Calendars in East Asia

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Successive attempts to improve a typical luni‐solar calendrical system for reconciling two fundamentally incommensurable periods – the tropical year and the synodic month – were made throughout the history of Chinese and Japanese calendars until their replacement by the Gregorian solar calendar in modern times, the Japanese in 1883 and the Chinese in 1912.

The length of a synodic month varies between 29.0 and 30.1 days. The luni‐solar calendar provided for “short” months of 29 days and “long” months of 30 days. Calendrical scientists attempted to arrange short and long months so that the moon's conjunction would take place on the first day of every month. The day notation of the lunar month represented the phase of the moon; for instance, the 15th day of the month was always a full moon, while the first day was a new moon.

In addition, the Chinese had an independent system of solar intervals (qi) for indicating seasonal changes, the most important phenomena in the regulation of agricultu ...