Estimation of harp string inharmonicity influenced by phantom partials

The pronounced presence of phantom partials in the spectra of harp tones constitutes a considerable challenge to the accurate estimation of the inharmonicity coefficient. Given the importance of the inharmonicity coefficient in tone synthesis and analysis of stringed musical instruments, a precise and automated estimation method is essential across the entire instrument register. To address this, a modification of the partial frequency deviation (PFD) algorithm was proposed, aimed at identifying and excluding phantom partials during inharmonicity estimation. The modified PFD algorithm was evaluated using a set of synthesized signals with systematically varied parameters, as well as a collection of recorded concert harp tones. Experimental results demonstrated that for 64% of real tones, the modified PFD algorithm yielded more accurate inharmonicity coefficient estimates compared to the original PFD algorithm, with improvements reaching up to 88.5% for certain tones. The accuracy of the inharmonicity coefficient estimation was found to depend primarily on the ratio between the number of phantom partials and the total number of partials used for estimation, as well as the spectral position and grouping of these phantom partials.