Tai Wu or Da Wu , personal name Zi Mi (子密), was a Shang dynasty King of China.

In the Records of the Grand Historian he was listed by Sima Qian as the ninth Shang king, succeeding his brother Yong Ji (太庚). He was enthroned with Bo (亳) as his capital. He appointed Yishe (伊陟) and Chenhu (臣扈) as his higher officers.

In the 7th year of his reign a mulberry tree (桑) and millet (谷) were found growing together in his palace. According to the Records of the Grand Historian, surprisingly, they grew to very tall trees within 7 days. This young king was quite scared and turned to Yishe for explanation, which was in regard to the king's former incapable governance. Tai Wu listen to his intelligent ministers and worked diligently; then, those two unusual trees withered very soon after he became a good king.

In the 11th year of his reign, he ordered Wu Xian (巫咸) to pray at Shanchuan (山川). In the 26th year of his reign, the Queen of West Rong (西戎) sent an envoy to Shang, the king later sent Wangmeng (王孟) on a return visit. In the 31st year of his reign, he appointed Zhongyan (中衍) of Fei vassal (费侯) to the position of Chezheng (车正). In the 35th year of his reign, he wrote a poem called Yanche (寅车). In the 46th year of his reign, there was a great harvest of crops. In the 58th year of his reign, he built the city of Pugu (蒲姑). In the 61st year of his reign, the nine east Barbarians Yi tribes (东九夷) sent envoys to Shang.

He ruled for 75 years, was given the posthumous name Tai Wu and was succeeded by his son Zhong Ding (仲丁).

Oracle script inscriptions on bones unearthed at Yinxu alternatively record that he was the seventh Shang king succeeding his uncle Xiao Jia, given the posthumous name Da Wu (大戊) and succeeded by his brother Lü Ji.

太戊（？ - ？），或作大戊，子姓，名密，《史記·殷本紀》記載其廟號為中宗，商朝君王，《史記·殷本紀》言為前任君王小甲弟，雍己之兄，繼雍己之後為國君，然而據甲骨文周祭卜辭，雍己卻排在大戊之後，因此學者認為雍己應為大戊之弟。《書·無逸》及《太平御覽》引《史記》皆謂太戊在位七十五年。太戊在位時，舉賢人伊陟為丞相，天下大治，諸侯歸附。諸子可証者有仲丁、止壬、河亶甲。

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