Giacomo Uncini was a trumpeter, flugelhorn player, composer and teacher from Jesi, in Italy's Marche region. He graduated in trumpet and jazz from the Conservatorio "Gioachino Rossini" in Pesaro and then studied in New York, where, according to the Istituto Italiano di Cultura's concert notice, he attended the New School for Jazz and Contemporary Music on a scholarship. His teachers there are named in Italian press coverage as Charles Tolliver and Cecil Bridgewater, and the same notice adds Vic Juris, Charlie Persip and Reggie Workman. He died on February 4, 2025, at 44, after a prolonged illness, which puts his birth in 1980 or early 1981; no birth date has been published.

Uncini built his career through the Marche's jazz scene, and two strands ran through it. The first was the Colours Jazz Orchestra, the big band founded around 2001 by trombonist Massimo Morganti in the Marche, where Uncini sat in the trumpet section as a stable member. The orchestra has worked with Kenny Wheeler since 2003, and Uncini is one of five trumpeters credited, Wheeler himself among them, on Nineteen Plus One (Astarte, 2009), a set of Wheeler's big-band arrangements of standards recorded at Naive Studio in Fano in June 2007. He is also credited on the orchestra's Home Away From Home (Neuklang, 2014), which plays the music of composer and conductor Ayn Inserto, and on Quando M'Innamoro In Samba (Incipit, 2013), a Latin-flavored project by the Latin Colours Jazz Orchestra with Franco Ambrosetti on flugelhorn.

The second strand was his own groups. In 2010 he founded the Spinning Quintet with pianist Mike Melillo; the group's album Nice If You Can (Notami Jazz, released July 19, 2012) adds saxophonist Antonangelo Giudice, bassist Gabriele Pesaresi and drummer Massimo Manzi, with Uncini credited as trumpeter and co-producer. In 2014 he formed a quartet with guitarist Carlo Petruzzellis, bassist Gianludovico Carmenati and Manzi. Its record Indian Summer (Notami Jazz, 2015, recorded October 31 and November 1, 2014) is billed to the quartet with keyboardist and multi-instrumentalist Giulio Carmassi, a member of Pat Metheny's quintet, as featured guest. His only album issued under his own name alone, Time Heals Everything (Notami Jazz, 2019), is a set of original compositions for a quintet with guitarist Andrea Molinari, pianist Pietro Lussu, bassist Luca Fattorini and drummer Marco Valeri, presented at the Fano Jazz by the Sea festival in July 2020.

Away from his own bands he was a regular sideman on Marche and Adriatic-coast sessions. Discogs credits him on Milo Lombardi's Going Nowhere Enjoying The Ride (2014), on guitarist Stefano Coppari's Eureka (AUAND, 2016) with pianist Claudio Filippini, on the Jazz Inc. album Jazz Inc. (2016), on singer Laura Avanzolini's Sings Bacharach (Koiné, 2019), on Manuele Montanari's film-music project Movie Medley. Il Grande Jazz A Cinecittà (Wysiwyg, 2020) with clarinetist Gabriele Mirabassi as soloist, and on Stefano Savini 5tet's Aliquid Novi (Dodicilune, 2020) with drummer Andrea Grillini. Italian press coverage lists Franco Cerri among the musicians he worked with, per the Istituto Italiano di Cultura notice; that claim is not backed by a Discogs credit, so Franco Cerri is named here without a recording connection.

Uncini also taught. At the time of his death he was on the jazz faculty of the Conservatorio di Benevento, according to the announcement of his memorial concert, and earlier listings name jazz trumpet posts at the conservatories of Messina and Mantova; he also taught at Scuola Opus1 in Chiaravalle and at the Scuola Musicale G.B. Pergolesi in Jesi. One of his last public performances, in the 2023 Festival Pergolesi Spontini at Jesi's Teatro Pergolesi, was a jazz reinterpretation of Pergolesi's Stabat Mater with guitarist Andrea Molinari.

He died in the hospice at Chiaravalle, near Ancona; his funeral was held on February 6, 2025, at the church of San Giovanni Battista (San Filippo) in Jesi, and the Comune di Jesi issued a public statement of condolence. In July 2025 the Ancona Summer Jazz festival held a "Giacomo Uncini Memorial" at the Mole Vanvitelliana, a jam-session evening built around Massimo Manzi, Andrea Molinari, Massimo Morganti, members of the Colours Jazz Orchestra and his conservatory students.

Uncini played in the mainstream and post-bop tradition. Cronache Ancona describes him as directing ensembles and curating repertoire in the bebop tradition, and another regional tribute says he blended traditional jazz elements with older and modern influences. His New York teachers, Tolliver and Bridgewater, are both trumpeters rooted in the hard bop and post-bop tradition, and his own record Time Heals Everything is built from original compositions written to showcase the solo and interplay skills of the quintet's members, rather than reworked standards. On the ensemble side, his years in the Colours Jazz Orchestra put him in front of arranged big-band writing by Kenny Wheeler and Ayn Inserto, a very different setting from his small groups, and the balance between the two is what most of his recorded output shows.