Definition
In the traditional Korean lunar calendar, which counts days by the changing shape of the moon, the leap month (yundal) is an extra month added once every few years so that calendar dates stop drifting away from the seasons. It is a clever buffer that reconciles the very different cycles of the moon and the sun.
It Happens Because the Sun and Moon Take Different Strides
Picture two people running on the same track. One takes short steps and laps the track quickly, again and again. The other takes long strides and loops around slowly and widely. The moon and the sun in the sky are just like these two runners.
A purely lunar calendar is built on the moon's cycle of changing shape (the synodic month). Add up all twelve of its months and you get only about 354 days in a year. A solar year, the time Earth takes to circle the sun once, is about 365.24 days. So every year the moon reaches the finish line about 11 days ahead of the sun, and an 11-day gap opens up each year.
What happens if you just leave that gap alone? In only three years, the error piles up to more than a month, about 33 days. After roughly 16 years, the first lunar month, which should be wintry, would land in the middle of a summer heat wave, and snowstorms would hit the harvest festival of Chuseok in the eighth month.
For our ancestors, who farmed and had to live by the flow of the seasons, a calendar that didn't match the seasons was useless. So, to correct this mismatch regularly, they invented a technique of inserting a whole extra month into the calendar like a bonus. That is the leap month.
The Rule of Seven Leap Months in 19 Years
So when, and how often, should this bonus month be added? After watching the sky for many long years, ancient astronomers found a magical rule that makes the sun and moon line up again exactly.
It is a method of adding a leap month about seven times every 19 years. Over those 19 years, the days the sun takes to pass (about 6,939.6 days) and the days of 235 full cycles of the moon's phases (about 6,939.7 days) match almost perfectly. In East Asia this was called the Zhang cycle, and in the West it is called the Metonic cycle, after the person who discovered it.
To be a little more precise, a leap month is not tacked onto the very end of the year like a "13th month." It is decided using the 24 solar terms, the seasonal markers that divide the year into 24 parts. When some lunar month turns out to contain none of the solar terms called "major terms" (jungi), that month becomes the leap month and borrows the name of the month before it. For example, one that follows the 4th month becomes "leap 4th month."
A Free Month When Even the Spirits Take a Break
Our ancestors treated this bonus month as a very special time. They believed that the gods and spirits who usually rule over heaven and earth and watch what people do would leave their posts and rest during this month.
Since it is a "free month" that isn't part of the original twelve, they thought of it as a month with no "son" (the troublesome spirits that get in people's way), a month beyond the spirits' watch. So things they were normally afraid to touch, for fear of bringing disaster (dongti), they eagerly carried out in the leap month, calling it a safe time free from bad luck.
Typical examples were making burial clothes in advance while wishing their parents a long, healthy life, moving an ancestor's grave to a new site, and repairing an old house. An old saying even arose that "in a leap month, you can stand a corpse upside down and nothing will go wrong," which shows how much people enjoyed the leap month as a carefree month of release.
Of course, from the viewpoint of modern science, the leap month has nothing to do with spirits. It is a refined mathematical device for matching the calendar to the seasons. Yet the warm feeling of our ancestors, who calmed their anxious minds wisely without going against the flow of nature, is still fully alive in leap month customs.
Common misconceptions
A leap month and a leap year are the same thing with different names.
A leap month adds a whole month (about 29 to 30 days) to the lunar calendar to fix the gap with the seasons. A leap year adds a single day (February 29) to the solar calendar, usually every four years. They are completely different. The leap year rule also has exceptions: years divisible by 100 are skipped, and years divisible by 400 are leap years again.
A leap month is always the 13th month, tacked onto the very end of the calendar.
A leap month is not added at the end of the year. The month that contains no "major term" among the 24 solar terms becomes the leap month and borrows the name of the month right before it, such as "leap 4th month" or "leap 7th month." It falls in the middle of a year.
Where you meet it
When a leap month follows the 5th lunar month, it is called "leap 5th month," and that year the 5th month happens twice.
A leap month itself comes once every two to three years, but for someone born in a leap 4th month, the same leap 4th month has to come around again for their birthday month to return, so they usually wait more than ten years.
In one sentence
The leap month is an extra month inserted seven times every 19 years to fill the gap between the lunar calendar, which falls about 11 days short each year, and the seasons.