For the past 40 years, he has been committed to the applications of advanced counterpoint in jazz and jazz derived styles. Dr. Stewart proclaims the art of counterpoint is the combinations of melodies into a higher unit, which creates the harmony.  "Europeans were masters of  the contrapuntal technique, and it was foundational in the beginnings of their musical developments. The music was principally polyphonic; in fact, the rhythmic composites of African-derived music enjoyed throughout the world is fundamentally polyphonic. By combining rhythm and melody in certain ways in the vernacular, one finds that baroque music is compatible."  Understanding this principle has resulted in Dr. Stewart's creation of inumerous jazz fugues, inventions, and other contrapuntal creations in the style of African and African-derived music.

Dr. Stewart’s works have been performed at venues in Louisiana, Texas, Massachusetts, New York, Alabama, North Carolina, California and Africa.  The Second Annual Louisiana Composers’ Symposium (1975), presented by The New Orleans Public Schools Jazz Artist In Residence Program, showcased Stewart’s "An Appropriate Title," (Identity 6),  performed by  jazz great Julian 'Cannonball' Adderley and the Southern University Percussion Ensemble.

In addition to conducting, Dr. Stewart’s compositions have been performed by soloists Brenda Wimberly and Carolyn Sebron; and jazz artists Jullian 'Cannonball' Adderly, Alvin Batiste and Kent Jordan. Ensembles who have performed his music include the Southern University Chorus (Baton Rouge, Louisiana); the Southern University Jazz Orchestra; the Boston Orchestra and Choral (Massachusetts); the Scott Joplin Orchestra of Houston (Texas); the University of California Jazz Orchestra; the Mobile Symphony Orchestra (Alabama); and members of the Louisiana Philharmonic Orchestra. 

The 1984 premier of his oratorio Al-Inkishafi (Identity 14) (The Soul’s Awakening), a choral symphonic setting of an East African (Kiswahili) poem, was performed in Austin, Texas.   It featured the Austin Symphony Orchestra under the direction of Maestro Sung Kwak; distinguished Mezzo-Soprano Barbara Conrad with the Metropolitan Opera; internationally known choreographer and master of African dance Chuck Davis; the Southern University Chorus of Baton Rouge, Louisiana; English narrator the nationally renowned actor Moses Gunn; and Kiswahili narrator John “Mtembezi” Inniss, along with local dancers.

He served as conductor and artistic director of the Boston Orchestra and Chorale from 1987-1991 and as guest conductor with the Scott Joplin Orchestra of Houston, Texas.   In addition, he had conductorial performances with the UCSB Jazz Orchestra.