How do lunisolar calendars work?

I have recently discovered that the traditional Chinese calendar is a lunisolar calendar rather than a lunar one. Well, what even is a lunisolar calendar? You might wonder. It is a combination of a lunar calendar and a solar calendar. The “month” in the traditional Chinese calendar is equivalent to the length of a moon phase cycle, which is about 29.53 days. With 12 months in a year, that would make 29.53 x 12 = 354.36 days per year.


But, as we all know, a solar year is 365.24 days. It wouldn’t make sense for the ancient Chinese to use a pure lunar calendar, because they are an agricultural culture, and in that sense the sun is far more important than the moon. They would need something to deal with the difference between 354.36 days per year and 365.24 days per year. For that, they have “leap month”, which is an extra month located here and there on the calendar. There are 7 leap months in 19 years, because there are (19 x 12 + 7) x 29.53 =6939.55 days in 19 lunisolar years and 365.24 x 19= 6939.56 in 19 solar years.