The Twelve Days of Christmas: An Analysis

There was a funny piece on the radio about the song "The Twelve Days of Christmas," imagining the woman's response to all those gifts. She starts out thrilled and touched by her partridge in a pear tree, but as the days go on and the presents keep piling up, she goes from gentle dissuasion to chilly formality to outright hostility.

It had not occurred to me that the woman would end up wilth twelve partridges in pear trees. Moreover, matters were getting worse, as she would get two turtledoves a day for days two through twelve, for a total of twenty-two turtledoves, and similarly, thirty French hens. On the other hand, the numbers did not keep increasing for all twelve days: she would get, fortunatelv, only twelve drummer drumming.

In fact, I realized, there are two effects in opposite directions: as the days go by, the gift gets bigger, but it is received for fewer days. Specifically, for the gift of day x, the recipient will get

x(13 - x)

copies, where the first part is copies per day (the number of geese a-laying or whatever), and the second part is the number of days the gift is received. This expression has a maximum between 6 and 7, and in fact our lucky love-object will get:

12 drummers druming;
22 pipers piping;
30 lords a-leaping;
36 ladies dancing;
40 maids a-milking;
42 swans a-swimming;
42 geese a-laying;
40 golden rings;
36 calling birds;
30 French hens;
22 turtledoves;
 and of course,
12 partridges in pear trees.

A few final comments: If you add up all the gifts, they total 364. If the true love had wished to demonstrate less romantic flamboyance and more dedication, he could have given her a present every day for an entire year, leaving her birthday as the one day when he gets her something she actually wants.

Of course, that would make a very long and and very dull song. "On the sixth day of March, my true love gave to me/ A French hen. On the seventh day of March, my true love gave to me/ Another French hen. On the eighth day of March, my true love gave to me/ Another French hen. On the ninth day of March, my true love gave to me/ Another French hen. On the tenth day of March...."