In a flashback to the honeymoon of Tracy Samantha Lord (Kelly) and C.K. Dexter Haven (Crosby), we hear "True Love" (which I believe is also the only time Grace Kelly ever sang on screen):
The film explains the musical content partly by positing Dexter Haven as a songwriter who is organizing a local jazz festival in Newport, Rhode Island. Thus the presence of Louis Armstrong and his band in the film, sometimes acting as a Greek chorus of sorts and goosing things along. Here, Louis prompts Dexter to sing the song he once wrote for Samantha:
The jazz festival all yields a song where Crosby and Armstrong explain what jazz is all about, in "Now You Has Jazz":
I mention above that the film includes Frank Sinatra, so of course, he has to get into the act with the film's music. He plays one of the two gossip reporters sent by SPY Magazine to cover the Tracy Samantha Lord wedding, and he's generally disgusted by the antics of the rich and wealthy -- until, in the course of getting to know some of them, he learns that they have their own real problems. Anyway, here's an early comedic number with Sinatra and Celeste Holm wondering "Who Wants to Be a Millionaire":
Sinatra also gets, of course, his own soulful love song, "You're Sensational", which he sings to Grace Kelly:
The film's best number brings Crosby and Sinatra together for the only time in the film. They're at a party and neither is particularly enthusiastic about the proceedings, so both duck into the bar for some frank talk about the rich and the gossip that surrounds them. Here's "Well Did You Evah":
This is the movie's only real show-stopper. I love the moment when Sinatra stops Crosby with the line "Don't dig that kind of croonin', chum," to which Crosby responds, "You must be one of the newer fellas."
The Philadelphia Story is probably the better film, but High Society is not at all without its charms.