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Lüli yuanyuan 律曆淵源 "Origins and Foundations of Musical Tuning, Calculation, and the Calendar"

The (Qinding) Lüli yuanyuan (御定)律曆淵源 "(Imperially Endorsed) Origins and Foundations of Musical Tuning, Calculation, and the Calendar" is a collection of three treatises on astronomy, mathematics, and music that assemble Chinese and Western knowledge in these three fields. It was compiled on imperial order during the Kangxi reign 康熙 (1662-1722) under the supervision of Prince Yunlu 允禄. The main compilers were He Guozong 何國宗 and Mei Gucheng 梅谷成. The emperor aimed to have this book compiled was that he had become aware that the Jesuit missionaries who worked as astronomers at the imperial court brought with them knowledge that covered issued which Chinese scientists had never asked about. The concrete occasion was that the Directorate of Astronomy (qintianjian 欽天監) had made an error in the calculation of the solar term Xiazhi 夏至 (see calendar). Kangxi therefore ordered the Director of Astronomy to make use of Western calculation methods that "did not fail in any salient point" (da dun bu wu 大端不誤).
The book was begun in 1713 and finished in 1722, and was printed by the imperial printing shop in 1724. The whole collection is 100 juan "scrolls" long and consists of the parts Lixiang kaocheng 曆象考成 (42 juan), Lülü zhengyi 律呂正義 (5 juan), and Shuli jingyun 數理精蘊 (53 juan). The Lixiang kaocheng consists of two parts (bian 編) and an appendix with tables with a length of 16 juan. The first part serves as an overview begins with a general discussion on the principles of the calendar, and then explains individual themes like celestial phenomena, the conditions of the earth, the calendar, the ecliptic, the celestial equator, the system of celestial coordinates and the precession. The second part informs about the calculation of the movement of celestial bodies and the time, like the path of the sun, calendric calculation by the moon phases, lunar eclipses, methods to predict solar eclipses and calendric calculation by the movements of the five planets and the position of the starry constellations. The Lixiang kaocheng is a concise book on all important matters of calculation of time as based on the movements of the planets and the stars. In this shape it assembles modern knowledge from both Chinese tradition and Western expertise, as transmitted by Jesuit astronomers, but only in a practical way, and it wholly neglects theoretical discussions about the solar system. The calculations are mainly based on Tycho Brahe's solar system, and therefore somewhat outdated. For this reason the Qianlong emperor 乾隆 (r. 1735-1796) had compiled the 10 juan long treatise called Lixiang kaocheng houbian 曆象考成後編 that fills some gaps in the collection.
The Shuli jingyun 數理精蘊 consists of two parts (bian 編) and an appendix with tables with a length of 8 juan. The first part represents a theoretical basis and explains the foundations of Chinese mathematical conceptions as found in the apocryphal texts on the Hetu 河圖 and Luoshu 洛書 and the early classic Zhoubi suanjing. It explains the basics of geometry and of arithmetics. The second part of the book consists of five chapters dealing with (XXX 首, 綫, 面, 體 and 末). The Shuli jingyun is a compendium on Chinese and Western mathematics and gives insight into the differences between Chinese and European concepts of mathematics, as can be seen in the book Dushushu 對數術 by Gu Guanguang 顧觀光 and its comparison with Henry Briggs' (1561-1630) writings.
The Lülü zhengyi consists of three parts. The first explains the foundations of the basic tone of the Yellow Bell pitchpipe, the second one how to calculate the other tones of the musical scale from this basic tone, and the third chapter gives an insight into the European method to back the difference between XXX. The third part was compiled by the Jesuits mathematicians Tomé Pereira (1645–1708, Chinese name Xu Risheng 徐日升) and Teodorico Pedrini (1671-1746, Chinese name De Lige 德理格).
It is divided into three chapters, the last of which is only 1 juan long. The first chapter (Shangbian 上編: Zhenglü shenyin 正律審音 „Investigation into the tones of the correct pipes“) describes how a full musical scale of pipes can be developed from the basic Yellow Bell pipe 黃鐘 by altering the length and diameter of the pipes according to a regular method, with a mutual addition and subtraction of one third of the length (sun yi 損益). The same method is also displayed for string instruments by altering the length of the cord. The second chapter (Xiabian 下編: Hesheng dingyue 和聲定樂 “Fixing music by harmonizing sounds”) gives instructions how to produce musical instruments with the correct range of sounds. The text provides illustrations and explains changes over time. The last chapter (Xubian 續編: Xiejun duqu 協均度曲), talking about the harmony of melodies, is also illustrated.
In spite of its lesser importance in the history of music theory, the Lülü zhengyi is included in the imperial reprint series Siku quanshu 四庫全書 because it was compiled on imperial order. It is also to be found in the descriptive catalogue Qinzaotang Siku quanshu huiyao 摛藻堂四庫全書薈要. It was planned that the Kangxi emperor write a preface, but he died before it was promulgated, and therefore his successor, the Yongzheng emperor 雍正 (r. 1722-1735), finished the work and had printed the collection.

