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Lüli zhi 律曆志 is a type of treatise on musical pitch-pipes, weights and measures, and the calendar. This kind of treatise is part of the "monographical" chapters in the official dynastic histories and also in some encyclopaedias, for example, the Qunshu kaosuo 群書考索 (Shantang kaosuo 山堂考索).
The term is first used in Ban Gu's 班固 (32-92 CE) history Hanshu 漢書, where the history of weights and measures and the Chinese calendar are described. Part of this treatise is the explanation of the calculation of the musical pitch-pipes and their relation to the universe, according to correlative thinking.
Most fundamental for traditional Chinese music theory is the system of the twelve pitch-pipes (shi'er lü 十二律). It is composed of a scale of twelve pipes called lülü 律呂. The term lǜ 律 means "measure", and is later also applied to "judicial measures" of the administrative law (see lü 律); the term lǚ 呂 means "row". One of the oldest definitions of the term lǜ 律 is to be found in the history Guoyu 國語, where the music master Ling Zhoujiu 伶州鳩 explained that lü meant something with the help of which standards for measurements are created (suoyi li jun chu du 所以立均出度). Measures are based on one fundamental unit, from which all other measurements are derived and stand in a row like vertebral bones (which is the actual meaning of the word lü 呂). Six of the pipes were called lǜ (liùlǜ 六律), and the others lǚ (liùlǚ 六呂). Music Master Zhoujiu discerned between odd-number pipes (danshu 單數) and even-number pipes (shuangshu 雙數) or "intermediate pipes" (liu jian 六間). These were later called the six Yang pipes (liu yanglü 六陽律) and the six Yin pipes (liu yinlü 六陰呂; see Yin and Yang).
The earliest system of the pitch-pipes is called "pure intonation" (chunlü 純律). The lengths of the pipes in this system are derived from the longest one, the basic Yellow Bell Pipe (huangzhong 黃鐘). By alternatively subtracting a third and adding a third of the length of the previous pipe, the higher tones of the musical scale are created. However, this method only works if the diameter of each pipe remains constant. According to legend, the system was invented by a certain Ling Lun 伶倫 (also written 泠綸), a minister of the Yellow Emperor (Huang Di 黃帝). When he heard the cries of phoenixes in the vales of Kunlun Range 崑崙, he came up with the idea to imitate their voices to create a tempered musical system. The Yellow Emperor ordered him to cast twelve bells (zhong 鍾) with different sizes.
In fact, bells are the oldest music instruments that give evidence of the pentatonic system used in China, and the names of the height of these tones. The oldest surviving bronze bells are inscribed with words like tuobin 妥賓 (later called ruibin 蕤賓) or wutai XXX 無旲 (corresponding to the later wuyi 無射).
The height of the twelve tones is derived from the basic tone of the Yellow Bell Pipe. Yet the problem of this system is that the absolute height of this tone was not fixed in an absolute way (the the Western concert pitch A with 440 Hz), and therefore also those of the other pipes, whose tone was always related to that of the basic tone. The "pure tone" of each pipe was seen as a "correct" tone (zhenglü 正律), creating a full-step interval to the next tone. For some musical instruments, especially the zither, reduced of half-tones were made use of that were called "altered tones" (bianlü 變律). They are also found in many musical modes (gongdiao 宮調) of operatic airs.
The term "six lǜ pipes" 六律 is first to be found in the Classic Zhouli 周禮, which was finalised during the Han period 漢 (206 BCE-220 CE). Older texts like the Guoyu (with Shi Bo's 史伯 discussion on music) or the history Zuozhuan 左傳 speak of five or six tones (wu yin 五音, liuyin 六音), and not of six pipes. Similarly, the oldest traces of the "intermediate tones" (jianyin 間音) in the inscriptions on the bells found in the Warring-States 戰國 (5th cent.-221 BCE)-period tomb of Yi, Marquis Zeng 曾侯乙, refer to altered tones, and not to the six lǚ pipes 六呂. The chapter Chunguan 春官 "Spring offices" in the Classic Zhouli includes a third term, namely "six equals" (liutong 六同), in the phrase diantong zhang liulü liutong zhi he 典同掌六律六同之和 "The manager of female, i.e., imperfect tones, controls the harmony of the six lǜ pipes and the six equals". Some commentators interpret the character tong 同 as a clerical error for jian 間 "intermediate", and others for a homophone of tong 銅 "bronze (pipes or tubes)". The Qing-period 清 (1644-1911) scholar Ji Dakui 紀大奎 (1756-1825) concluded that the "six equals" might be another series of tones that included only altered tones (bianlü).
