The unusual form of this double-gourd vase with its round upper section and square lower section is one which first seems to appear in the Ming dynasty Jiajing reign (1552-66). Essentially the shape refers to the relationship between Heaven and Earth, with Heaven represented by the circular upper section and the Earth represented by the square lower part. In the Jiajing reign these symbolic shapes were part of Daoist beliefs, of which the emperor was an enthusiastic adherent.
For a Jiajing example of a large blue and white double-gourd vase of this shape, see J. Harrison-Hall, Ming Ceramics in the British Museum, London, 2001, p. 230, no. 9:34. The construction of such vessels must have presented a number of challenges to the potter, however, and the form largely fell from favour after 1566, until it was revived at the imperial kilns in the 18th century. Even with the technical expertise available in the 18th century, firing these vessels would have been difficult, and they remain very rare. They may have been made in the Qianlong reign in conjunction with the rebuilding of the relevant altars in 1751-2.
A blue and white example with a very similar design of bats and gourds was included in the 45th Anniversary Exhibition of the Min Chiu Society, Hong Kong, Auspicious Emblems: Chinese Cultural Treasures, 25 November 2005 - 19 July 2006, p. 156, no. 65.