Huangyou xin yue tuji 皇祐新樂圖記

Huangyou xin yue tuji 皇祐新樂圖記 "New illustrated record on music from the Huangyou reign" is a treatise on music written on imperial order by Ruan Yi 阮逸 (jinshi degree 1027, courtesy name Tianyin 天隱) and Hu Yuan 胡瑗 (933 –1059, courtesy name Yizhi 翼之). In 1036 Emperor Renzong 宋仁宗 (r. 1022-1063) ordered them to compile an official text on the practice of ritual court music. The book of 3 juan was finished in 1053, at the end of the Huangyou reign 皇祐 (1049-1053), and presented to the throne.

The book was rediscovered during the Ming period 明 (1368-1644) in the imperial library of the Wenyuan Hall 文淵閣. This version had a preface written by the bibliographer Chen Zhensun 陳振孫, author of the book catalogue Zhizhai shulu jieti 直齋書錄解題. A later preface was written in 1329 by Wu Shoumin 吳壽民 (dates unknown), and a third one in 1601 by Zhao Kaimei 趙開美 (1563-1624).

The illustrated book is very important for concrete details on the measurements of the basic Yellow Bell pitch pipe (huangzhong 黃鐘) which had a volume of 810 cubic fen 分 (see weights and measures) or 1200 millet seeds (shu 黍). Another calculation was made according to the mathematical book Jiuzhang suanshu 九章算術 and explains that the proportions of the Yellow Bell Pipe were such that for every fen of length there was an (inner) surface of 9 square fen and a volume of 13⅓ millet seeds, and while the diameter of the bore of the pipe was 3.46 fen, its circumference was 10.38 fen. Yet in this calculation there is an error in the relation between circumference, volume and diameter. The two authors also do not consistently use one of their most important measuring tools, namely millet seeds. While the length of the foot (chi 尺) is calculated with large millet seeds (dashu 大黍), the length and volume of pipes are measured with small millet seeds (xiaoshu 小黍).

The first part of the book describes methods to calculate the length of pitch pipes (lülü 律呂), of length measures (chi) with the help of millet seeds, the "four volume measures" (si liang 四量: dou 斗, sheng 升, ge! 合 and yue 龠) and weights (quanheng 權衡), with an illustration of a steelyard. The second and third part of the book explain the tuning and arrangement of sets of bells (zhong 鐘) and soundstones (qing 磬), drums from the region of Jin (i.e. Shanxi jingu 晉鼓), sets of sacrificial tripods whose legs were ornated with cow heads (sanshengding 三牲鼎) and sets of "phoenix knives" (luandao 鸞刀) with which to butcher sacrificial beasts.

Figures 1-4. Illustrations of measures

Indications for the length of the sixteen pitch pipes. The longest, "Yellow Bell" (huangzhong 黃鐘) has a standard length of 9 cun 寸, and a diameter of 3 fen 分 4 li 釐 and 6 hao 毫, see weights and measures. Siku quanshu 四庫全書 edition.

Ruler with a lengt of 1 chi 尺, corresponding to 10 cun 寸, and each cun to a row of 10 millet grains (shu 黍).

Volume measures yue 龠, ge (!) 合, sheng 升, and dou 斗. The measures of a yue are 1 × 1 × 0.81 cun, with a volume (ji 積) of 810 fen3. The measures of a dou are 6 × 6 × 4.5 cun, with a volume of 162,000 fen3.

The Huangyou xin yue tuji can be found in the series Congshu jicheng chubian 叢書集成初編, Siku quanshu 四庫全書 and Xuejin taoyuan 學津討原.