The Week’s guide to what’s worth watching

Six by Sondheim

In this unique tribute to a living Broadway legend, the story of Stephen Sondheim’s career is told through a study of six great songs, including “Send in the Clowns” and West Side Story’s “Something’s Coming.” Sondheim talks about his craft in old interviews, while vintage stage footage and new performances give each song brilliant life. Monday, Dec. 9, at 9 p.m., HBO

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At last, a reality TV challenge that matters. In this inspiring one-off, cameras follow teams of Stanford University students as they dream up and design products intended to improve the lives of the world’s poor. On the innovators’ drawing boards: a means of storing drinking water in Indonesia, a low-cost IV infusion apparatus, and a breathing device to prevent infant pneumonia deaths in Bangladesh.Wednesday, Dec. 11, at 10 p.m., PBS; check local listings

Another Day, Another Time: Celebrating the Music of ‘Inside Llewyn Davis’

Folk music lives. In this all-acoustic benefit concert filmed in New York City, Joan Baez, Patti Smith, and Jack White head an all-star lineup of performers who tear through an array of classic folk tunes, many of them featured in the new Coen brothers movie Inside Llewyn Davis. Elvis Costello and Marcus Mumford also pitch in, but the show-stealer might be singer Rhiannon Giddens, of the Grammy-winning Carolina Chocolate Drops, who delivers a riveting Gaelic medley. Friday, Dec. 13, at 10 p.m., Showtime

Evacuate Earth

What would humankind do if the universe threw an apocalyptic meteor storm our way? In this two-hour special, physicists, astrobiologists, and other scientists contemplate the potential for an end-days countdown and explain how a spacecraft roughly four times the size of Manhattan could become a new ark, propelling a genetically diverse group of humans to a distant, Earth-like planet. Saturday, Dec. 14, at 9 p.m., National Geographic

Psych: The Musical

Seven years after Psych’s debut, the quirky detective series unfurls a two-hour musical episode. Anthony Rapp of Rent guests as a crazed ex-playwright (and escaped convict), while series stars James Roday and Dulé Hill sing and dance their way through the investigation. Barry Bostwick and Ally Sheedy also appear. Sunday, Dec. 15, at 9 p.m., USA Network

Other highlights

The Sing-Off

A fourth season begins for a show on which the competition between a cappella groups could make anyone a fan of the genre. Monday, Dec. 9, at 9 p.m., NBC

Undersea Edens: Coral Kingdoms

Australia’s Great Barrier Reef is 6,000 years old and facing unprecedented challenges. Explore them, and the wonders of the reef, in this visually arresting special. Wednesday, Dec. 11, at 8 p.m., Smithsonian Channel

Alpha House

Time to decide if you’re in or out on Amazon’s top original comedy series, which was created by Doonesbury’s Garry Trudeau and stars John Goodman as one of four U.S. senators who share a Capitol Hill house. To access more than three episodes, you’ll need an Amazon Prime subscription, but that also buys free shipping on holiday gifts. Available for streaming at Amazon.com