The slab serif is Stymie Extra Bold Condensed. Take note that ATF’s Stymie for manual typesetting is partly different from Monotype’s Stymie for machine typesetting. The Extra Bold Condensed drawn by Sol Hess is unique to the Monotype version. It sports two forms for the letters A and R (and a). This 1940s specimen by W. Longyear shows the R as used on the cover, while this specimen by the California Type Foundry has the correct A without top serif.
The song names are in Lightline Gothic, a light version of News Gothic.