Genkareki is one form of Chinese calendar, a lunisolar calendar formerly used in China and Japan.
It is rekiho (method of making calendars) organized by He Chengtian, an astronomer in Song (Southern Dynasty) during the period of the Northern and Southern Dynasties (China). It was used in Song, Qi (Southern Dynasty) and Liang (Southern Dynasty) for sixty-five years from 445 to 509.
There are seven leap months in nineteen years; one solar year consists of 365 and 75 over 304 days (≒365.2467 days) and one synodic month consists of 29 and 399 over 752 days (≒29.530585 days).
He Chengtian pointed out that the winter solstice in the Jingchu calendar was three days away from the actual winter solstice because it was based on measurements used in the quartered calendar of the Later Han Dynasty, and conducted astronomical observation again. Furthermore, he tried to use the true conjunction, in which the slow motions of the moon were taken into consideration, for determination of the first day of a month, but it was not adopted because of many adverse opinions.
As a Japanese calendar
Genkareki was introduced to Japan via Baekje in the Korean Peninsula around the 6th century. It is believed that at first Reki hakase (Chief court calendar-maker) who had come from Baekje organized the calendar or that a calendar of Baekje was used as it was. In 602, Kanroku, a scholar monk, came to Japan from Baekje with calendar books and had the naturalized citizens' descendants study those books. In "Seiji Yoryaku (Brief Outline of Government)," a book written in the Heian Period, it is recorded that the first calendar made by the Japanese people was distributed on the first day of January in 604, and it is believed that the said calendar was based on Genkareki.
As a preparation for adoption of Gihoreki, a new calendar imported from China, Genkareki and Gihoreki started to be used together in 692 (or 690, according to some theory), and after five years Genkareki was abolished and Gihoreki was formally adopted in 697.
On February 26, 2003, mokkan (a narrow strip of wood on which an official message is written) which showed guchureki (Japanese Lunisolar calendar) based on Genkareki was discovered in Ishigami site in Asuka-mura, Nara Prefecture, which is considered to have been a guest house in the Asuka Period. Nara National Research Institute for Cultural Properties announced that inspection showed that it was a calendar of March and April of the year 689. No actual calendar based on Genkareki exists even in China, so the said mokkan is a very valuable material.