Zhu Zaiyu (朱載堉; 1536 – 19 May 1611) was a Chinese mathematician, physicist, choreographer, and musician. He was a prince of the Chinese Ming dynasty. In 1584, Prince Zhu innovatively described the equal temperament via accurate mathematical calculation.

Zhu was born in Qinyang, Henan Province to an aristocratic family, the sixth-generation descendant of the Hongxi Emperor, the fourth emperor of the Ming Dynasty. Zhu inherited the title the Prince of Zheng in 1593, but quickly resigned it to his cousin. On the emperor's order, he was granted a new princely title in 1606, the year he delivered a set of ten musicological treatises to the court, establishing his scholarly merit. His posthumous name was 鄭端靖世子 ("His Excellency The Dauphin of Zheng").

Zhu wrote on music theory and temperament (five treatises survive), music history (two treatises survive), dance and dance music (five treatises survive), and several other works. Three music theory works in particular are associated with the ideas of equal temperament, the「律學新說」 (" on the equal temperament ", 1584), 「律呂精義」("A clear explanation of that which concerns the equal temperament", 1595/96), and 「算學新說」(" Reflection on mathematics", 1603). His work has been described as "the crowning achievement of two millennia of acoustical experiment and research (Robinson 1962:224)" and he is described as "one of the most important historians of his nation's music."

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File:乐律全书全-121.jpg|Zhu Zaiyu's equal temperament ratio in The Complete Works in Yuelu

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Zhu also wrote treatises (three survive) on astronomy, physics, mathematics and calendrics, calculated the magnetic declination of Peking, the mass density of mercury and accurately described the duration of one tropical year to correct the Ming calendar.

Zhu's work on equal temperament didn't get any official recognition during his lifetime nor during the Qing dynasty. This was due to the Ming and Qing emphasis on classical scholarship and discouragement of ideas based on empirical observation rather than textual interpretations.

朱載堉（1536年 - 1611年），字伯勤，號句曲山人、九峰山人。明宗室鄭恭王朱厚烷嫡子，河南河內（今河南沁陽）人。為明仁宗第二子鄭靖王朱瞻埈之後，明太祖朱元璋的八世孫。明代樂律學家、音樂家、數學家、樂器製造家、物理學家、天文學家、散曲作家，首創十二平均律。

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