The golden ratio in the acoustic tuning of the sitar: nonlinear self-consistency of frequencies as a physical law

This study investigates the acoustic structure of the Indian sitar from a physical and mathematical perspective. It proposes that the frequencies of the sympathetic strings form a logarithmic geometric scale optimized by the golden ratio, which minimizes low-order resonances and enhances spectral stability. The work combines variational analysis, nonlinear oscillator modeling, and empirical spectral data from real instruments. The paper is provided in Russian, with figures and formulas fully annotated in English.