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The *Treatise on Music and Ritual* of the Tang Dynasty states: "Sound is formless, whereas music (Yue) has instruments." The ancients who created music understood that instruments would inevitably deteriorate, while sound could not be fully conveyed through words. Fearing that if instruments were lost, the music would also be forgotten, they devised numerous methods to record it. Thus, those seeking pitch standards relied on *Lü* (pitch pipes), and those crafting *Lü* pipes relied on millet grains.

From the width of a single millet grain, units such as *cun* (inch) and *fen* (line) were accumulated; from the volume of a single millet grain, units such as *yue* (a measure of capacity) and *he* (a smaller unit of capacity) were accumulated; and from the weight of a single millet grain, units such as *zhu* (grain-weight) and *liang* (tael) were accumulated. Since these three types of measurements would also eventually wear out or change, their methods were summarized and codified into numbers, ensuring that *cun*, *fen*, *yue*, *he*, *zhu*, and *liang* all originated from the standard of the *Huangzhong* (Yellow Bell) pitch pipe. In this way, *Lü* (pitch), *Du* (length), *Liang* (capacity), and *Heng* (weight) served as inner and outer counterparts to one another. This allowed those skilled in making pitch pipes to establish standards for length, capacity, and weight, and conversely, those with standards for length, capacity, and weight could establish pitch pipes. This demonstrates that ancient sages understood the beginning and end of things, harboring deep concerns for the world. Their meticulous and detailed formulation of methods was truly exemplary.

However, the length of the *Huangzhong* pipe was derived from the *chi* (foot/ruler), which in turn was derived from millet grains. Accumulating millet grains to create a ruler involved only three methods, all of which existed since antiquity. The first is called "transverse millet" (*heng shu*), where the width of one millet grain equals one *fen*; the second is called "longitudinal millet" (*zong shu*), where the length of one millet grain equals one *fen*; and the third is called "diagonal millet" (*xie shu*), where grains are arranged diagonally, leaning against each other.

Regarding the total length of the *Huangzhong* pipe: expressed in terms of transverse millet, it is 100 *fen*, which corresponds to Sima Qian's statement of "one *zi* equals one *fen*"; expressed in terms of longitudinal millet, it is 81 *fen*, corresponding to the *Huainanzi*'s statement that "its number is eighty-one"; and expressed in terms of diagonal millet, it is 90 *fen*, corresponding to the statements in the *Book of Han* and *Book of Later Han* regarding "ninety *fen*." Although these three methods differ, the resulting pitch pipe standard is the same.

The method for selecting millet is that grains produced in fertile lands within the Shangdang region are considered superior. These are essentially glutinous millet, commonly known as yellow millet. Prince Zheng stated: Ancient Shangdang Commandery corresponds to modern Luzhou Prefecture in Shanxi Province, where five-colored millet varieties grow. Among them, black millet has several subtypes: soft black millet suitable for brewing wine is called *Ju* (black millet); hard black millet suitable for cooking rice is called *Ji* (millet); and millet with two kernels per husk is called *Ji* (foxtail millet). Musicians and theorists used only *Ju*.

The ancient saying "select the middle millet" refers to millet that is centrally sized for practical use, not millet of an "average" grade. This is similar to the colloquial expression asking whether an item is "useful" (*zhong yong*) or not, which does not refer to average quality. Some argue that "Zhong" should be pronounced with the departing tone, meaning "standard-compliant," which is also a valid interpretation. The *Classic of Poetry* states: "He sent down fine seeds, only *Ju* and *Pi*." The use of the character "Jia" (fine/excellent) makes the meaning clear: only exceptional varieties are considered fine seeds. Furthermore, "Pi" implies "large," indicating that the largest grains are the best.

If millet grains are too large, the resulting ruler will be long, causing the *Huangzhong* pitch to be low and muddy; if millet grains are too small, the resulting ruler will be short, causing the *Huangzhong* pitch to be high and clear. The note of *Huangzhong* belongs to the Gong (Palace) mode, characterized by being the longest and having the lowest, most resonant tone; this is its essential nature. Therefore, the largest millet grains constitute the true *Ju*. Later generations, unaware of this principle, rigidly adhered to the text in the *Book of Han* regarding "middle millet." Consequently, the rulers they constructed were too short, and the music they produced sounded mournful rather than harmonious and balanced. This discrepancy must be clarified.

(Note: *Yue* is pronounced like "yao". *Ju* is pronounced like "ju". *Ji* [hard millet] is pronounced like "ji". *Fu* means husk. *Pi* is pronounced via the fanqie spelling "piao-mi".)