Which Dynasties Didn't Build the Great Wall?

The construction work of the Great Wall had been carried out in nearly all the dynasties in China's history, except Yuan (1271 – 1368) whose northern border reached far beyond the wall. In addition, Tang (618 – 907), Song (960 – 1279), and Qing (1644 – 1911) dynasties didn't implement large-scale constructions like others.
 

After unifying the prairie north of the Great Wall, the Mongolians established the Yuan Dynasty in 1271 and continued to march southwards into the central plain. The regime finally annexed the Southern Song Dynasty in 1279, and the adjoining kingdoms on the north and west all became its tributary states. At this time, land inside and outside the Great Wall were all governed by the Yuan Dynasty and its territories even extended to the Europe. Even though, the territories expansion was far from over and they still coveted the eastern land across the East Sea and South Sea. In this case, emperors definitely won't bother to consider building the wall for defensive purpose.
 

The central government of Tang accepted enlightened policies towards northern tribes, stating that they enjoy equal treatment with the Han people in the central plain. On the other hand, Tang always gained the upper hand in several battles with northern tribes because of superior equipment and mature tactics. Therefore, spending mass of money and human power building the Great Wall was really unnecessary.
 

The military strength, especially the cavalry, of the Song Dynasty was so weak that it lost vast northern territories and its northern frontier fell back away from the Great Wall to the south of Beijing. Instead of largely building stone ramparts, the emperor ordered to drew water from rivers and lakes into wide trenches along the boundary. This unique 'Water Great Wall' not only contained nomadic cavalries but was also good for the irrigation.
 

The Qing Dynasty was originated from the Nomadic Jurchen and they surely won't need to beware of their clansmen outside the wall. Plus the previous Ming Dynasty carried out massive construction of the Great Wall and equipped it with perfect facilities, leaving not much room for improvement. On the other hand, cannons were widely used in the war during the Qing Dynasty and the Great Wall couldn't stand for very long under gunfire, so a massive construction was not necessary.
 

In history, Emperor Taizong of Tang (595 – 649) and Emperor Kangxi of Qing (1654 – 1722) depreciated the Great Wall. Both believed that the most effective way to guarantee the peace and stable in frontier areas was to implement policies of conciliation towards northern tribes. Building the wall cost too much money and human resources, and might even cause turbulences in the central plain like the Sui Dynasty (581 – 618) which was replaced by Tang. Additionally, the wall failed to stop attacks of Mongol troops, proving that it was not as powerful as it used to be. Kangxi Emperor even announced a ban for constructing the Great Wall.