Lunisolar calendar

A lunisolar calendar is a calendar in many cultures whose date indicates both the Moon phase and the time of the solar year. If the solar year is defined as a tropical year, then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year, then the calendar will predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In this case ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.

The Five Phases and Four Seasons of the traditional Chinese lunisolar calendar, with English translation.
1729 Japanese calendar, which used the Jōkyō calendar procedure, published by Ise Grand Shrine
Record of the Chinese lunisolar calendar for 1834, 1835, and 1836 during the Qing Dynasty under the Daoguang Emperor's Reign (道光十四年,道光十五年,道光十六年)

Their months are based on the regular cycle of the Moon's phases. So lunisolar calendars are lunar calendars with – in contrast to them – additional intercalation rules being used to bring them into a rough agreement with the solar year and thus with the seasons.

The main other type of calendar is a solar calendar.