He is the inventor of The Harmonics Guitar and a theory of music based on the Harmonic Series and various tuning systems. He has designed and built many of the instruments used in his pieces. He is also a founder of The No Wave Movement that started in downtown New York City during the late 1970s that is now an international movement in the underground music scene. Branca has collaborated with artists including Twyla Tharp, David Bowie, Peter Greenaway, Eiko and Koma, Eric Bogosian, Robert Longo, Laura Dean, and Dan Graham.