Music in "Miss Aggie's Farewell Performance"
The show-within-a-show in this episode is set in Indiana, and its theme music, appropriately enough, is the chorus of "On the Banks of the Wabash," the official state song of Indiana, published by Paul Dresser in 1897.
If you ask a hundred Hoosiers for the name of their state song, though, I'm willing to bet that nearly all of them will say it's "Back Home Again in Indiana" (a blatant ripoff of "Banks of the Wabash," published some years after Dresser's death).
I'm not one to sit and listen to a show's background music when there's a story in progress, but I have the distinct impression that the incidental music in this series is mostly bits and pieces of Elmer Bernstein's theme music. Use of (the presumably out-of-copyright) "Banks of the Wabash" contributed some variety at no extra cost.