A new algorithm is presented for estimating the inharmonicity coefficient of slightly inharmonic stringed instrument sounds. In the proposed partial frequencies deviation method, the inharmonicity is estimated in an intuitive way by minimizing the deviation of the expected partial frequencies compared to the frequencies of the high amplitude peaks in the spectrum. This is done in an iterative process, where the algorithm converges towards the target estimation value. The algorithm is tested using both synthetic and recorded piano tones. The results show that the new algorithm produces accurate results with a small computation cost compared to other methods.