Lǜlǚ xīn lùn 律呂新論
New Treatise on the Pitch-Pipes by 江永 (Jiāng Yǒng)
About the work
A two-juan music treatise by the Wǎnpài kǎozhèng master Jiāng Yǒng — author of KR1i0021 Lǜlǚ chǎnwēi — and one of the most theoretically and computationally precise music treatises in the entire SKQS yuèlèi. The upper juàn opens with a critique of Cài Yuándìng’s Lǜlǚ xīnshū (KR1i0003) and proceeds through chapters on the five tones, the huáng-zhōng-of-gōng (Jiāng’s distinctive doctrine that the huángzhōng zhī gōng is in fact the half-pitch / clear of the huángzhōng and not its full length), the huángzhōng length, the huángzhōng volumetric basis, the eleven other pitches, sānfēn sǔnyì, the èr biàn shēng (two derived tones), and biànlǜ (derived pitches). The lower juàn covers the qín, the four clear-tones, xuán gōng (modal rotation), yuè diào (musical modes), pitch-pipe construction, hòu qì (wind-watching), and concluding lǜlǚ yú lùn (residual essays). Jiāng’s distinguishing intellectual move is to derive every doctrinal proposition from empirical sources — the qín string-fret nodes (huī 徽), the actually-cut pitch-pipes, the geometric volumetric basis of the Zhōu fǔ 鬴 measure (computed using Zǔ Chōngzhī’s π = 22/7 to high precision) — rejecting the speculative apparatus of biànlǜ, sānfēn sǔnyì, and wind-watching as insufficiently anchored in observable reality.
Tiyao
[Your servants] respectfully report: Lǜlǚ xīn lùn in 2 juàn, by Jiāng Yǒng of our dynasty. Jiāng Yǒng’s Zhōulǐ yíyì and other works are catalogued separately. The present compilation is his treatise on music. The upper juàn begins with a discussion of Master Cài’s Lǜ shū; then on the five tones; the gōng of huángzhōng; the length of the huángzhōng; the volumetric basis of the huángzhōng; the eleven pitches; sānfēn sǔnyì; the two biàn shēng; biànlǜ. The lower juàn opens with the qín; the four clear-tones; xuán gōng; musical modes; pitch-pipe casting; wind-watching; and the residual lǜlǚ yú lùn. The book’s main thesis works out from the qín — examining the ancient pitch-pipes in pipe form for tone-fixing. Hàn Jīng Fáng was the first to construct jūn (cylindrical bow), and from twelve pitches generated 60, then from 60 generated 360 — the beginning of using strings to find tones. Jiāng Yǒng’s doctrine is presumably derived from this. But pipe-tone and string-tone differ slightly in how they generate pitch and select from the pitch-system, hence there are forced accommodations. Yet his discussions of the huángzhōng volumetric basis, of the errors of the Sòng Confucians’ arithmetic, and of pitches-being-generated-from-the-calendar — all show him capable of reaching new insights. Lǜ and lì both arise from arithmetical accumulation; hence the Hàn shū combines them into a single monograph. Jiāng Yǒng was deep in arithmetic, hence on lǜ and lì he could push their subtleties forward. — As to fixing the huángzhōngzhī gōng, he relies on Cài Yōng’s Yuèlìng zhāngjù to correct the Lǚshì chūnqiū (rejecting “sān cùn jiǔ fēn” as a textual corruption of “sì cùn wǔ fēn”); he corrects the Hàn shū compilers’ deletions; and he distinguishes sǔnyì xiāngshēng from jūnyún jiéguǎn (uniform pipe-segmentation), so that one is not led to “go without returning.” All these are points he has been able to bring forth which were not adequately stated by earlier authors. The work is preserved as one school’s contribution. Respectfully edited and presented in the tenth month of Qiánlóng 46 (1781). Editor-Generals: Jì Yún, Lù Xīxióng, Sūn Shìyì. Editor-in-chief: Lù Fèichí.
Abstract
The Lǜlǚ xīn lùn is a major theoretical break with the entire post-Hàn pitch-pipe tradition, written by the most accomplished Qing-period mathematical synthesist before Dài Zhèn. Jiāng Yǒng’s principal positions: (1) he rejects sānfēn sǔnyì (third-up-third-down generation) as a human convention not natural law, on the ground that the actual qín string-fret nodes do not yield the sānfēn sǔnyì values for the biàn tones; (2) he proposes that the twelve pitches should instead be derived by uniform segmentation (jūnyún jiéguǎn) of the huángzhōng over the seasonal calendar — each pitch corresponding to one calendar segment, with the segments uniform in length and the huángzhōng volumetric basis matching the actual length of two solar years, an argument anchored in the geometric volumetric calculation of the Zhōu fǔ 鬴 measure of the Kǎogōng jì; (3) he rejects the speculative apparatus of biànlǜ (60-pitch, 300-pitch, 12-pitch biàn-systems) entirely, holding that the orthodox 12 pitches plus their octave clear-tones suffice for all musical needs; (4) he reads the Lǚshì chūnqiū’s huángzhōng zhī gōng of “3 cùn 9 fēn” as a textual corruption (he proposes “4 cùn 5 fēn” — i.e. the half-pitch / clear huángzhōng) — a position that the Sìkù compilers note is plausible but speculative. Composition is not precisely datable; Jiāng’s preface mentions twenty years of cogitation, and the work is mature; the bracket 1730–1745 spans the period of his active kǎozhèng programme. The companion Lǜlǚ chǎnwēi (KR1i0021) is a related work but is dedicated to expounding 朱載堉’s mathematical method of equal temperament, while the present Lǜlǚ xīn lùn is Jiāng’s own positive doctrine.
Translations and research
- Joseph Needham. 1962. Science and Civilisation in China, vol. IV.1. — Treats Jiāng Yǒng as the principal mid-Qing musical theorist anchoring the kǎo-zhèng approach to lǜ-lǚ.
- 戴念祖. 1994. 中國聲學史. — Detailed treatment.
- Catherine Jami. 2012. The Emperor’s New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign. OUP. — Notes Jiāng Yǒng’s role in extending Méi Wéndǐng’s synthesis of Western and Chinese mathematics into the lǜ-lǚ domain.
- 楊蔭瀏. 1981. 中國古代音樂史稿. — Treats the Lǜ-lǚ xīn lùn as the principal mid-Qing critical alternative to the Cài-Yuán-dìng tradition.
- No further substantial Western-language secondary literature located.
Other points of interest
The work documents an important moment in the eighteenth-century kǎozhèng movement: Jiāng Yǒng explicitly states (juan 1, opening essay) that the orthodox tradition’s “sānfēn sǔnyì” is on a par with the obsolete “diameter 1, circumference 3” of pre-Zǔ-Chōng-zhī mathematics and the obsolete yī jiǔ suì qī rùn (19-year intercalation cycle) of pre-Tang astronomy — that all three are convenient approximations now superseded by precision computation in their respective domains, and that lǜlǚ alone has resisted the corresponding revision out of mere conservatism. This is one of the clearest mid-Qing statements of the kǎozhèng programme as applied to the music-theoretical tradition.