I recently read Lost Chords: White Musicians and Their Contributions to Jazz 1915-1945, an impressive tome by the late Richard M. Sudhalter. In it he quotes from drummer Ray McKinley in discussing the Dorsey brothers sound:
'The idea, as McKinley remembered it, was to build a band sound around the middle-register sonority of the trombones and tenors, a kind of instrumental cognate to the vocal timbre of Bing Crosby. "Bing was the biggest thing around in those days," said McKinley, "There was nobody who sang like him. The Dorseys had often played with Bing, and they felt - or the Rockwell-O'Keefe Agency felt - that they could achieve something if they pitched their sound like his."'
Interesting that Bing's tonality was an influence on the sonority they chose for the orchestra.