Lüli zhi 律曆志

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 "monographic" 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 history Hanshu 漢書, where the history of weights and measures and the Chinese calendar is 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.

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 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 and Luo Xiahong 落下閎. 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 meaning of the calendar as well as 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).