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Lü (Pitch-pipes) is the righteous qi (vital energy) of heaven and earth, and the central sound within humans. Lü arises from sound, and Yin (musical tones) is generated by sound. The *Book of Rites* states: "When sounds are organized into patterns, they are called Yin." There are five Yin tones (Gong, Shang, Jue, Zhi, Yu), and six Lü pitches. Dividing them into Yin and Yang, the five Yin tones are divided into 'Tai' (Greater) and 'Shao' (Lesser) categories, resulting in ten pitch levels; thus, Yin corresponds to the days (of a cycle). The six Lü (Yang pitches) are Huangzhong (Yellow Bell), Taicu (Great Cluster), Guxi (Thoroughly Cleaned), Ruibin (Guest of the Southern Palace), Yize (Punishment), and Wuyi (No Repentance); these are the Six Lü. The six Lv (Yin pitches) are Linzhong (Forest Bell), Nanlv (Southern Lv), Yingzhong (Responding Bell), Dailv (Great Lv), Jialv (Joined Lv), and Zhonglv (Central Lv); these are the Six Lv. Together, they form the Twelve Lü, so Lü corresponds to the Earthly Branches (time periods). Each Lü generates five Yin tones; the twelve Lü generate sixty Yin tones. Multiplied by six, this yields three hundred and sixty tones, corresponding to the days of a year. Thus, it is said that the mathematics of Lü and Li (Calendar) embody the Way of Heaven and Earth. However, both Lü and Lv originate from Huangzhong, which is the root of all things and the Lü of initial Yang. 'Huang' (Yellow) represents the color of the virtue of Earth; 'Zhong' (Bell) represents where qi is planted; hence it is called the root. Lü is born at the Winter Solstice, when qi begins with the emergence of one Yang line; hence it is called the beginning. Therefore, the sound of Huangzhong is central and upright, harmonizing with the virtue of Earth; its tone is heavy and mellow, emitted at the very beginning. Consider the poem by Mr. Kangjie (Shao Yong) on the Winter Solstice: "At the half-way point of Zi hour on Winter Solstice, the Heavenly Heart does not shift or move. At the place where one Yang first rises, when all things have not yet been born. The taste of Xuanjiu (dark wine) is just faint, the Zhengyin (correct sound) is just rare. If you do not believe this, go ask Fuxi again." Here, 'Xuanjiu is just faint' refers to the initial birth of Tianyi (Heaven One); 'Zhengyin is just rare' refers to the impending rise of Huangzhong. Understanding this reveals the meaning of Huangzhong.

Ouyang Xiu said: Those who created the Lü used millet grains. The width of one grain of millet accumulates to form cun and fen (units of length), establishing the standard for measurement; the weight of one grain of millet accumulates to form gui and he (units of volume), establishing the standard for capacity; the heaviness of one grain of millet accumulates to form zhu and liang (units of weight), establishing the standard for balance. These three originate from Huangzhong, hence it is called the root of all matters.

Prince Zheng said: The reason why measures of length, capacity, and weight take their model from Huangzhong is because it is valued for its correspondence with the qi of heaven and earth. As Zhu Xi stated, this is akin to the Xiantian Tu (Prior Heaven Diagram). The so-called Xiantian Tu is the Hetu (River Chart) and Luoshu (Lo River Map). The position number of Hetu is ten, representing the substantive numbers of heaven and earth; the position number of Luoshu is nine, representing the functional numbers of heaven and earth. Generally, all matters do not depart from Yin and Yang. The two meanings of Hetu and Luoshu exhaust the Dao of Yin and Yang; they are the origin of Lü and Li, and the ancestors of mathematics. Thus, the ancients considered the subtlety of Lü to lie only in these two methods. One method uses the length of longitudinally arranged millet grains as 'fen'; nine fen make one cun, and nine cun make the length of Huangzhong. Nine multiplied by itself nine times yields eighty-one fen, taking imagery from the number nine in Luoshu squared; this is called the Root of Lü, recorded in *Huainanzi*. The other method uses the width of transversely arranged millet grains as 'fen'; ten fen make one cun, and ten cun make the length of Huangzhong. Ten multiplied by itself ten times yields one hundred fen, taking imagery from the number ten in Hetu squared; this is called the Mother of Measurement, recorded in Sima Qian's *Records of the Grand Historian*. Although these two methods differ, the essence of Lü is the same. The eighty-one fen of longitudinal millet correspond exactly to the one hundred fen of transverse millet, and the width of transverse millet coincides exactly with the length of longitudinal millet. This is the interweaving of the even numbers of Hetu and the odd numbers of Luoshu, making the standards of Lü and measurement complete. It is truly the natural wonder of heaven and earth, not arranged by human effort. Outside these two methods, there was originally no concept of using ninety fen as the length of Huangzhong. Later, Liu Xin and Ban Gu used ninety fen as the length of Huangzhong, which combined the method of diagonally arranged millet grains. Tracing the error back to its source, it likely began with Jing Fang. Although Jing Fang lived close to ancient times and knew the ancient law was nine fen to an inch, his calculations were cumbersome and difficult for beginners to understand, so he invented a new method changing nine to ten. Consequently, both the *Book of Han* and *Later Book of Han* state nine cun. People today who revere the nine-cun standard over others are confused by the biased view in the *Book of Han*. If one could adapt and not be confined to a single bias, then longitudinal, transverse, and diagonal millet arrangements would all conform to the Lü of Huangzhong.