Music and dance thematically link routines from around the world in “Play On,” the largely new 31st annual edition of the Big Apple Circus, currently at City Hall Plaza.

A few performances during the first half still need tuning up, like the singing of British ringmistress Carrie Harvey and the low-wire boogy-ing of Sarah Schwarz. But the identical twin La Salle brothers have always incorporated jazz dancing into their mirror-image juggling and acrobatic routine, making their “Double Time” a perfect fit for the overall musical motif.

In the betcha-haven’t-seen-this before category, classical ballerina Zhu Zhengshen balances en pointe (tiptoe) on various parts of her partner An Nan’s anatomy.

Iconic clown Grandma (Barry Lubin) still tickles kids’ funny bones with his silent slapstick, parodying previous routines and Dancing with the Stars. More discriminating comedy connoisseurs might prefer Belgian guest artist Olivier Taquin, playing a tuxedoed mannequin come to life. Taquin is especially hilarious when robotically lurching through a tango, dragging along a hapless female plucked from the audience.

Some performers specialize in fancy footwork of a non-choreographed sort. In a welcome change of pace from previous Big Apple’s equestrian acts (which showcased horses going through their paces), “Play On” features daredevil riding by Christine Zerbini and Sultan Kumisbayev. The latter, a member of a Cossack troupe in his native Kazakstan, leaps on and off his fast-galloping steed, providing real rodeo thrills.

The show’s only other animal routine is a sure-fire audience pleaser, a dog act “gone wrong.” Pompous, mustachioed Luciano Anastasini seems to lose complete control of his “pound puppies,” all rescued from US shelters. Their mischievous tricks are wildly different from the ones he commands them to perform.

Other international “high notes”: China’s Guiming Meng, balancing on his head a succession of ever bigger and heavier ceramic jars and the Russian barre act of the Rodion Trio, who won the Golden Clown, the world’s most prestigious circus award.

Again benefiting the Children’s Museum, the Big Apple continues at City Hall Plaza through May 10. Tickets may be purchased by calling 888-541-3750, logging on to bigapplecircus.org, or stopping by the box office in front of the Big Top any day.