萬年曆備考

Wànnián lì bèikǎo 萬年曆備考

Reference Materials for the Perpetual Calendar by 朱載堉 (撰)

About the work

The Wànnián lì bèikǎo 萬年曆備考 is the supplementary evidentiary apparatus by the Míng prince-scholar Zhū Zàiyù 朱載堉 (1536–1611) to his Shèngshòu wànnián lì 聖壽萬年曆 calendrical reform proposal — a comparative survey of fifty principal historical calendar systems, computing back to the winter solstice in each year of each historical regime and tabulating the discrepancies. The work belongs to Zhū’s late corpus of mathematical-musical writings centred on his Yuèlǜ quánshū 樂律全書 and his calendrical reform proposal of Wànlì 23 (1595).

Abstract

The work opens with the author’s formal self-identification — “鄭世子臣載堉謹撰” (your servant Zǎiyù, Prince-Heir of Zhèng, respectfully composes this) — and the heading 諸曆冬至考 (“Verification of the winter solstice across the historical calendars”). The methodological prologue argues that newer calendar systems agree better with later observations not because their authors were more brilliant than their predecessors but because each generation refined what it inherited; the corollary is that retrojecting any single system far back leads to systematic error, so a bèikǎo — a cross-section of all major systems against a single observable event (the winter solstice) — is the appropriate empirical instrument.

The body enumerates the principal historical calendar systems — Tàichū lì 太初曆 of Dèng Píng 鄧平 under Hàn Wǔdì, Sāntǒng lì 三統曆 of Liú Xīn 劉歆 under Hàn Píngdì, the Sìfēn 四分 of the Hòu Hàn, Liú Hóng’s 劉洪 Qiánxiàng lì 乾象曆, Jiāng Jí’s 姜岌 Sānjì lì 三紀曆, Hé Chéngtiān’s 何承天 Yuánjiā lì 元嘉曆, Zǔ Chōngzhī’s 祖沖之 Dàmíng lì 大明曆, the Táng Dàyǎn 大衍 of Yī Xíng 一行 and the Xuānmíng 宣明 of Xú Áng 徐昂, the Sòng Jìyuán lì 紀元曆 of Yáo Shùnfǔ 姚舜輔, the Yuán Shòushí lì 授時曆 of Guō Shǒujìng 郭守敬 — back-computing the winter solstice for each against its own new method, comparing in detail with Yī Xíng’s calculations, and citing the Táng zhì discussion of the disagreement between Tàichū, Sāntǒng, Zhōu lì, and Líndé lì readings of the winter solstice in Tàichū 1 (104 BCE) and Lǔ Xī 5.

The text contains an internal reference to computations down to Wànlì 22 (1594), establishing 1594 as the earliest terminus a quo; Zhū’s death in 1611 sets the terminus ad quem. NotBefore is therefore 1595, notAfter 1611. The work is part of the supporting apparatus that Zhū Zàiyù assembled around his calendrical reform memorial of Wànlì 23 (1595) — see the related Lǜlì róngtōng 律厤融通 in 4 juàn (preserved as the methodological appendix to KR3f0007 Shèngshòu wànnián lì).

The Sìkù editors of the related works judged that Zhū’s actual measurements did not surpass Guō Shǒujìng’s, but praised his diagnostic critique of contemporary calendrical drift as substantively sound and his evidentiary apparatus as exemplary. The present Bèikǎo, as a piece of comparative-history evidentiary scholarship, is the most accessible illustration of that exemplary apparatus.

Translations and research

• Cho, Gene J. 2003. The Discovery of Musical Equal Temperament in China and Europe in the Sixteenth Century. Lewiston, NY: Edwin Mellen Press.
• Robinson, Kenneth G. 1980. A Critical Study of Chu Tsai-yü’s Contribution to the Theory of Equal Temperament in Chinese Music. Wiesbaden: Steiner. — Although focused on music theory, includes substantial material on Zhū’s calendrical writings.
• Needham, Joseph. 1962. Science and Civilisation in China, vol. 4 part 1: Physics. Cambridge: Cambridge University Press. — Sustained attention to Zhū as “the prince of musicology”; treats his calendrics in the parallel chapters on astronomy.
• 陳美東 Chén Měidōng. 2003. Zhōngguó kēxué jìshù shǐ: Tiān-wén-xué juǎn 中國科學技術史·天文學卷. Beijing: Kē-xué chū-bǎn-shè.
• Wilkinson, Endymion. Chinese History: A New Manual. — Cites Zhū multiple times (Zhōu chǐ calculations from coin sizes, the discovery of equal temperament in the late Míng, his ritual-dance illustrations).

Other points of interest

Zhū Zàiyù’s renunciation of the principate of Zhèng (七次讓封) over two decades is unique among Míng princes and explicitly noted in the Míng shǐ; the Wànnián lì bèikǎo was composed in retirement at Huáiqìng 懷慶, in the same scholarly milieu as his work on equal temperament (Lǜxué xīnshuō 律學新説, 1584). The internal reference to 1594 places this Bèikǎo alongside the Yuèlǜ quánshū materials he was actively preparing for presentation to the throne in 1595–96.

Links

• The author’s parent calendrical reform proposal: KR3f0007 Shèngshòu wànnián lì 聖壽萬年曆.
• Wikipedia: https://zh.wikipedia.org/wiki/朱載堉