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Yuelü quanshu 樂律全書

Oct 7, 2013 © Ulrich Theobald

Yuelü quanshu 樂律全書 "The whole book on musical tuning" is a book on music written during the Ming period 明 (1368-1644) by Zhu Zaiyu 朱載堉 (1536-c. 1610), courtesy name Boqin 伯勤, style Gouqu shanren 句曲山人. He was a son of Zhu Houwo 朱厚焥 (or Zhu Houwan 朱厚烷, d. 1591), Prince Gong of Zheng 鄭恭王, a member of the imperial house of the Ming, but was not allowed to dwell inside the palace because his father had been eliminated from the line of princely succession.

Zhu Zaiyu wrote quite a few books on music, including Lüxue xinshuo 律學新說, Yuexue xinshuo 樂學新說, Lülü jingyi 律呂精義 (part of the Yuelü quanshu), Yuelü zhenglun 律呂正論, Lülü zhiyi bianhuo 律呂質疑辨惑, Sepu 瑟譜, Zaoman guyue pu 操縵古樂譜, Shigong heyue pu 施官合樂譜, Xiangyin shiyue pu 鄉飲詩樂譜, Liudai xiaowu pu 六代小舞譜, Xiaowu yuepu 小舞鄉樂譜 and Lüli rongtong 律曆融通, as well as some books on mathematics, Jialiang suanjing 嘉量算經, and Suanxue xinshuo 算學新說.

The 42-juan long book was finished in 1595 and submitted to the throne during the Wanli reign 萬曆 (1573-1619). The imperial bibliography in the official dynastic history Mingshi 明史 speaks of 40 juan of length. In fact, the Yuelü xinshu consists of eleven texts part of which is not divided into juan, so that it is not quite sure which statement is correct.

The chapter Lülü jingyi 律呂精義 "Essence of the meaning of the pitchpipes" is the most important part of the book, in which the basics of musical tuning are explained. Zhu Zaiyu argues that a line of 100 grains of millet in the long direction (hengshu 橫黍) has the same length as that of 81 grains of millet arranged side by side (zongshu 縱黍), and this length corresponds to 1 chi 尺 (the carpenter's foot, yingzao chi 營造尺, see weights and measures). He also explains that a pipe with half the length of the Yellow Bell pipe (huangzhong 黃鐘) does not harmonize (ying 應) with that of the full length, but half a Taicu pipe 太蔟 does. This theory was reproduced in the book Lülü zhengyi 律呂正義 from the Kangxi reign-period 康熙 (1662-1722) because it was the most exact explanation of the creation of a full musical scale out of the basic pipe (the Yellow Bell pipe).

The method of the deduction of a system of pitchpipes from the Yellow Bell pipe and the associated "main pipes" (zhenglü 正律) and "doubling pipes" (beilü 倍律) is based on two different mathematical operations, namely the Pythagorean method (gougu qiuxian 勾股求弦) and the hypotenuse (fangqiuxie 方求斜) method, but the former cannot any more be made use of when constructing the Nanlü pipe 南呂 from the Ruibin pipe 蕤賓 on.

The Lülü quanshu is included in the imperial series Siku quanshu 四庫全書.

Table 1. Contents of the Yuelü quanshu 樂律全書 as is the series Siku quanshu 四庫全書
1 律呂精義內篇 十卷 Lülü jingyi neipian Essence of the meaning of the pitchpipes, inner chapters
2 律呂精義外篇 十卷 Lülü jingyi waipian Essence of the meaning of the pitchpipes, outer chapters
3 律學新說 四卷 Lüxue xinshuo A new treatise on the science of pitchpipes
4 鄉飲詩樂譜 六卷 Xiangyin Shi yuepu Musical scores of village drinking songs in the Classic Shijing
5 樂學新說 一卷 Yuexue xinshuo A new treatise on the discipline of music
6 算學新說 一卷 Suanxue xinshuo A new treatise on mathematical science
7 操縵古樂譜 一卷 Caoman gu yuepu Ancient musical scores of songs for the zither
8 六代小舞譜 一卷 Liudai xiaowu pu Scores of lesser dances from the Six Dynasties period
9 八佾綴兆圖 一卷 Bayi chuozhui tu Sketches of dancing steps of old royal dances
10 靈星小舞譜 一卷 Lingxing xiaowu pu Scores of lesser dances of the Numinous Star
11 旋宮合樂譜 七種 Xuangong he yuepu qi zhong Scores of seven modulations for orchestra
Table 2. Contents of the Yuelü quanshu 樂律全書 as is the catalogue Zhongguo congshu zonglu 中國叢書綜錄
樂律全書 Yuelü quanshu
(Ming) 朱載堉 Zhu Zaiyu (comp.)
書名, length in juan Title Title in English
律學新說 四卷 Lüxue xinshuo A new treatise on the science of pitchpipes
樂學新說 一卷 Yuexue xinshuo A new treatise on the discipline of music
算學新說 一卷 Suanxue xinshuo A new treatise on mathematical science
律呂精義內編 十卷 Lülü jingyi neibian Essence of the meaning of the pitchpipes, inner chapters
律呂精義外編 十卷 Lülü jingyi waibian Essence of the meaning of the pitchpipes, outer chapters
操縵古樂譜 一卷 Caoman gu yuepu Ancient musical scores of songs for the zither
施宮合樂譜 一卷 Shigong he yuepu Scores of seven modulations for orchestra
鄉飲詩樂譜 六卷 Xaingyin shi yuepu Musical scores of village drinking songs in the Classic Shijing
六代小舞譜 一卷 Liudai xiaowu pu Scores of lesser dances from the Six Dynasties period
小舞鄉樂譜 一卷 Xiaowu xiang yuepu Scores of lesser dances of the districts
二佾綴兆圖 一卷 Eryi zhuizhao tu Sketches of dancing steps of old royal dances
靈星小舞譜 一卷 Lingxing xiaowu pu Scores of lesser dances of the Numinous Star
曆書 Calendar:
聖壽萬年曆 二卷 Shengshou wannian li The ten-thousand-years calendar of Eternal Sageness
萬年曆備考 三卷 Wannian li beikao Prompt analysis of the ten-thousand-years calendar
律曆融通 四卷
(附) 音義 一卷
Lüli rongtong
app. Yinyi
Relation of the pitchpipes with the calendar, app. phonetic commentary
Shanghai tushuguan 上海圖書館 1982), Vol. 1, 616.
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