Set-theoretic Solution for the Tuning Problem (eBook)

Why do some notes sound harmonious while others clash? Many theories attempt to explain consonance and dissonance, but each has its limitations. In this book, I explore the boundaries of today’s most compelling theories and introduce a new approach rooted in set theory. This mathematical framework gives rise to naturally dynamic tuning systems — suitable for both harmonic and inharmonic timbres, from pure sine waves to complex sounds. Most importantly, it provides a method for quantifying the consonance of intervals and chords, opening the door to a wide range of practical applications for musicians, composers, and software developers alike.