Quarter-Tone Music: A Tuning System Rooted in Natural Harmonic Series

The objective of this work is to study quarter-tone music through the lens of harmonic series. The 11th harmonic (11/8), which corresponds to the major fourth interval, offers a remarkably precise approximation of the quarter tone. By employing the “circle of major fourths,” we may encompass the complete spectrum of 24 notes and establish a tuning system of quarter-tones that is based on overtones. We analyze its distinct attributes and perform a detailed examination of its impact, specifically on maqam music. To solve issues specifically related to modulation, a non-octave tuning is proposed by dividing the major fourth interval into 11 quarter-tones.