Mary Halvorson might be the most original jazz guitarist in a generation. She improvises lines that bend and swoop atonally, notes folding back on themselves, to create sounds that evoke both warped audiotape and ricocheting bullets. But she’s a composer, too, and (despite lots of unique six-string work) that’s where the focus lies on her challenging but riveting second album, Saturn Sings. Its 10 tracks are all originals, and six of them feature horns (Jon Irabagon’s alto sax and Jonathan Finlayson’s trumpet) in addition to her regular players (bassist John Hebert and drummer Ches Smith)—foregrounding Halvorson the writer and de-emphasizing Halvorson the musician. As with her playing, her tunes evade convention. Aficionados of the 4/4, 32-bar song will have their work cut out for them with the 62-bar “Crescent White Singe (No. 13),” which alternates between 4/4 and 3/4, and with “Sequential Tears in It (No. 20),” whose 56-beat head is nearly impossible to meter. These kinds of oblong structures can often be unlistenable, but Halvorson is more clever than that. On her constructions hang taut, propulsive melodies that are actually augmented by their unusual shapes: The sudden changes of direction create suspense and intrigue. “Mile High Like (No. 16),” for example, starts with a tense but upbeat flamenco, with Irabagon and Finlayson’s assertions chafing against Halvorson and Hebert’s chords; then the songs shifts into a frantic ensemble workout that slows to a crawl before launching off again, this time into a rock rhythm with an urgent, horn-led melody. Of course, that unpredictability goes both ways—the tunes’ relative friendliness is comfortable furniture for obscure improvisations. The title track is a terse march with fluid, somersaulting (if slightly off-key) horns that are, well, jazzier than anything else on the album. Finlayson and Irabagon veer into a counterpoint so stately that it seems prewritten (it isn’t), with soft autoharp-like chording from Halvorson in the rhythm section; slowly, though, Smith’s accents begin to clump, Hebert’s notes start bleeding together, and Halvorson’s warped tones stab into their rhythmic mess, which Finlayson and Irabagon resist until finally succumbing to the chaos just before the close. The musicians’ interplay is key to the album’s success, especially when some slip into bedlam while the others keep control. “Crack in the Sky (No. 11)” is another splendid example: When Irabagon’s solo casts sunshine and animation onto the piece’s melancholy, Halvorson lets fly her weird barbs of guitar, abrasive as Ajax, attempting to hijack Irabagon’s streak of hope. Instead, he does the hijacking, and Halvorson’s following solo develops from a dissonant lament into a lively traipse. Even so, it’s Halvorson’s writing that makes all this creativity possible. Her innovative guitar playing is an essential component—but riding on such high-grade material, it feels more like a bonus. Saturn Sings ultimately passes muster on compositional grounds: It’s an ideal balance of formal experiment and compelling listen.