Zhū Zàiyù 朱載堉
Style name Bóqín 伯勤, hào Jùqǔ Shānrén 句曲山人. Hereditary Prince-Heir of Zhèng 鄭世子 — son of Zhū Hòuwǎn 朱厚烷, the Gōngwáng (Reverent Prince) of Zhèng (canonized later as Duānqīng 端清). His ancestral seat was at Huáiqìng 懷慶 (modern Qìnyáng 沁陽 in Hénán). Born Jiājìng 15 (1536), died Wànlì 39 (1611).
His youth was shaped by political crisis: in 1550 his father, charged with criticizing the Jiājìng emperor’s Daoist excesses, was stripped of his princely office and confined to the imperial prison at Fèngyáng 鳳陽 — where he remained for nineteen years. The teenage Zhū Zàiyù vowed not to enter the family’s restored palace until his father was vindicated, and lived in a hut at the gate, devoting himself to the liùyì (Six Arts) — mathematics, music, calendrics, classical philology. After his father’s release and posthumous restoration in 1567, Zhū Zàiyù inherited the right to the principate but, in an extraordinary gesture, formally renounced it (ràngfēng 讓封) seven times across two decades to allow the line to pass to a collateral branch — a self-effacement explicitly noted in the Míng shǐ and unique among Míng princes.
Universally recognized as one of the great polymaths of late-Míng science. His three principal achievements:
(1) Equal temperament: in Lǜxué xīnshuō 律學新説 (1584) — and in expanded form in his collected Yuèlǜ quánshū 樂律全書 — he derived the twelve-fold equal division of the octave (“xīnfǎ mìlǜ” 新法密率) by computing the twelfth root of two to twenty-five-decimal-place accuracy. This is the first mathematically explicit derivation of equal temperament in any tradition; it predates Simon Stevin’s European derivation by roughly a decade. The intellectual transmission of the result to Europe (whether independent re-derivation or transmission via Jesuits) remains debated.
(2) The Shèngshòu wànnián lì 聖壽萬年厯: presented to the throne in Wànlì 23 (1595) together with the methodological appendix Lǜlì róngtōng 律厯融通 (4 juàn), this is his calendrical reform proposal — preserved in the present catalog as KR3f0007. Building on the earlier work of his maternal uncle Hé Táng 何瑭 (in his memorial-of-presentation he ascribed the underlying method to Xǔ Héng 許衡 of the Yuán Shòushí lì compilation, allegedly to lend the work the authority of an earlier figure than the still-recent Hé Táng), he proposed mediating between the Yuán-derived Shòushí’s over-rapid loss-of-precision and the Dàtǒng’s static failure to adjust by adopting average rates derived from collation of both systems. The Sìkù editors judge his actual measurements as not surpassing Guō Shǒujìng’s 郭守敬, but his diagnostic critique of contemporary calendrical drift as substantively sound, and his evidentiary apparatus as exemplary.
(3) Mathematical and dance theory: the Yuèlǜ quánshū also contains Suànxué xīnshuō 算學新説 (a contribution to mathematical pedagogy emphasizing the abacus over rod-numerals); Lǚlǚ jīngyì 律呂精義; and Liùdài xiǎowǔ pǔ 六代小舞譜 (with the first systematic Chinese notation of court ritual dance).
The Míng shǐ Yìshù zhì says of him: “Zàiyù devoted himself to musical-theoretical learning… his books all set forth what earlier men did not say. He was wholly given to silence-and-restraint, paying no attention to mundane affairs; people of his time esteemed him as a man of the Realm of Spirit ( shénjiè zhī rén)“. Joseph Needham judged him “the prince of musicology” and devoted extended attention to his work in Science and Civilisation in China vol. 4.1.