This thesis investigates how to apply a new microtonal harmonic system in compositions for acoustic ensembles in the Western art music notated score tradition. Two compositions are included, and contribute to the development of the research. A key question concerns how to communicate a diverse row of microtones from the composer to the musician through notation. What level of precision in intonation of the microtones can be expected in the given situation, and what level is needed to express the particular microtonal content? Which factors influence the production and perception of microtones? The findings indicate that the musical context must always be considered. I argue that knowledge about premises for pitch perception is enabling composers to control the musical context while converting theoretical microtonal concepts into sound through musical notation.