The Taien calendar (大衍暦 Taien-reki?), also known as Daien or Daiyan or Dayan calendar, was a Japanese lunisolar calendar (genka reki). It was developed in China; and it was used in Japan from about 746 to 857.
The Taien-reki system corrected errors in the Genka calendar and Gihō calendar which were used in Japan in the first half of the 8th century. It was the work of Yixing, who was a Chinese astronomer.
- Nussbaum, Louis-Frédéric. (2005). "Calendar" in Japan Encyclopedia, pp. 98-99; Bramsen, William. (1880). Japanese chronological tables, p. 25.
- Trimble, Virginia et al. (2007). "Yixing" in Biographical Encyclopedia of Astronomers, pp. 1252-1253, citing Ohashi, Yukio. (1995).“Daien-reki no hokan-hō nit suite.” (On the Interpolation used in the Dayan calendar) Kagakusi Kenkyu (Journal of History of Science), ser. 2, 34, 195: 170–176.
- Clement, Ernest W. (1902). "Japanese Calendars," in Transactions of the Asiatic Society of Japan, Vol. 30, pp. 1-82, 73; Japan, Monbushō. (1876). An outline history of Japanese education: prepared for the Philadelphia International Exhibition, 1876, p. 160.
- Charlotte von Verschuer (1985). Les relations officielles du Japon avec la Chine aux VIIIe et IXe siècles (Hachi-kyū-seiki no Nitchū kankei), pp. 243-245 n. 114. (French)