’Tis the season of a cappella vocal music. Christmas is the time when large choruses come into their own and small vocal ensembles — the King’s Singers, Chanticleer or the Tallis Scholars — tour from city to city, combining early and modern music in resonant tapestries against the winter cold. For these groups, like the Tallis Scholars, which came to the Kennedy Center last week, or the D.C.-based ensemble the Thirteen, which performed the first of three iterations of its holiday program at the Virginia Theological Seminary in Alexandria on Friday night, the Christmas repertoire represents the equivalent of the Great American Songbook to a jazz singer: a firm clay with which to fashion your own particular creation.

It’s a more fluid repertoire, to be sure. These concerts extended from Palestrina through church carols to Nico Muhly, the 37-year-old composer (of “Marnie” at the Met Opera this fall) whose “Rough Notes” received its world premiere performances on the current Tallis Scholars tour. And both groups pushed the idea of seasonal repertoire to its limits.

“Rough Notes” is hardly a festive piece; at most, it’s a wintry one. Its text is excerpted from the journals Captain Robert Scott wrote on his expedition to the South Pole in 1912, which ended with the death of all five of his team members, including himself. The first excerpt is a beautiful description of the Northern Lights, in which Muhly’s music arcs and ripples like the curtains of light Scott describes. The second is a poignant evaluation of the value of a trip that the writer already saw was doomed, stiff-upper-lipping English fortitude as a wan thread of light against the descending night. Muhly, who was a boy chorister himself, writes beautifully for choruses, understanding how to work with the taut cushions and lines of sound, moving freely between richness and asceticism, like gold leaf in a cold church.

The Thirteen focused on David Lang’s 2008 Pulitzer Prize-winner, “The Little Match Girl Passion,” a watershed piece that catapulted that composer into widespread acceptance in the classical music world. The premise is presenting the Hans Christian Andersen fairy tale through the filter of a Bach Passion, with choral commentary on the story of a child’s suffering and death and redemption — the connection to Christmas being that the child has visions of a Christmas tree as she is freezing to death. It’s a spare and lovely piece, moving concisely through a lot of emotional weight with the tight pings of bells and glockenspiels offsetting the vocal lines.

Both these works showed composers finding contemporary ways to interpret tradition; both set a tone for the pieces that surrounded it. “Rough Notes” was the centerpiece of a program of taut Renaissance polyphony by an ensemble that is still led by the director who founded it in 1973, Peter Phillips, though not one of the singers from the original group remains. Palestrina’s “Hodie Christus natus est,” subsequently worked into a full mass, was one central pole, intricate with interwoven double choirs; Pretorius’s “Magnificat,” also for double chorus, worked familiar Christmas carols into its texture.

In contrast to the Tallis Scholars’ slightly dry sound, the Thirteen sings with striking color and richness — an aesthetic choice rather than a qualitative distinction, though tarnished a bit by some harshness from the uppermost sopranos. This group is anchored more to the present than the past; though William Byrd was represented on the program, it mainly supported Lang’s “Passion” with other contemporary reworkings of Christmas traditions, like 35-year-old Nathan Jones’s version of “In the Bleak Midwinter” or Benjamin Britten’s beautiful “Corpus Christi Carol.” The final “Silent Night” was arranged by the group’s young director and founder, Matthew Robertson, in a veritably baroque exegesis that piled up voices in a pulsing superstructure around the familiar tune. Who says tradition can’t be creative?

The Thirteen’s next program, “A word too small: Love,” takes place Feb. 9 and 10.