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*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 large words on the top are the words of the air (關關雎鳩，在河之洲). Below that, the basic tone of each syllable is written in terms of the pitch pipe designations (姑[洗], 蕤[賓], 應[鐘], 南[呂], etc.). Each syllable of the air is accompanied by a qin 琴 and a se 瑟 zither for which different notation systems are used, namely the gongche 工尺 system for the qin (the "strange" characters with 艹 tops and 乚 bottoms), and the pitch pipe designations for the se zither. |

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 pitch pipes" 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).

Diameters and lengths of the 16 pitch pipes. The Yellow Bell pipe ( huangzhong 黃鐘) has a length of 8 cun 寸 or 80 fen 分, according to the length of the carpenter's foot (yingzao chi 營造尺), which in turn corresponds to the Shang foot (Shangchi 商尺). The diameter of the huangzhong pipe was 4 fen (0.4 cun), that of the notch 2.82 fen. |

Set of 12 pitch pipes from the Han period 漢 (206 BCE-220 CE) in which the Yellow Bell pipe had a nominal length of 9 chi, corresponding to nine times the diameter of a standard coin (quanhuo 泉貨). |

The method of the deduction of a system of pitch pipes 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.

I (1-10) | 律呂精義內篇 十卷 | Lülü jingyi neipian |
Essence of the meaning of the pitch pipes, inner chapters |

II (11-20) | 律呂精義外篇 十卷 | Lülü jingyi waipian |
Essence of the meaning of the pitch pipes, outer chapters |

III (21-24) | 律學新說 四卷 | Lüxue xinshuo |
A new treatise on the science of pitch pipes |

IV (25) | 樂學新說 一卷 | Yuexue xinshuo |
A new treatise on the discipline of music |

V (26) | 算學新說 一卷 | Suanxue xinshuo |
A new treatise on mathematical science |

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 四巻 (附) 音義 一卷 |
Lüli rongtongapp. Yinyi |
Relation of the pitch pipes with the calendar, app. phonetic commentary | |

VI (27-28) | 操縵古樂譜 一卷 | Caoman gu yuepu |
Ancient musical scores of songs for the zither |

VII (29-30) | 旋宮合樂譜 七種 | Xuangong he yuepu qi zhong |
Scores of seven modulations for orchestra |

VIII (25) | 鄉飲詩樂譜 六卷 | Xiangyin Shi yuepu |
Musical scores of village drinking songs in the Classic Shijing |

IX (37-38) | 六代小舞譜 一卷 | Liudai xiaowu pu |
Scores of lesser dances from the Six Dynasties period |

X (39) | 小舞鄉樂譜 一卷 | Xiaowuxiang yuepu |
Scores of lesser dances of the districts |

二佾綴兆圖 一卷 | Eryi chuozhui tu |
Sketches of dancing steps of old royal dances | |

XI (40) | 宋儒朱子論舞大略 一卷 | Song Ru Zhuzi lun wu dalüe |
Outlines of the Confucian Master Zhu [Xi]'s discussion of dances from the Song period |

XII (41) | 靈星小舞譜 一卷 | Lingxing xiaowu pu |
Scores of lesser dances of the Numinous Star |

Note: The sequence of individual texts as presented in the series Siku quanshu 四庫全書 differs from the original arrangement in the 1596 print. Compare Shanghai tushuguan 上海圖書館 1982), Vol. 1, 616. |

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, 622.

Li Ying 李穎 (2005). "Mingdai Yuelü quanshu zhong de changyue jilu 明代《樂律全書》中的唱樂記錄", *Yuefu xinsheng* (*Shenyang Yinyue Xueyuan xuebao*) 樂府新聲(沈陽音樂學院學報), 2005 (12).

Liang Liting 梁李婷 (2013). "Shixi Yuelü quanshu zhong dashao de yanchu chengshi 試析《樂律全書》中“大韶”的演出程式", *Shaoguan Xueyuan xuebao* 韶關學院學報, 2013 (5).

Qin Peiheng 秦佩珩 (1963). "Zhu Zaiyu yu Yuelü quanshu 朱載堉與《樂律全書》", *Renmin yinyue* 人民音樂, 1963 (5).

Shanghai tushuguan 上海圖書館, ed. (1982). *Zhongguo congshu zonglu* 中國叢書綜錄 (Shanghai: Shanghai guji chubanshe).

Wang Xiaoru 王曉茹 (2008). "Lun Zhu Zaiyu Yuelü quanshu de wuyue sixiang 論朱載堉《樂律全書》的舞樂思想", *Beijing Wudao Xueyuan xuebao* 北京舞蹈學院學報, 2008 (2).

Wang Xiaoru 王曉茹 (2009). "Zhu Zaiyü Yuelü quanshu zhong wupu yu heyuepu de yanjiu 朱載堉《樂律全書》中舞譜與合樂譜的研究", *Beijing Wudao Xueyuan xuebao* 北京舞蹈學院學報, 2009 (9).

Wu Feng 吳楓, ed. (1987). *Jianming Zhongguo guji cidian* 簡明中國古籍辭典 (Changchun: Jilin wenshi chubanshe), 265.

Zhang Junhui 張峻琿 (2019). "Rujia wenhua shijiao xia Yuelü quanshu zhong de wuxue tixian 儒家文化視角下《樂律全書》中“和”的舞學體現", *Yishu pingjian* 藝術評鑒, 2019 (8).

Zhu Xingchen 朱星辰 (2013). "Cong shuxie fuhao dao zhiti biaoyan: Lun Zhu Zaiyu Yuelü quanshu zhong wupu yaosu ji qi xianshi yiyi 從書寫符號到肢體表演 論朱載堉《樂律全書》中舞譜要素及其現實意義", *Wudao* 舞蹈, 2013 (8).