Bass strings of piano consists of a core string and a wire wound around the core. Although this construction is essential for creating strings with low frequency in the presence of moderate tension force, the increased bending stiffness shifts the overtones of the strings. This inharmonicity is more significant for upright pianos with shorter string lengths. In the literature, we can find conceptual ideas for compensation of this effect that is considered acoustically unpleasant. In the present research, we analyse the effect of adding concentrated masses to reduce the amount of inharmonicity. We focus on improvements in the acoustically most significant overtones. The proper parameters are found by using both a finite-element method and experiments.