The chapter on measures and the calendar (Lüli zhi 律曆志) in the history Hanshu 漢書 is one of the oldest surviving descriptions of the measures of the pitch-pipes. Other sources are the books Guanzi 管子, Lüshi chunqiu 呂氏春秋 (part Jixia ji 季夏紀) and the chapter Tianwen xun 天文訓 in the Daoist book Huainanzi 淮南子. The chapter on the pitch-pipes (Lü shu 律書) in the history Shiji 史記 is corrupted and is practically useless with respect to mathematical exactness.
The Hanshu explains that Ling Lun used bamboo tubes to produce the twelve pipes, six of which represented the voice of the male phoenix, and six that of the female bird. Six is the central Yin number, and therefore reigns the number of the pipes, while five is the central Yang number and also that of the five tones (wuyin) in the pentatonic scale. Also under the influence of cosmological concepts popular during that time, the method of creating the next pipe by subtracting and adding a third of the foregoing pipe was invented. Three was seen as the number of Heaven, and two as that of the Earth.
From the length of the Huangzhong Pipe 黃鐘 (with a length of 9 cun "inches", see weights and measures), one third is subtracted, resulting in the 6-cun-long Linzhong Pipe 林鐘. To the length of the Lingzhong Pipe, one third is added, resulting in the 8-cun-long Taicu Pipe 太族. When subtracting one third again, the Nanlü pipe 南呂 is produced, with a length of 5 1/3 cun. Adding one third again results in the Guxian Pipe 姑洗 with a length of 7 1/9 cun, etc.
| pipe | length (in cun = approx. inch) | corresponding month | ||
| The six lǜ pipes 六律 | ||||
|---|---|---|---|---|
| 黃鐘 Huangzhong Pipe | 9 | 9 | 11 | 子 |
| 太族 Taicu Pipe | 8 | 1 | 1 | 寅 |
| 姑洗 Guxian Pipe | 7 1/9 | 7.111 | 3 | 辰 |
| 蕤賓 Ruibin Pipe | 6 26/81 | 6.321 | 5 | 午 |
| 夷則 Yize Pipe | 5 451/729 | 5.619 | 7 | 申 |
| 亡射 Wuyi (!) | 4 6524/6561 | 4.994 | 9 | 戌 |
| The six lǚ pipes 六呂 | ||||
| 林鐘 Linzhong Pipe | 6 | 6 | 6 | 未 |
| 南呂 Nanlü Pipe | 5 1/3 | 5.333 | 8 | 酉 |
| 應鐘 Yingzhong Pipe | 4 20/27 | 4.741 | 10 | 亥 |
| 大呂 Dalü Pipe | 4 52/243 | 4.214 | 12 | 丑 |
| 夾鐘 Jiazhong Pipe | 3 1631/2187 | 3.746 | 2 | 卯 |
| 中呂 Zhonglü Pipe | 3 6487/19683 | 3.330 | 4 | 巳 |
Dimensions of the Twelve Pitch-Pipes according to the chapter Lüli zhi 律曆志 in the history book Hanshu 漢書. |
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Ban Gu's monography is a more systematic development of Sima Qian's 司馬遷 (145-86 BCE) treatises Lü shu 律書 and Li shu 曆書 (see Tianguan shu 天官書) in the history book Shiji 史記 that are both only transmitted with many textual errors. For the history of the calendar, the Taichu reform of 104 (the Taichu Calendar 太初曆) is very important. It was carried out by the astronomers Deng Ping 鄧平 (c. 100 BCE) and Luo Xiahong 落下閎 (156-87). The Lüli zhi explains the calendric treatise Santong lipu 三統曆譜, which was one of the oldest books on the calendar, but has not survived.
The treatise included a theoretical explanation of the calendar and a concrete description of the solar terms (jieqi 節氣), the beginnings of the months on new moon days (shuowang 朔望), lunar and solar eclipses and the movements of the five planets (wuxing 五星: Mercur, Venus, Mars, Jupiter and Saturn), and the method to calculate the position of the starry constellations through the year (tuibu fangfa 推步方法).
Calendric treatises are to be found in the official dynastic histories Houhanshu 後漢書, Jinshu 晉書, Songshu 宋書, Weishu 魏書, Suishu 隋書, Jiutangshu 舊唐書, Xintangshu 新唐書, Jiu Wudaishi 舊五代史, Songshi 宋史, Liaoshi 遼史, Jinshi 金史, Yuanshi 元史, Mingshi 明史, Qingshigao 清史稿 and Xin Yuanshi 新元史.
Of these, the Hanshu, Houhanshu, Jinshu, Songshu, Weishu, Suishu and Songshi merge the themes pitch-pipes and measures with that of the calendar (the treatise has therefore the title Lüli zhi), while the others (except the Shiji) have no separate treatise on musical tuning. In those books, the treatise has therefore the name Li zhi 曆志 "Treatise on the calendar". All of these histories (except the Liaoshi) additionally include a separate treatise on astronomy (Tianwen zhi 天文志).