The HOMA geometrical aromaticity index is unique. It is simple, based on observable bond distances, and can be defined using experimental or computational bond values. Moreover, its mathematical form expresses geometric similarity to the archetypal aromatic benzene. Here, we show that HOMA is simply a kind of mean of the errors squared (MSE). This is why the index is such a good measure of aromaticity. Thus, only a slight modification grounds the HOMA index on electronic or magnetic properties, producing an electronic or magnetic molecular measure expressing electronic or magnetic similarity/dissimilarity to benzene. Based on an analysis of over 70 neutral or charged carbocyclic rings, we compare the HOMA indices based on bond distances, selected electron density properties in bond or ring critical points, chemical shifts, and spin-spin coupling constants. We conclude that using electronic and magnetic variables discloses separate trends that are invisible if CC bond lengths are used. Such new HOMA indices can be used to study different facets of aromaticity and as more general molecular structure descriptors.