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*Lülü xinlun* 律呂新論 "A new discussion on the pitch pipes"
is a book on music compiled during the Qing period 清 (1644-1911) by Jiang Yong 江永 (1681-1762).

The book of 2 *juan* length is only one of his many contributions to the study of ancient books, particularly the Confucian Classics. The first part discusses Cai Yuanding's 蔡元定 (1135-1198) book *Lülü xinshu* 律呂新書 from the Song period 宋 (960-1279), and then goes on to explain the five notes of the pentatonic scale (*wu sheng* 五聲: *gong* 宮, *shang* 商, *jue* 角, *zhi* 徵 and *yu* 羽), the basic tone of the Yellow Bell pitch pipe (*Huanglü zhi gong* 黃鐘之宮), the length and volume of the pitch pipe, the twelve half-tones of the full gamut (*shier lü* 十二律), the method of deriving the tones from the Yellow Bell Pipe by alternatively adding and subtracting a third (*san fen sun yi* 三分損益), the alternating of two of the tones by reducing it somewhat (*er bian sheng* 二變聲), and corrective mutations of the tones to reach the Yellow Bell tone again (*bianlü* 變律) after the Zhonglü Pipe 中呂.

The second part of the book discusses the noble instrument of the zither (*qin* 琴), the four "pure tones" (*si qingsheng* 四清聲), modulations of the gamut (*xuangong* 旋宮), musical modes (*yuediao* 樂調), the production of the pitch pipes (*zaolü* 造律) and the relations between the musical tones, time and the universe (*houqi* 候氣).

The book focuses on the use of the zither as the most important musical instrument of the literati-officials. In oldest time the musical tones of the gamut were fixed by the size of pipes (*guan* 管). During the Han period 漢 (206 BCE-220 CE) the Confucian scholar Jing Fang 京房, an expert of the *Yijing* "Book of Changes", first described how the twelve-tone gamut can be transposed to five different modes (each mode beginning with one of the five pentatonic notes), so that Chinese music was able to produce sixty different tones (*liushi lü* 六十律).

The musician Qian Lezhi 錢樂之 (424-453) from the Liu-Song period 劉宋 (420-479) extended these to 360 different tones by using chords instead of pipes (*xianqiusheng* 弦求聲 "searching tones by chords"). While Jiang Yong's discussions are mainly based on these precursors, he does not see that the mathematical operations to produce higher tones are different for pipes and chords.

The book is nevertheless of a certain value in his explanation of the volume of the Yellow Bell Pipe, the analysis of errors in the calculations of Song period scholars, and the remarks that the mathematical relations of the pipes originally had an important connection to the calendar. It is also very exact in the description of the mathematical operations and quotes Cai Yong's 蔡邕 (132-192) text *Yueling* 月令 with remarks errors in the music chapters in the book *Lüshi chunqiu* 呂氏春秋 and such in the bibliography *Yiwenzhi* 藝文志 in the official dynastic history *Hanshu* 漢書.

Jiang Yong's book is included in the series *Siku quanshu* 四庫全書, *Shoushange congshu* 守山閣叢書 and *Congshu jicheng chubian* 叢書集成初編.

Sources:

Li Xueqin 李學勤, Lü Wenyu 呂文鬰, ed. (1996). *Siku da cidian* 四庫大辭典 (Changchun: Jilin daxue chubanshe), Vol. 1, 624.

Zhao Xiangqun 趙向群 (1989). "Lülü xinlun 律呂新論", in Zhao Jihui 趙吉惠, Guo Hou'an 郭厚安, ed. *Zhongguo ruxue cidian* 中國儒學辭典 (Shenyang: Liaoning renmin chubanshe), 395.