Arrigo Cappelletti was born February 12, 1949, in Brunate, a small town above Lake Como. He first trained and worked as a philosophy teacher in Italian high schools through the 1970s, turning to jazz piano as a full-time pursuit only after that decade in the classroom, drawing on the pianists he names as his own touchstones: John Lewis, Lennie Tristano, Bill Evans, and Paul Bley. He built his first reputation in the piano-trio format, and his 1987 leader debut, Reflections (Splasc(h) Records, with bassist Roberto Della Grotta and drummer Massimo Pintori), was named to Cadence magazine's year-end list of the ten best records of 1988. Alongside performing, he taught jazz in public and private schools for years before, from 2001, taking conservatory posts in Sassari, Reggio Calabria, and Alessandria; since 2006 he has directed the Jazz Department at the Conservatorio Benedetto Marcello in Venice, where he also organizes seminars and concerts.

His first prominent co-billed group was the Cappelletti-Ottaviano Quartet with saxophonist Roberto Ottaviano, documented on Samadhi (1986, Splasc(h) Records), with bassist Piero Leveratto and drummer Massimo Pintori. In the late 1980s Cappelletti pivoted toward cross-genre work, founding what is described as Italy's first tango-jazz ensemble; Open Spaces (1989, Splasc(h) Records) paired his duo and trio with bassist Barre Phillips, and Pianure (1990, Splasc(H) Records), billed to his New Latin Ensemble, featured accordionist Gianni Coscia. He and Coscia, together with vocalist Gioconda Cilio, also recorded Todos Los Nombres Del Agua (1995) and The Moon and the Cat (Mingus Live Production), the latter also featuring Stefano Maltese and Davide Zaccaria.

In 2001 Cappelletti extended the same cross-cultural instinct into Portuguese fado on Terras Do Risco (Dez Canções) (Amiata Records), a project he conceived with singer-guitarist Jorge Fernando and built around poems by 20th-century Portuguese writers, with singers Alexandra and Jorge Fernando, Portuguese guitarist Custódio Castelo, and bandoneonist Daniele di Bonaventura, already profiled on jazzprofiles.com.

From the mid-2000s, Cappelletti built a parallel body of work with American avant-garde and free-jazz musicians. Little Poems (2002, Splasc(H) Records, with saxophonist and flutist Giulio Visibelli) carries a Discogs-documented, if sleeve-uncredited, bass contribution from Steve Swallow. Hard Lights (2007, Music Center) is a trio billed to Cappelletti, trumpeter Ralph Alessi, and drummer Nicola Stranieri. Metamorphosis (2011, Leo Records), recorded in Trieste in November 2010, added guitarist Andrea Massaria and violist Mat Maneri to a quartet built, in Cappelletti's own words, around "a process of constant change and metamorphosis"; the same trio-plus-Maneri lineup, billed as the Cappelletti-Massaria-Maneri Trio, also recorded The Edge of Becoming, taped live at the 2011 Iseo Jazz Festival. Homage to Paul Bley (2015, Leo Records) is a trio session with bassist Furio Di Castri, already profiled on jazzprofiles.com, and drummer Bruce Ditmas, both of whom had themselves worked with Bley.

Cappelletti is also a published essayist and biographer. His first book, Il profumo del jazz (1996), mixes memoir with an introduction to jazz improvisation for newcomers. He followed it with a full-length study of Paul Bley, Paul Bley: La logica del caso (2004, LEPOS, Palermo), translated into English by Gregory Burk as Paul Bley: The Logic of Chance (2010, Véhicule Press, Montreal). Two further books followed: La filosofia di Thelonious Monk (2014) and Le avventure di un jazzista filosofo (2016).

More recently, Cappelletti recorded a piano-duo album, Memories of the Last Century (Jazz Improvisations for Piano Duo) (2018, Da Vinci Jazz), with pianist Pietro Girardi, and returned to solo piano on Tough Love (2023, Da Vinci Jazz). Press materials also describe an association with Giorgio Gaslini, performing under Gaslini's direction with an Italian Jazz Orchestra project in the early 1990s; no specific dated release documenting that collaboration was found on Discogs, so it is noted here as bio-sourced rather than discography-verified.

Cappelletti's own reference points, by his own account, run from the Modern Jazz Quartet's John Lewis and the cool severity of Lennie Tristano through Bill Evans to the open, chance-based language of Paul Bley, on whom he later wrote a full biography. Discogs' style tags for his catalog cluster around "Contemporary Jazz" and "Free Jazz," with "Latin Jazz" attached to the tango- and Latin-inflected New Latin Ensemble period. Critic Art Lange, quoted on Amiata Records' own artist page, credited him with the ability to "improvise with simplicity and lyricism" while carrying "a thoughtful, often introspective attitude" - a description that holds across both his trio recordings and his more exploratory duos and quartets with American free-jazz players.