Mick Hartley

This is so early Sixties hip. Dave Brubeck's 1961 piece from his Time Further Out album:

It's not entirely certain who the dancers are, but a YouTube commenter suggests the Hugh Lambert Dancers on the Ed Sullivan Show, Nov. 11th 1962, and they are indeed listed here as one of the acts on that show:

Summary: Music: –Robert Goulet sings "Don't Be Afraid of Romance" and "Gonna Build A Mountain." –Phyllis McGuire and Robert Goulet – "Darn It, Baby, That's Love" duet. –Phyllis McGuire sings "It's Magic" and "Old Devil Moon." Dance: –Hugh Lambert Dancers – dance to Dave Brubeck's "Unsquare Dance." Comedy: –Rowan & Martin (comedy team) – do two sketches. –Jerry Shane (comedian) – auto assembly line sketch. –Senor Wences (ventriloquist) –Charlie Cairoli and Co. (musical clown & troupe) – perform two routines. Also: –The Five Olanders (family of acrobats/tumblers) –Tribute to Eleanor Roosevelt (who died on November 7, 1962) – includes a clip of her last Sullivan appearance. 

What a cornucopia of delights.

On the song itself:

Written in 7/4 time, the piece is an example of Brubeck's exploration of time signatures. According to Brubeck, it was written during a single trip from his home to the recording studio and was recorded the same day. The song is based on a blues structure but also has a distinct country and western feel, as implied in the title (a square dance being a fixture of western US culture). "Unsquare Dance" is driven by a strong bass figure, with percussion provided primarily by the rim of the snare drum and hand claps. It combines duple and triple meter.

The piano enters with descending phrases crossing the 7/4 rhythm. The speed of the piece gradually increases from start to finish. The main theme then develops initially without left accompaniment and then with a characteristic figure based around the use of tenths. A drum solo using rim shots follows, then a restatement of the theme and a distinctive conclusion.

Brubeck says in his liner notes:

"Unsquare Dance", in 7/4 time, is a challenge to the foot-tappers, finger-snappers and hand-clappers. Deceitfully simple, it refuses to be squared. And the laugh you hear at the end is Joe Morello's guffaw of surprise and relief that we had managed to get through the difficult last chorus.

According to one music teacher, "Brubeck calls it 'Unsquare Dance' and it ends with 'Turkey in the Straw' which is as 'square' as you can get!" At the very end, right after referencing "Turkey in the Straw", the song quotes the well known musical couplet known in some circles as shave and a haircut … two bits, with the last note being the seventh beat in the measure.