Lǜlǚ chéng shū 律呂成書
Completed Treatise on the Pitch-Pipes by 劉瑾 (Liú Jǐn)
About the work
A two-juan synthesis combining Cài Yuándìng’s 蔡元定 Lǜlǚ xīnshū (KR1i0003) with Péng Sī’s 彭絲 Huángzhōng lǜ shuō, by the Yuán-period Zhū-Xī-school Shī scholar Liú Jǐn. The work was completed in summer 1347 (Zhìzhèng dīnghài) and printed by the Shānnányǐnsuǒ 山南隱所 of Zhōu Fū 周旉 in the same year. Juàn 1 (chapters 1–13) gives the wind-watching method for fixing the huángzhōng and computes its volumetric basis, area, perimeter, and diameter using mathematical methods drawn from the Jiǔzhāng suànshù, Zǔ Chōngzhī, and Lǐ Chúnfēng. Juàn 2 (chapters 14–26) covers the generation of the eleven other pitches, the biànlǜ, the variant-tones (biànshēng), the 84-sound diagram, and the 60-mode chart. The Sìkù compilers note that, although the work is doctrinally orthodox and uncritical, it is the most systematic Yuán-period synthesis and is preserved in part because Yuán-dynasty music writings are otherwise scarce.
Tiyao
[Your servants] respectfully report: Lǜlǚ chéng shū in 2 juàn, by Liú Jǐn of the Yuán. Liú Jǐn’s Shījí zhuàn tōngshì is already catalogued. The book takes wind-watching as the basis for fixing the pitch-pipes, and from this proceeds to compute their square-and-round perimeter and diameter and so to derive their volumetric basis. Liú’s learning was committed to the Sòng Confucians, and so just as his Shī commentary keeps strictly to Zhū Xī, his music-treatise stays strictly within the views of Master Cài [Yuándìng] and Master Péng [Sī]. — Now, examining the Guǎnzǐ “Dìyuán piān” (the chapter “Earth and Roundness”), where it speaks of “calling the tone zhǐ” or “calling it yǔ,” and the Lǚshì chūnqiū “Gǔ yuè piān” (Ancient Music chapter), where Líng Lún is said to have first cast the huángzhōng mode, then the twelve tǒng (cylinders) — neither passage mentions wind-watching. It is only with Sīmǎ Biāo’s Xù Hànshū zhì (Continued Han History Treatise) that this method first appears, traditionally attributed to Jīng Fáng — but with no clear independent attestation. The Suíshū records that during the Northern Qí, Xìn Dūfāng could use a pitch-pipe to watch the qì, gazing up at the colour of the air and saying as he conversed: “It points to heaven — the qì of the first month of spring has arrived.” When others tested this against the pipes, the ash indeed flew. It also says that Máo Shuǎng wrote a manual of wind-watching, recounting how since HànWèi the pitch-pipe foot-rule had grown gradually longer and the ash no longer flies; only the pipes made by his ancestor Máo Bǐngchéng and his elder brother Máo Xǐ together produced ash that flew with verifiable response. After this, however, the method was no longer used. — Cài Yōng has said: “The ancients in making bells and pitch-pipes used the ear to align the pitches; later men, no longer able to use a single instrument to fix length and capacity, must rely on writing and oral tradition — but this is no substitute for the clarity of judgement-by-ear.” Then to set aside the audible tone in pursuit of the unfathomable qì is, by this measure, only secondary. — Cài [Yuándìng]‘s Lǜlǚ xīnshū extends the old text and still speaks of wind-watching; the volumetric numbers are computed by treating diameter 1 / circumference 3 as the basis — too crude. Péng [Sī] noticed that this did not fit and changed to Zǔ Chōngzhī’s jìng 7 / zhōu 22 ratio; but consulting the Suíshū yuèlǜzhì, even this is the yuēlǜ (approximate ratio), not the mìlǜ (close ratio). Liú Jǐn brought the two books together and reciprocally extended their reasoning to compose the present compilation. As against the ancients’ direct intuition his work cannot pretend to penetrate the subtlety; but the Sòng Confucians’ views on music go no further than this, and given the scarcity of Yuán-period composition the present book is at least not too tortuous, and the long and short complement each other, so we shall preserve it as one further account. Respectfully edited and presented in the ninth month of Qiánlóng 46 (1781). Editor-Generals: Jì Yún, Lù Xīxióng, Sūn Shìyì. Editor-in-chief: Lù Fèichí.
Abstract
Liú Jǐn’s Lǜlǚ chéng shū belongs to the second wave of SòngYuán Lǜlǚ literature. After Cài Yuándìng’s Lǜlǚ xīn shū established the doctrinal foundations in 1187, the next major contribution was Péng Sī’s 彭絲 (hào Lǔzhāi 魯齋, of Ānchéng 安成) Huángzhōng lǜ shuō, which corrected Cài’s volumetric mathematics by replacing the 1:3 / 3:9 yuánzhōu ratio with Zǔ Chōngzhī’s jìng 7 / zhōu 22 (i.e. π ≈ 22/7). Liú Jǐn — the same Yuán-period Zhū-Xī-school scholar who composed the dominant YuánMíng intermediary between Zhū Xī’s Shī jízhuàn and the Míng Shījīng dàquán (his Shī zhuàn tōngshì, KR1c0028) — combines the two treatises into a 26-chapter systematization completed in summer 1347 (Zhìzhèng dīnghài) and printed by Zhōu Fū’s Shānnányǐnsuǒ. Catalog correction: the catalog meta’s “d. 1510” is incorrect; this Liú Jǐn (zì Gōngjǐn 公瑾, of Ānfú 安福, Jiāngxī) is the late-Yuán ZhūXī Shī scholar, not the homonymous Míng eunuch (d. 1510). The dating evidence — the author’s own preface dated Zhìzhèng dīnghài (1347), Zhōu Fū’s printer’s preface of the same date — places him fully in Yuán Toghon Temür’s reign. The Sìkù compilers value the work as a clear and accessible Yuán-period synthesis, useful at least as a witness to how Sòng-Confucian lǜlǚ doctrine was received under the Yuán; they criticize it as derivative and as inheriting Cài and Péng’s commitment to the speculative wind-watching method.
Translations and research
- Joseph Needham. 1962. Science and Civilisation in China, vol. IV.1 (Physics). Cambridge: CUP. Chapter 26h on acoustics treats Liú Jǐn as a derivative source.
- 戴念祖. 1994. 中國聲學史. 河北教育出版社. — Standard Chinese-language history of acoustics; treats the Lǜ-lǚ chéng shū in its account of the post-Cài tradition.
- No further substantial secondary literature located.
Other points of interest
The work’s significance is partly negative: it is the most explicit Yuán-period testimony to the exhaustion of the Sòng xiàngshù approach to lǜlǚ and to the impasse over the huángzhōng volumetric basis. Within a generation, the Míng music reformer Zhū Zàiyù 朱載堉 (in KR1i0009) would explicitly break with the huángzhōng / wind-watching framework and propose the world’s first equal-temperament system; Liú Jǐn’s failure to find a solution within the orthodox framework is part of the historical motivation for that break.