After participating in the Six-Day War, Yannay returned to the US in 1968 at the invitation of the musicologist Dr. Alexander Ringer to complete a doctorate at the University of Illinois Urbana–Champaign.
As Yannay started composing in the early 1960s, he was immediately drawn to avant-garde innovations in music: serialism, open-ended form, graphic notation, and new sound materials generated through electroacoustic devices.
According to him: "the minimal definition of an object named musical is an arrangement of sound and silence, which may or may not have imply functional order and it exists in a conceptual space and time."
By the late 1950s, there evolved a sense of a new freedom to stay away from monolithic "composition schools" that instigated factionalism among established and younger composers.
The dissertation's last chapter contains analyses/descriptions of excerpts from Yannay's Mirkamim, Textures of Sound for Large Orchestra (1967), Mutatis Mutandis for six players (1968), and preFIX-FIX-sufFIX for bassoon, horn and cello (1971).
The School of Music at University of Illinois Urbana–Champaign was an internationally recognized hotbed of new-music activity from the 1950s to the 1970s, led by composers such as Kenneth Gaburo, Salvatore Martirano, Ben Johnston, Lejaren Hiller and Herbert Brün.
His principle cohorts at that time were Kenton Meyer, flutist, Monte Perkins, bassoonist, and Raymond Weisling, a composer, tuba player, and experimenter in electronics.
An encounter with the Theater of the Absurd in the late 1950s inspired his theatrical-performance works that led eventually to collaborative filmmaking and acting in such films as Jidyll (1990) and Houdini's Ninth (1973).
Quoting from the notes of the CRI album (SD 437) that contains the first recording of his song cycle At The End Of The Parade (1974) for baritone and six players Yannay writes: "In 1970 my music took a gentle turn.
This fresh zeitgeist, as perceived by Yannay, signaled a need to move beyond "International Style" in composition and transition to an individualized approach in creating every single new work.
The carryover into this maturing phase of his oeuvre is the continuing exploration and realization of new challenges in terms of subject matter and media, extended and invented vocal and instrumental techniques, and required virtuosity and perseverance from performers.
The trombone solo piece, along with the choral Le campane di Leopardi (1979) use a fixed drone of tuned glasses and electronics, diatonic and just-intonation proportions to a central note that extends the entire work.
A number of his orchestral scale compositions were performed and commissioned by Edwin London after he established the Cleveland Chamber Symphony (1980), which became a unique forum for larger-scale pieces for living composers.
These pieces represent on grander scale the maturation of a Yannay compositional style that can be traced back to "Trio" for clarinet, cello and piano (1982).
This piece occupied an evening of performance and exhibition space for invented metal instruments (in collaboration with Steven Pevnick) played in multi-tempi polyphonies and visuals.
His millennial period started with a close collaboration with the bayan/accordion virtuoso Stas Venglevski that produced a multitude of chamber and ensemble works expanding the repertory for the instruments.