Contemporary Western music composition operates almost exclusively within the framework of twelve-tone equal temperament (12-TET), a system designed in the 18th century as a practical compromise for fixed-pitch instruments. While this system enables transposition across keys, it constrains composers to a discrete lattice of 12 pitches per octave, resulting in a harmonic vocabulary that — despite centuries of use — remains fundamentally limited and increasingly exhausted. This paper presents Phase Ratio Synthesis (PRS), a frequency-native compositional framework that abandons named notes and fixed scales in favor of natural frequency ratios derived directly from wave phase synchronization. In PRS, an interval is defined as a ratio p:q between two frequencies, meaning that every p cycles of the fundamental, a second voice completes exactly q cycles. Consonance and dissonance emerge naturally from this relationship — intervals with small integer ratios produce high phase coherence and are perceived as consonant, while complex ratios generate beating patterns that the ear perceives as tension. I demonstrate that this approach unlocks a continuous harmonic space inaccessible to equal temperament, in which chords can be constructed from arbitrary generative sequences — such as Fibonacci numbers or prime series — and modulation between tonal centers can occur as a smooth frequency drift rather than a discrete key change. A browser-based implementation using the Web Audio API is presented, along with a dissonance model based on the Plomp-Levelt critical bandwidth framework. Initial exploration suggests that the system produces numerous consonant or quasi-consonant harmonic configurations that have no equivalent in 12-TET.
Leonardo Maria Miliacca (Fri,) studied this question.