A triacontagon is a polygon with thirty sides, which sounds like the sort of fact someone might bring up at a party when the conversation has become dangerously enjoyable. But the title of this collaboration between Brazilian saxophonist Ivo Perelman, American experimental guitarist Elliott Sharp and Brazilian percussionist Cyro Baptista makes more sense as a description of how its music behaves than as a geometry lesson. Thirty sides imply neither symmetry in any immediately useful sense nor a particularly convenient way of getting from one point to another. They suggest a shape with too many possible approaches to be grasped at a glance. Across six lengthy improvisations, these three musicians construct something similarly difficult to reduce to a single perspective, though there is nothing random about the results. The music has its own internal logic, even when that logic seems to have been drafted by a committee whose members refuse to attend the same meeting.

Perelman has spent decades developing a tenor-saxophone language that can move from searching lyricism to an almost physical confrontation with the instrument. His early musical education included classical guitar, but the saxophone eventually became his principal means of expression, leading to a formidable catalogue of recordings and collaborations with figures such as Matthew Shipp and William Parker. Sharp comes from another corner of the experimental universe, with a practice encompassing guitar, electronics, composition, mathematical systems and the unruly history of New York’s downtown scene. Baptista, meanwhile, brings a percussion vocabulary informed by Brazilian traditions but never confined to them. His work can be rhythmic, theatrical, mischievous or unexpectedly delicate, sometimes within the space of a few seconds. The three are not merely specialists brought together to demonstrate their respective expertise. They are musicians with strong personal identities, and the interest lies in what happens when none is granted permanent control.

The first surprise is that Perelman does not automatically get first word. "Dionysus in the Amazon" begins with Sharp and Baptista establishing a restless exchange of guitar figures and percussion, a rhythmic presence that feels more like an invitation to move than a conventional beat. When the saxophone enters, it does not simply rise above the other instruments and claim the foreground. Perelman bends, stretches and roughens his phrases in response to the activity already underway. The sound can be exuberant without becoming celebratory, as though Dionysus had arrived at the party only to discover that the furniture had been assembled incorrectly and the guests were enjoying themselves anyway. Baptista’s contributions are especially important here: his percussion gives the music momentum while remaining too unpredictable to function as a dependable rhythmic floor.

That balance becomes more elusive in "Sacred Geometry of the Tropics". Sharp’s guitar can sound brittle, granular or strangely luminous, with tones that appear to have been drawn out of the instrument by methods its manufacturer would prefer not to discuss. Baptista responds with an assortment of timbres rather than a fixed pattern, while Perelman moves between piercing cries and phrases that seem to circle an idea without settling on a final statement. The tropical imagery in the title might encourage expectations of exotic colour or an imagined wilderness, but the music does not offer an easy postcard version of either. Its atmosphere emerges from the interaction of the players: a humid density one moment, a sudden opening the next, then another layer of activity that changes the apparent scale of everything around it. The geometry is less about orderly design than about the way separate lines keep altering one another’s direction.

"Inside a Broken Circle" makes that instability more explicit. A circle should, in theory, be reassuring: continuous, closed, uncomplicated by corners. Break it, however, and its parts begin to imply different destinations. The trio explores that possibility through shifts in density and emphasis, allowing individual sounds to acquire prominence before being absorbed into the ensemble again. Sharp’s guitar can supply a recognisable pulse, only for its texture to make that pulse feel uncertain; Baptista can suggest a rhythm without obliging it to behave; Perelman’s saxophone responds with a mixture of breath, pressure and melodic fragments. There is a strong sense of mutual listening, but not the polite kind in which everyone waits for their turn to speak. These musicians listen in order to interfere productively.

Then comes "Electric Bacchanalia", the one piece that begins with Perelman’s saxophone. Its title promises excess, and the performance has a more immediate physical charge, with the saxophone pushing forward while Sharp and Baptista create a lively, sometimes abrasive framework around it. Yet the track is not simply a release of pent-up energy. Even at its most animated, the music retains a flexibility that prevents it from becoming a prolonged contest in who can play loudest or fastest. Baptista’s sense of theatrical timing and Sharp’s ability to make the guitar function as both a rhythmic instrument and a source of unstable texture keep the proceedings mobile. It is the closest the album comes to an unruly celebration, though anyone hoping for a tidy chorus to take home will have to settle for the memory of a good argument.

The two closing pieces offer different kinds of resistance. "Irregular Forms in Humid Space" is particularly effective when the musicians allow small sounds to remain exposed before introducing something that unsettles their apparent significance. Baptista’s vocalisations and unusual percussive gestures can lend the music a distinctly playful character, while Sharp’s guitar and Perelman’s saxophone make the atmosphere more ambiguous. There is humour here, but it is not the humour of a novelty act. It comes from the musicians’ willingness to make sounds that might be conventionally labelled inappropriate and then demonstrate that they belong exactly where they are. "Disordered Continuum", shorter than its predecessors, closes the album without pretending to resolve the questions raised by the preceding hour. Its jagged exchanges and shifting momentum feel less like a conclusion than the point at which the recording decides it has made its case and declines to provide further documentation.

The album’s freedom is not the absence of structure. It is a structure that develops through attention, reaction and the capacity to abandon an idea before it becomes an obligation. That distinction matters, because free improvisation can sometimes mistake the removal of rules for the removal of responsibility. Here, each player has to do more than produce an identifiable sound: each must recognise what the others are doing and decide whether to reinforce it, oppose it or change the conditions altogether. Sharp’s textural ingenuity, Baptista’s rhythmic imagination and Perelman’s expressive range create a group dynamic in which no contribution remains entirely private. Even the more abrasive moments carry traces of exchange rather than mere collision.

There are passages where the density and extended duration may test listeners who prefer improvisation to provide a clearer sense of arrival. The six pieces occupy more than an hour, and their titles sometimes promise a conceptual precision that the music deliberately refuses to deliver. But that mismatch is part of the record’s appeal. "Triacontagon" gives us neither a mathematical proof nor a ceremonial performance with a clearly defined beginning, middle and end. Instead, it captures three musicians working out a temporary set of relationships, with all the mischief, concentration and occasional confusion that entails. Thirty sides may be an awkward shape to draw, but these three players make a persuasive case for listening from more than one direction. The final result is adventurous without being self-important, physically engaging without leaning on brute force, and funny in the way serious creative people can be funny when they stop trying to look serious. It leaves the pleasing suspicion that the music has discovered several more possibilities than it has actually had time to explore.