Li Xueqin 李學勤, Lü Wenyu 呂文鬰 (1996). Siku da cidian 四庫大辭典, Changchun: Jilin daxue chubanshe, vol. 1, p. 623.
Wu Boya 吳伯婭 (2002). "Kangxi yu Lüli yuanyuan de bianzuan" 康熙與《律曆淵源》的編纂", in: Gugong bowuyuan yuankan 故宮博物院院刊 2002, 4, pp. 62-67.

The (Yuzhi) Lülü zhengyi houbian (御製)律呂正義後編 is a considerably enlarged version of the Lülü zhengyi 律呂正義 from the Kangxi reign 康熙 (1662-1722) of the Qing period 清 (1644-1911). In 1746 the Qianlong emperor 乾隆 (r. 1735-1796) ordered to add the themes musical instruments (Yueqi 樂器) and musical composition (Yuezhang 樂章) to the Zhengyi and to rearrange the whole text. The resulting text was 120 juan "scrolls" long, in comparison to only 5 juan of text in the Lülü zhengyi. It is divided into ten chapters in which music at particular occasions (offerings, audiences, banquets, contemplation, entertainment) is played, and how this is done, for instance, which types of music is to be played in which sequence (a kind of "suite") and in which key or mode. The modes were to change in the course of the year, each of the twelve months corresponding to one mode. The book includes instructions to the tunes of airs, dances and highly ceremonial drum performances. The second part of the book includes illustrated information on musical instruments, the "system of music" from ancient times to the Ming period 明 (1368-1644), musical compositions from ancient times on, an investigation into weights and measures as related to the length measure of pitchpipes, and finally question-and-answer section in which the basic meaning of music is explained.
The compendium is included in the imperial reprint series Siku quanshu 四庫全書 and the Qinzaotang Siku quanshu huiyao 摛藻堂四庫全書薈要.

Source: Li Xueqin 李學勤, Lü Wenyu 呂文鬰 (1996). Siku da cidian 四庫大辭典, Changchun: Jilin daxue chubanshe, vol. 1, p. 623.
Chiu Lulu (2009). "From 1746 to 1786: The Continued Revision of the Imperial Music Treatise 'Yuzhi lülü zhengyi houbian'", Fontes Artis Musicae, 56/3: 272-281.

1 祭祀樂 Jisi yue Music for ancestral offerings
2 朝會樂 Chaohui yue Music for court audiences
3 宴享樂 Yanxiang yue Music for court banquets
4 導引樂 Daoyin yue Music for physical and mental exercises
5 行幸樂 Xingxing yue Music for inspection tours
6 樂器考 Queqi kao Musical instruments
7 樂制考 Yuezhi kao The music system
8 樂章考 Yuezhang kao Music composition
9 度量權衡考 Duliang quanheng kao Weights and measures
10 樂問 Yuewen Questions about music
Chinese literature according to the four-category system

October 7, 2013 © Ulrich Theobald · Mail