Amir ElSaffar is an Iraqi-American trumpeter from Chicago, trained in classical music and jazz. In the first years of the new century, after having won some prestigious trumpet competitions and worked with improvisers dedicated to the new, including Cecil Taylor, Vijay Iyer, and Rudresh Mahanthappa, he started to explore a centuries-old tradition of Arabic music.

Sixteen years later, he is still exploring the Iraqi branch of the maqam, an complex and endangered musical system. The maqam, which means “situation” or “place,” is both a repertoire of musical material and a set of rules. It is a family of modes (seven-note scales, in which sometimes the notes are quarter-tones, falling between two adjacent notes on a piano); specific modes correspond to specific emotions. It is also denotes an ordering of sections within larger structures of vocal and instrumental music, and a set of rules for improvising within those structures and modes.

ElSaffar arrived in Baghdad in March, 2002, in his mid-twenties, having visited there only once previously and knowing little of the language. Over time, and with the help of various mentors and teachers—including the London-based singer Hamid Al-Saadi, believed to be the only musician who knows the entire maqam repertoire—he learned to speak Arabic, as well as to sing and play the santur (the Persian hammered-dulcimer), and to alter and expand his trumpet-playing language.

His last decade-plus of recorded work, including the sextet albums “Two Rivers,” “Inana,” and “Crisis,” as well as the quintet album “Alchemy,” and the most recent “Not Two,” by his 17-piece Rivers of Sound Orchestra, have found various elegant ways to make the modal maqam music merge with the jazz tradition. In the large ensemble especially, this merging happens at every level: between Arabic and western tuning systems, between collective-improvisation strategies and the cathartic upswellings that result from them, and between the timbres of individual instruments.

ElSaffar’s hybrid musical conception has passed far beyond experiment. “Nothing is more natural to me,” he has said. “the maqam is as natural as bebop, or certain types of free jazz, or playing in symphony orchestras. So if I’m going to going to have a piece that happens to have elements of these different traditions, it’s just autobiographical, it’s just what’s coming out of my experience.”

Ben Ratliff teaches cultural criticism at NYU’s Gallatin School of Individualized Study. He is the author of “Every Song Ever: Twenty Ways to Listen in an Age of Musical Plenty” and “The Jazz Ear: Conversations over Music.”