The model of potential gains from mergers provides a useful decomposition into technical efficiency, returns to scale, and the harmony effect. While technical efficiency and returns to scale have been well elaborated, interpretation of the harmony effect remains open. We provide analytic insight into the aforementioned decomposition. We express the harmony effect as a function of the relative difference between the structures of the firms involved and the relative difference in their sizes. These factors can play an important role and, in some cases, can even outweigh a potentially negative merger outcome due to decreasing returns to scale. Furthermore, we show that the sign of the harmony effect is dependent not on the specific form of the production function but rather on its shape. In the case of a concave production function, the harmony effect contributes in a positive sense to the gains from mergers. Incorporating information on given input prices, the harmony effect is described as the product of technical, price, and allocative efficiency. The potential effects of the technical-physical based harmony effect are illustrated for the Slovak hospital sector. This application provides a detailed look at the reallocation process.