A Harmonic-Based Musical Scaling Method With Natural Number Frequencies

Abstract

General acceptance arises from the most convincing method among the available options. Similarly, while the Western chromatic scale is the most widely used system today, it has limitations in representing harmonious intervals, microtonal performances, and the weak resonant effects of fractional frequencies This study introduces the Safir method, a novel approach to redefining musical note frequencies within an octave interval. Unlike traditional scales, Safir employs natural number-based values, ensuring more harmonious intervals and enhanced tuning consistency. A key strength of Safir lies in its ability to overcome the limitations of conventional tuning systems. The Safir method enhances spectral coherence by aligning note frequencies with the harmonic distribution of the Fourier series and strengthening the resonance effect through natural frequencies. This method has significant potential for various applications including music, speech and signal processing, spectral leakage reduction, and healthcare. Four key advantages of the Safir scale system are its its alignment with the harmonic series,, the strong resonant effect of note frequencies derived from natural numbers, the suppression of dissonant intervals in higher frequencies across the octave band, and its linear spacing within the octave, which ensures minimal deviation from compatible intervals even in microtonal divisions. This novel method represents a major advancement in tuning and musical scales. By providing a more precise, harmonious, and resonant frequency system, Safir addresses key shortcomings of traditional musical scales and opens new possibilities in both theoretical and practical domains. © 2025, Genc Bilge Yayincilik. All rights reserved.