To gain a better understanding of the chemistry of cyclic allenes, in the present work six-membered monocyclic systems containing second- (B-O) and third-row elements (Al-S) of the periodic table of elements are studied in detail, regarding the energetic order of the electronic states and the planarization energies, which together determine their chemical behavior. The data obtained by high-level ab initio methods show that the properties of the compounds strongly depend on the heteroatoms and can be related to trends in the periodic table of elements. These trends in the series B to O and Al to S are rationalized by the degree of the interaction between the various fragments and the interplay between this interaction and the strain in the allene moiety. In addition, by applying the model to charged species, we reveal an unexpected link between the cyclic allenes and the phenyl anion. Furthermore, our computations answer open questions about the chemical properties of 1-aza-2,3-cyclohexadienes. Finally, we analyze how the various kinds of interaction influence the chemistry of this important class of intermediates.