Recent research regarding the star formation in star clusters on galaxy wide scales indicates that, in the hypothesis that all stars are born within clusters, the supposedly universal initial stellar mass function (IMF) within young star clusters, does not necessarily yield the same IMF for whole galaxies. As star clusters also follow an embedded cluster mass function (ECMF), the whole integrated galaxy initial stellar mass function (IGIMF) has to be steeper than the individual IMFs of star clusters -- depending on the steepness of the ECMF (Kroupa & Weidner 2003, ApJ, 598, 1076; Weidner & Kroupa 2005, ApJ, 625, 754). This result has found to be able to explain the mass-metallicity relation of galaxies (Köppen et al. 2007, MNRAS, 375, 673). Investigating the effects of the IGIMF further, this project concentrates on the expected temporal evolution of the supernova rate in comparison with a rate for a single-slope Salpeter-like IMF, for a wide range of galaxies with different masses and star-formation histories. Type II and type Ia supernovae are included at a later stage, as well as the influence of massive starbursts.