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The Prince of Zheng stated: According to the principle, Yang Lü (Yang pitch-pipes) generating Yin Lü (Yin pitch-pipes) occurs from below; Yin Lü generating Yang Lü occurs from above. Regarding the division of Yin and Yang, there have been two ancient theories. The first theory posits that the Twelve Lü (Twelve Pitch-pipes) correspond to specific directions: those east of the Zi-Wu line belong to Yang, and those west of it belong to Yin. Thus, Huangzhong at Zi corresponds to the Fu Hexagram (Return); Dalu at Chou corresponds to the Lin Hexagram (Approach); Taicu at Yin corresponds to the Tai Hexagram (Peace); Jiazhong at Mao corresponds to the Da Zhuang Hexagram (Great Power); Guxian at Chen corresponds to the Guai Hexagram (Breakthrough); Zhonglü at Si corresponds to the Qian Hexagram (The Creative); Ruibin at Wu corresponds to the Gou Hexagram (Coming to Meet); Linzhong at Wei corresponds to the Dun Hexagram (Retreat); Yize at Shen corresponds to the Pi Hexagram (Standstill); Nanlü at You corresponds to the Guan Hexagram (Contemplation); Wuyi at Xu corresponds to the Bo Hexagram (Splitting Apart); Yingzhong at Hai corresponds to the Kun Hexagram (The Receptive). Qian represents Old Yang, therefore Zhonglü is extreme and does not generate; Kun represents Old Yin, therefore Yingzhong is extremely short and serves as the end. Dalu, Jiazhong, and Zhonglü are three Lü positioned in Yang places, thus they all belong to Yang; Ruibin, Yize, and Wuyi are three Lü positioned in Yin places, thus they all belong to Yin. All clear pitch-pipes generate upwards, and all turbid ones generate downwards. This is the first theory.

Another theory states: The Six Lü (Yang pitch-pipes) with odd numbers belong to Yang, and the Six Lü (Yin pitch-pipes) with even numbers belong to Yin. Therefore, Huangzhong at Zi corresponds to the Initial Nine of Qian; Taicu at Yin corresponds to the Second Nine of Qian; Guxian at Chen corresponds to the Third Nine of Qian; Ruibin at Wu corresponds to the Fourth Nine of Qian; Yize at Shen corresponds to the Fifth Nine of Qian; Wuyi at Xu corresponds to the Top Nine of Qian. These six Lü have odd numbers and reside in their original positions, belonging to Yang. Linzhong at Chou corresponds to the Initial Six of Kun; Nanlü at Mao corresponds to the Second Six of Kun; Yingzhong at Si corresponds to the Third Six of Kun; Dalu at Wei corresponds to the Fourth Six of Kun; Jiazhong at You corresponds to the Fifth Six of Kun; Zhonglü at Hai corresponds to the Top Six of Kun. These six Lü have even numbers and reside in opposing positions, belonging to Yin. Those in original positions generate downwards, while those in opposing positions generate upwards. This is the second theory. Since the Han Dynasty until now, the validity of these two theories remains undetermined. Sima Qian's *Book of Music* includes both views, leading to disputes during the Han, Jin, Liang, and Tang dynasties. However, Zhu Xi's explanation in *Jingshi Daxun* is very clear. Generally speaking, regarding a year, the period after Winter Solstice belongs to Yang, and the period after Summer Solstice belongs to Yin; regarding a day, the time after Zi hour belongs to Yang, and the time after Wu hour belongs to Yin. This is called "Great Yin and Yang." Examples like Zi-Yang/Chou-Yin, Yin-Yang/Mao-Yin are called "Small Yin and Yang." The generation of Yin from Yang Lü and Yang from Yin Lü refers to the general principle. Whenever Yin Lü resides in a Yang position, it belongs to Yang; whenever Yang Lü resides in a Yin position, it belongs to Yin. Therefore, discussing Small Yin and Yang is a special variation; for other Lü, only Great Yin and Yang are discussed, which is the standard rule. Zhu Xi's argument surpasses that of Cai Yuanding. One view holds: Lü on the left, Lü on the right, their movements differ, similar to divination methods. Thus, from Huangzhong to Zhonglü, from Zi to Si, Yang rises and Yin retreats; hence, when Lü generates Lü, it is called "generating downwards," and when Lü generates Lü, it is called "generating upwards"; from Ruibin to Yingzhong, from Wu to Hai, Yin rises and Yang retreats; hence, when Lü generates Lü, it is called "generating upwards," and when Lü generates Lü, it is called "generating downwards." Change occurs at Wu, so Ruibin re-generates upwards. If discussing a convenient method, it does not go beyond the Six Yang and Six Yin of Qian and Kun. Zi, Yin, Chen, Wu, Shen, Xu; Huang, Tai, Gu, Rui, Yi, Wu, exactly like the counter-clockwise rotation of Qian, this is called "Lü generating downwards"; Wei, Si, Mao, Chou, Hai, You; Lin, Zhong, Jia, Da, Ying, Nan, exactly like the clockwise rotation of Kun, this is called "Lü generating upwards." This is Xuan Zheng's statement on divination methods, derived from Yang Xiong's *Taixuan*.