What do medieval music and John Zorn  have in common? In the hands of the JACK Quartet, a lot more than you might think. Between concerts on the east and west coasts, the group stopped in Cleveland for two nights of challenging music in unorthodox settings. Their first performance was at the Transformer Station, a small contemporary art gallery, where they played Georg Friedrich Haas’s “In iij. Noct.” in total darkness. The music critic for the local daily confessed to breaking into a claustrophobic sweat and nearly fleeing before being mesmerized by the hour-long cacophony. Modern music will do that to the uninitiated.

In iij. Noct.” contains a quote from Gesualdo, which provided a thread to the next night’s performance at the Cleveland Museum of Art, a mash-up of early and contemporary music. As the program unfolded, other connections became apparent – in sources of inspiration, varieties of musical language and helpful explanations provided by members of the group involved in building bridges between disparate worlds.

The concert opened with violinist Ari Streisfeld’s arrangement of three short pieces by medieval French poet and composer Guillaume de Machaut. Intriguing but uneven, they were ancient in content yet totally modern in form, a synthesis that did not always work. After a sleepy opener offering beautiful sonorities, a stiff reworking of a ballad gave way to a lively finale that sounded very much like a Celtic dance. The approach was interesting and the music expertly played, but overall the melding of genres felt like an uncomfortable fit.

Zorn’s The Remedy of Fortune put the ensemble back on more familiar footing, with impressive results. The title comes from a de Machaut poem and the music included what sounded like several de Mauchat references. But it’s all Zorn, every skittering line, pizzicato pop and lingering sound loop, which the group played with finesse. The JACK players know the piece well – they premiered it at a Zorn tribute in New York last year. Still, their ability to hold together a work that seems constantly on the verge of flying apart is remarkable, and their technique was exquisite. At one point, it seemed impossible that an ultrafine string line could come from four instruments, sounding instead like a whisper of one.

Had Cenk Ergün’s Celare been performed the previous night, the audience would have missed its most interesting effect – passages scored for left hand only. Watching the musicians noiselessly finger the necks of their instruments offered a promising start, though by the end of the piece it seemed little more than a gimmick to break up intermittent phrases and an extended hum that built to a deep, metallic drone. Celare was the first of two world premieres on the program by Ergün, a well-regarded Turkish composer with a taste for electronics. The quartet lent the works gravitas, but couldn’t do much for ideas that essentially sat in one place, never developing any legs.

Cellist Kevin McFarland’s arrangement of two selections from Monteverdi’s Orfeo was a more successful blend of early and contemporary genres, hewing closer to the source material and giving the players an opportunity for emotional expression that modern music seldom provides. Classic in intonation and emphasis, their brief excursion into the birth of opera was warm and engaging, tinged with contemporary colors and showing convincing mastery of a traditional form.

A 21st-century fan of Monteverdi, Pulitzer Prize-winning composer (and violinist and vocalist) Caroline Shaw, used the prologue of Orfeo as a departure point for Ritornello 2.sq.2. Started in 2012, her playful exploration of musical interludes continues to evolve. For this performance the quartet played the “j” version, which skips along in happy melodies and plucking rhythms, then turns wistful, melancholy and sweetly sentimental before spinning itself into a tizzy and finishing with a series of atonal variations and cartoonish bouncing effects. The JACK players balanced the serious and humorous elements of the piece nicely, showing range and restraint.

Ergün’s Sonore provided a noisy finale, a high-volume ostinato that buzzed and hummed like an angry beehive. As a minimalist riff it offered a vibrant hook, but like his earlier piece, never developed into anything else. Particularly coming on the heels on the wildly imaginative Ritornello, it seemed well-informed but static.

Otherwise, a smart and satisfying program, played with precision and panache. The ideas were fresh, the connections revealing and the journey across eras an exhilarating adventure. Even in the light.