are in 1915 and 1924. In these cases, the first full moon in each series falls just a bit before the season starts.

One can work around this, though, if one assumes that only the calendar date, in local time (Universal time minus five hours), is used. In that case, both the full moon and the autumnal equinox occur on 23 September 1915, for example. (Working in this manner of considering full days rather than exact instants is common in many calendars. For example, in the Chinese calendar, one considers the dates on which new moons and "Principal Terms" occur, rather than their exact times.)

This leaves only 1924 as a totally unresolved case. I tried all sorts of possible assumptions, but I can find no rule explaining why February 1924 would contain a Blue Moon. I'm inclined to suspect a printer's error, but am open to alternative interpretations.

So the "Blue Moon" can apparently be summarized as follows:

If there are four full moons during a given season of the year, the third full moon is considered to be the Blue Moon.