Read about picks 40 through 31 and 30 through 21.

Part three of this year’s countdown:

20) Mette Henriette, Mette Henriette (ECM)
Young Norwegian reedist and composer Mette Henriette released one of the year’s most distinctive and assured debuts—a double CD on the prestigious ECM label—and I hope it portends a great deal more to come. Henriette grew up focusing on improvisation, but she spent many nights composing at home by herself, writing delicate miniatures (mostly between one and two minutes) that serve as vessels for spontaneous, richly textured playing both serene and turbulent. She made the first disc with a nimble trio featuring pianist Johan Lindvall and cellist Katrine Schiøtt, and the shapes of its songs frequently recall the music of Erik Satie; the second disc, for which she enlisted the Cikada Quartet and a slew of Norway’s best jazz artists (among them trumpeter Eivind Lonning and drummer Per Oddvar Johansen), opens up much bigger spaces. The intimacy and power of Henriette’s playing comes through clearly in both settings.

19) Eve Risser, Des Pas Sur la Neige (Clean Feed)
French pianist Eve Risser has played in all sorts of contexts lately, including the New Songs with first-rate Scandinavians and her homeland’s Orchestre National de Jazz. But she saved her boldest work for this solo debut, one of the most creative demonstrations of prepared piano I’ve ever heard. Using a variety of devices (including an Ebow) to generate hovering, sustained tones, Risser uncovers a rich sonic world, assembling the results of her research with unerring compositional logic.

18) John Luther Adams, The Wind in High Places (Cold Blue)
Another remarkable evocation of natural beauty from composer John Luther Adams, The Wind in High Places takes inspiration from the principles of the Aeolian harp (in a piece performed by New York’s fantastic JACK Quartet), the song of the canyon wren, and the way atmospheric conditions can create the suggestion of a multitude of suns or moons in the arctic and the Sonoran Desert. You don’t necessarily need to know this sort of backstory to be enriched by this meticulously articulated music, but it helps.

17) Naçao Zumbi, Naçao Zumbi (Circular Moves)
This long-running Brazilian band had a tough slog finding an identity after charismatic front man Chico Science was killed in a car crash in 1997. But Naçao Zumbi’s latest album proves they’ve succeeded: it retains the thunderous Maracatu rhythms at the core of the Mangue Beat sound they helped define, but also adopts a more guitar-driven approach that shows signs of chilling out. The new recording, produced by Kassin and Berna Ceppas, even includes a sensual ballad called “A Melhor Hora de Praia,” with lovely guest singing from Marisa Monte. Current singer Jorge de Peixe has never tried to copy Science’s extroverted, hectoring shout, instead favoring a more conversational tone that fits these full-bodied tracks like a glove.

16) Jeph Jerman & Tim Barnes, Matterings (Erstwhile)
For this otherworldly collaboration, veteran Arizona sound artist Jeph Jerman and Louisville percussionist Tim Barnes lugged bits of electronic gear outside to create music that melds environmental recordings (rain, wind, a passing airplane) with shifting splashes of feedback, pings, sine waves, telephone dial tones, metallic friction, and a wealth of hard-to-place noises that Jerman makes by rubbing, rustling, and otherwise manipulating objects he finds in nature. Together they twist the line between natural and man-made with profound simplicity.

15) Ryley Walker, Primrose Green (Dead Oceans)
Chicago guitarist Ryley Walker has already moved on from this stirring album, produced by Cave’s Cooper Crane and featuring instrumental contributions from some of Chicago’s most talented and versatile musicians—among them drummer Frank Rosaly, guitarist Brian Sulpizio, keyboardist Ben Boye, and bassist Anton Hatwich. Walker is a bona fide seeker, a guy who eats and breathes music and never stops listening, digesting, and evolving. For live performances, he and his band take the material way out, dilating it with extended improvisational passages, but Primrose Green itself focuses on Walker’s post-Tim Buckley songs, whose lovely arrangements caress his skyward voice.

14) Amir ElSaffar & the Two Rivers Ensemble, Crisis (Pi)
Oak Park native Amir ElSaffar, a triple threat on trumpet, santor, and vocals, has injected new urgency into his long-running Two Rivers Ensemble—though he also continues to mine riches from his marriage of Iraqi maqam and free jazz. The title of the album addresses the turmoil wracking the Middle East, and turbulence and tension replace much of the serenity of earlier Two Rivers recordings. ElSaffar’s compositions retain their meticulous plotting, structural ingenuity, and lyrical beauty, but his top-notch band digs into them purposefully, driven by fury, anxiety, and devotion.

13) Chris Lightcap’s Bigmouth, Epicenter (Clean Feed)
The second album by Chris Lightcap’s Bigmouth celebrates the bassist’s adopted hometown of New York: the title Epicenter refers to the city’s position in the world of jazz, and his compositions reflect its melting-pot ethos. Saxophonists Tony Malaby and Chris Cheek, inventive drummer Gerald Cleaver, and brilliant keyboardist Craig Taborn (playing a lot of Wurlitzer here) join Lightcap to dig deep into a collision of African grooves, postbop modes, classic minimalism, and blues, all of it given a thoroughly contemporary drive. And as though the album weren’t New York enough, it closes with a terrific cover of the Velvet Underground’s “All Tomorrow’s Parties.”

12) Vijay Iyer Trio, Break Stuff (ECM)
In the liner notes for his latest trio album, pianist Vijay Iyer writes, “A break in music is still music: a span of time in which to act. It’s the basis for breakdowns, breakbeats, and break dancing.” He and his sidemen (bassist Stephan Crump and drummer Marcus Gilmore) make the most of those sometimes undefined, wide-open spaces; they tackle Thelonious Monk and salute techno artist Robert Hood. On the surface Iyer’s trio is a model of composure and grace, but the ideas darting beneath the surface of its music are as electric and bold as anything in jazz today.

11) Mary Halvorson, Meltframe (Firehouse 12)
With Meltframe guitarist Mary Halvorson salutes some of her favorite music—she makes room for formative jazz influences as well as more recent material by close colleagues. In each case she brings her strong personality to the fore, boldly interpreting if not flat-out remaking the songs. Nowhere does that tendency manifest itself more radically than on her version of Oliver Nelson’s classic “Cascades,” a complex, buoyant postbop standard from his album The Blues and the Abstract Truth. Halvorson envisions the slashing horn charts as overdriven, serrated guitar work, ripping apart the melodic lines and threatening to wash them all away with floods of barely contained feedback.

Today’s playlist:

Achim Kaufmann, Verivyr (Pirouet)
Steve Reich, Radio Rewrite (Nonesuch)
Shorty Rogers & His Jazz Giants, Clickin’ With Clax (Atlantic, Japan)
Paragons, On the Beach With the Paragons (Trojan)
Music Music Music, Macbeth (Hoob Jazz)