I heard that "Itsbynne Reel" features stylistic elements of rock and jazz (especially bebop), but I don't recall that this song had bebop elements, can anyone clarify?
Yes, according to this article, bebop
http://www.scaruffi.com/history/jazz17e.html
"Philadelphia-born white tenor saxophonist Michael Brecker and his brother, trumpeter Randy Brecker, an original founder of the rock group Blood, Sweat and Tears, formed the jazz-rock outfit, Dreams, that included John Abercrombie on guitar and Billy Cobham on drums, and released Dreams (december 1970) and Imagine My Surprise (1971). Michael Brecker also joined Billy Cobham's group (1974), where they basically reunited with the members of Dreams. However, Michael and Randy Brecker also created a fusion band out of a group of veteran session-men such as alto saxophonist David Sanborn and keyboardist Don Grolnick. Most of their sophisticated and intricate material was composed by Randy Brecker. The compositions and the improvisation on Brecker Brothers (1975), with their signature tune Some Skunk Funk and the lengthy A Creature Of Many Faces, made for some of the most adventurous and innovative fusion sound of the era, bridging the world of bebop and hard bop with the world of funk-jazz, although subsequent albums rapidly descended into trivial dance music: Back to Back (1975), that also added guitarist Steve Kahn, Don't Stop the Music (1977), with Funky Sea Funky Dew and Squids, Heavy Metal Bebop (1978), that added Inside Out to their repertory and was perhaps the best display of their electronically-modified horns, Detente (1980), dominated by keyboardist George Duke, and Straphangin' (1980).
In the meantime, Michael Brecker played on many albums by other artists, including Joni Mitchell and Paul Simon. In particular, he participated in the recording of veteran pop-jazz arranger Claus Ogerman's ballet Some Times (originally composed in 1972) for Gate of Dreams (october 1976). They collaborated again on Cityscape (january 1982), that contained Ogerman's three-movement suite In The Presence And Absence Of Each Other arranged for jazz band and strings.
Michael Brecker then joined Mike Mainieri's Steps Ahead (1981-86), with whom he refined his electronic sound.
He finally debuted as a leader with Michael Brecker (1986), that featured guitarist Pat Metheny, keyboardist Kenny Kirkland, bassist Charlie Haden, and drummer Jack DeJohnette, emphasized Brecker's unique style at the "electronic wind instrument" and introduced Becker's compositional skills, very much in the bebop vein (Syzygy). The music rapidly progressed towards a facile mainstream sound engineered by the producer, and group interplay more and more reminiscent of John Coltrane, on Don't Try This at Home (1988), with Don't Try This at Home and Itsbynne Reel (both co-written by pianists Don Grolnick), Now You See It Now You Don't (1990), that added a synthesizer, Tales from the Hudson (january 1996), with African Skies, Two Blocks from the Edge (december 1997), with Two Blocks from the Edge and with pianist Joey Calderazzo frequently stealing the show, Time Is of the Essence (1999), virtually a Coltrane tribute thanks to Brecker's extended compositions Arc of the Pendulum and Outrance.
Wide Angles (january 2003), credited to the Quindectet, a 15-piece ensemble with trumpet, trombone (Robin Eubanks), oboe, French horn, violin (Mark Feldman), cello (Eric Friedlander), bass (John Patitucci), guitar and accordion, but no keyboards, was the first significant change in his career. Showing that he matured immensely as a composer, Brecker crafted the luxuriant Scylla and Timbuktu, while displaying his introspective bebop side. TM, ®, Copyright © 2006 Piero Scaruffi All rights reserved."
Thanks for the information.