Lülü xinshu 律呂新書 "New book on the pitch pipes" is a book on music compiled by the Song-period 宋 (960-1279) scholar Cai Yuanding 蔡元定 (1135-1198), courtesy name Jitong 季通, who hailed from Jianyang 建陽 (modern Jianyang, Fujian). The Neo-Confucian master Zhu Xi 朱熹 (1130-1200) called his method of tuning very exact.
The 2-juan long book is divided into two parts with 23 chapters. The first part (Lülü benyuan 律呂本原) describes the basics of musical tuning, while the second (Lülü zhengbian 律呂證辨) discusses particular problems of the production of pitch pipes (lülü 律呂).
Cai Yuanding describes the method of the Han-period 漢 (206 BCE-220 CE) scholar Jing Fang 京房 (77-37 BCE) to derive the pitch pipes of a whole gamut from the basic Yellow Bell Pipe (huangzhong 黃鐘) with determined measures by alternatively subtracting and adding a third of the dimension of a pipe to produce the next in the series. Cai adds to this method the possibility to deviate from this method and to create "changed pipe tones" (bianlü 變律) with tone steps lesser than a full tone, but only for six of the twelve pipes, so that his gamut consists of eighteen tones.
He stressed that it was important to check that the diameter of the pipes was always equal, which is not very easy in a natural product like bamboo tubes. For the calculation of the length of the pipes he made use of an old method of the "progessing nine" (jiujin zhi 九進制), meaning that it was necessary to deduct one tenth of each digit to exactly meet the correct tone. He therefore also commented on the treatise on the pitch pipes, Lü shu 律書, in the history Shiji 史記.His chapter on the musical modes is particularly interesting to understand the concept of harmony and musical mode during the Song period 宋 (960-1279).
There were several studies on Cai Yuanding's book, like Xu Zhen's 許珍 Lülü xinshu fenzhu tuzuan 律呂新書分注圖纂, Li Wencha's 李文察 (c. 1493-1563) Lülü xinshu buzhu 律呂新書補注, Zhou Mo's 周模 Lülü xinshu zhu 律呂新書注, Han Bangqi's 韓邦奇 (1479-1556) Lülü xinshu zhijie 律呂新書直解, Wang Chaoxi's 王朝璽 Lülü xinshu sijie 律呂新書私解 or Wen Zaoxiang's 文藻翔 Lülü xinshu jianshi 律呂新書淺釋.
Unfortunately the book is full of errors in the quotations of older texts and has therefore much been criticized.
|律呂本原 The origin and development of the pitch pipes|
|1||黃鐘||The Yellow Bell Pipe|
|2||黃鐘之實||The volume of the Yellow Bell Pipe|
|3||黃鐘生十一律||Creating the other eleven pitch pipes from the Yellow Bell Pipe|
|4||十二律之實||The volumes of the twelve pitch pipes|
|5||變律||The alteration of pipes|
|6||律生五聲圖||Chart of producing the five tones by the pipes|
|7||變聲||The alteration of tones|
|8||八十四聲圖||Chart of the 84 tones|
|9||六十調圖||Chart of the 60 keys|
|10||候氣||Relations of the tones to the months|
|11||審度||Diligence for length measures|
|12||嘉量||Excellence in volume measures|
|13||謹權衡||Carefulness in weight measrues|
|律呂證辨 Discussion of the pitch pipes|
|1||造律||The production of pipes|
|2||律長短圍徑之數||The dimensions of diameters, circumferences and lengths of the pipes|
|3||黃鐘之實||The volume of the Yellow Bell pipe|
|4||三分損益上下相生||The mutual production of pipes by adding and subtracting a third|
|6||五聲大小之次||The order of the higher and lower of the five tones|
|7||變宮變徵||Alteration of the first and the fourth tone|
|8||六十調||The 60 keys|
|9||候氣||Relations of the tones to the months|
|10||度量權衡||Length, volume and weight measures|