Eyal Talmudi grew up in Givatayim and started on classical clarinet at eight. By twelve he wanted the saxophone instead, and the reason he gives is his older brother, the pianist and producer Assaf Talmudi, who had begun playing jazz and had gone to the Thelma Yellin High School of the Arts. Eyal followed him there, switched horns, and, in his own words, started playing a great deal of jazz. He was performing at improvised-music evenings from fifteen, much of it at HaGada HaSmalit, the Tel Aviv club whose politics meant an unknown teenager could have the stage and five-shekel beer for the asking. He did his military service in the IDF Orchestra as a saxophonist, spent about a year in New York afterwards playing reggae and rock in clubs, and came back to Israel to join the electronic group HaMalben and then the Maghreb Orchestra.

Two things happened in the second half of the 2000s that set the shape of everything since. In 2006 he joined Oy Division, the Tel Aviv klezmer band whose name is a joke at Joy Division's expense, playing clarinet alongside his brother on accordion, Noam Inbar on vocals, Avichai Tuchman on bass and Gershon Leizersohn on violin. Then, in 2007, he formed Mãlox with the drummer Hagai Fershtman. The duo's first record, One Day, was improvised and cut in a single day at Vibromonk Studios in Brooklyn and issued on Rosh Tiferet, Talmudi's own imprint. All About Jazz reviewed it in January 2008 and heard exactly what it is: Hasidic dance tunes and Talmudi originals played with a saxophone attack the reviewer traced to the World Saxophone Quartet, a cover of Hamiet Bluiett's "Nali Kola" from the 1987 Black Saint album, and a piece called "Ganelin" written in tribute to Slava Ganelin. Talmudi's own name for what the band does is Hora Punk.

Mãlox is the through-line of his career and it has taken him further abroad than anything else he leads. The duo played the Israeli Night showcase at jazzahead! in Bremen in April 2013, the year Israel was the fair's partner country, with Aviv Bonen in the drum chair; the German daily taz covered the set and compared the spare violence of the music to Ted Milton's jazz-inflected post-punk. Roy Chen took over on drums soon after and has held the seat since. Polka For Punks (2012) was recorded and mixed in Tel Aviv by Tamir Muskat with Maya Dunietz guesting, Gaza Trip followed in March 2016, and a German club run that April took the duo through Berlin, Karlsruhe and Bremerhaven. In September 2019 the band spent four nights at Klub Alchemia in Kraków with Assaf Talmudi added on Hammond organ, and the tapes became Shit to Gold, released in February 2020 by Nana Disc and the Polish label Alchemia and filed under klezmer, punk, polka and avant-garde jazz all at once.

His own name went on the front of a record for the first time in October 2014, when Saved My Eyes From Tears, credited to Eyal Talmudi and Roy Chen, came out on Time Grove Selections, the Tel Aviv imprint Rejoicer opened as a Raw Tapes sublabel. Rejoicer produced, mixed and played synthesizers, and the guest list is a snapshot of the Raw Tapes circle: Omri Mor, Maya Dunietz, KerenDun, Shai Tsabari, Miss Red and Rony Iwryn. Three years later came the record that reads most straightforwardly as a jazz album. Even If, released December 15, 2017 by Chant Records, put Talmudi at the head of a quintet with Sefi Zisling on trumpet, Uzi Feinerman on guitar, Gilad Abro on bass and Aviv Cohen on drums, cut in one session at Kicha Studios with the engineer Uri Barak, half the material written in advance and half invented on the spot. Talmudi described the label to Columbus as one founded by people who came up around John Zorn and Tzadik, Shanir Ezra Blumenkranz among them. Three weeks before the album appeared he led an octet at the Tel Aviv Jazz Festival on December 7, 2017 for the Thelonious Monk centenary, with Zisling, Gershon Waiserfirer, Feinerman, Assaf Talmudi, Abro and Aviv Cohen.

He is a founding member of Time Grove, the studio collective Rejoicer built around a rotating group of Israeli players, and he is on seven of the eleven tracks of its album More Than One Thing (Wah Wah 45s, 2018) on tenor, clarinet, flute and percussion, having also co-written the A-side of the band's 7-inch single. That collective is where his path crosses Amir Bresler's: both are listed members, though the two of them do not share a track on the album, and the record they demonstrably play on together came seven years later. Since 2019 his jazz-side sideman work has run through Nitai Hershkovits, Rejoicer, Sefi Zisling's two Tru Thoughts albums and the Amir Bresler project Liquid Saloon. Two further duo records widened the leader catalogue: Two Days with the trio Tatran, eleven pieces improvised in the studio and released almost untouched in March 2020, and The Audience with Rejoicer in November 2022, ten tracks of pared-back free jazz for saxophone, clarinet, flute, piano and synthesizer.

The most recent work has turned inward. Sonolodge, released by Raw Tapes on February 14, 2025, is a set of recorded meditations built out of live improvisation and modelled on the sweat lodge; two sequels followed within the year, Sonolodge II in August with Hershkovits and the cellist Ester Valladares, and Sonolodge III in December with Bresler on drums, the ney and setar player Itzhak Ventura and Nomok. The Jerusalem International Jazz Festival, produced by the Israel Festival at the Israel Museum and directed since 2026 by Hershkovits, programmed the material as a solo performance in four chapters of overtone singing, clarinet, saxophone and bagpipes, staged inside a three-wall video installation in the museum's galleries. A further album, Train To Chill, appeared on Rosh Tiferet in July 2026. Alongside all of it he has kept a thirty-year sideline as one of the most heavily used reed players in Israeli rock and pop, and a parallel career as a producer: he assembled and mixed the 2010 Meir Ariel tribute Rishumei Pecham BeTzeva with Ben Handler, and produced, arranged and played on the poet Haim Gouri's 2015 album Asui Me'Otiot.

Talmudi is a loud, physical, deliberately unpolished player who says he loses interest in music the moment it starts being cut and arranged and calculated too finely, and his range runs from a hard bebop-shaped head to twenty minutes of unmetered noise without his tone changing much in between. The saxophone lineage he claims is the free-jazz one: the influences he names from his teens are David Murray and Hamiet Bluiett, and All About Jazz heard the World Saxophone Quartet in the thick multitracked reed choirs of the first Mãlox record, which also carries a cover of Bluiett's "Nali Kola." Set against that is an equally deep grounding in folk repertoire, Ashkenazi first through Oy Division and then North African, which he learned by ear in Jerusalem after the bassist Hagai Bilitzky introduced him to the Andalusian orchestra leader Nino Biton. He describes his own project as bringing that rootsiness into punk, and the critical reception has followed him there: All About Jazz located Mãlox between klezmer, dub and free jazz, the Israeli press has called the duo a crazy and impossible act moving from klezmer to jazz, and Tatran's own sleeve note for their improvised meeting with him simply calls him a punk-jazz virtuoso. The Sonolodge records are the same musician at the other end of his dynamic range, using overtone singing, long saxophone tones and bagpipe drones for something closer to spiritual jazz than to anything he had recorded before.