Vanderbilt's Central Library has microfilm of selected past issues of the Tennessean in its microfilm collection, located on the 6th floor of the Central Library.
To locate the library's versions of the newspaper, choose a Browse Search in the Library Search. Select title and enter "Tennessean" to find the record for all versions held by the Vanderbilt Libraries, including electronic access options. The library collections include access to the newspaper dating from 1972 forward.
If you have a card for Nashville Public Library, they have access to back issues (from 1812 forward) and selected features such as obituaries online from 2001 onward at https://www.library.nashville.org/research/databases?age=All&subject=73.
The Tennessee State Library and Archives has earlier years from 1920 forward (under the newspaper's various titles) on microfilm.