How many songs by Louis Jordan can you name? If prompted, you might remember Is You Is Or Is You Ain’t (My Baby) and his cover of Ain’t Nobody Here But Us Chickens, but for all Jordan’s phenomenal success as a mid-century band leader, and for all his status as the father of rhythm and blues, much of his music can still seem like a well-kept secret.

It’s a testament, therefore, to Jordan’s skill as a composer – and to the elan with which his songs are performed – that Five Guys Named Moe is such a happy and accessible show. This is a jukebox musical with none of the familiarity of Mamma Mia! or Never Forget and yet all of the feelgood spirit. It’s a heady celebration of a man you never knew you were a fan of.

It’d be asking too much of this latest incarnation to match the laid-back cool of writer Clarke Peters, who played the central part of Nomax in 2010, but director Paulette Randall’s revival is no less persuasive. Performed under canvas with a revolving stage encircling half the audience, the Underbelly/Cameron Mackintosh production is a masterclass in close-harmony singing, funky choreography and back-beat swing.

True, it doesn’t so much have a plot as a pretext, and we could surely do without the mirthless running gag about a raffle prize, but with Philip Gladwell’s lighting adding rainbow hues to Tom Rogers’s primary-coloured costumes, it’s too bright and breezy a show for us to care about anything but the fabulous music.

• At Festival Square theatre, Edinburgh, until 7 January. Box office: 0131-510 0395.