In 1938, Miller "realized that he needed to develop a unique sound, and decided to make the clarinet play a melodic line with a tenor saxophone holding the same note, while three other saxophones harmonized within a single octave. George Simon discovered a saxophonist named Wilbur Schwartz for Glenn Miller. Miller hired Schwartz, but instead had him play the lead clarinet. According to Simon, 'Willie's tone and way of playing provided a fullness and richness so distinctive that none of the later Miller imitators could ever accurately reproduce the Miller sound.' With this new sound combination, the Miller band found success. Miller talked about his style in the May, 1939 issue of Metronome magazine. 'You'll notice today some bands use the same trick on every introduction; others repeat the same musical phrase as a modulation into a vocal. [...] We're fortunate in that our style doesn't limit us to stereotyped intros, modulations, first choruses, endings or even trick rhythms. The fifth sax, playing clarinet most of the time, lets you know whose band you're listening to. And that's about all there is to it.'
Most of his 'classic' hits, including Chattanooga Choo-Choo, Tuxedo Junction, Moonlight Serenade and In the Mood, use this sound trick.
https://en.wikipedia.org/wiki/Glenn_Miller