In Pizzi (J. Log. Lang. Inf. 31:451–463, 2022) the author introduces a system for the notion of dyadic contingency \(K\triangle ^2 \) based on the definition \(\triangle (B, A) =_{df} \Diamond B \land (B \mathcal A \lor B \mathcal \lnot A)\) . In the present paper attention is called on an alternative system \(K\blacktriangle ^2 \) based on the definition \(\blacktriangle (B, A) =_{df} \Box B \land (B \mathcal A \lor B \mathcal \lnot A)\) . \(K\blacktriangle ^2 \) is proved here to be translationally equivalent to K, while \(K\triangle ^2 \) is equivalent to KD. In §3 it is proved that the definition of \(\blacktriangle (B, A)\) leads to the equivalence between \(\blacktriangle (B, A)\) and \(\Box B \land \blacktriangle A\) (where \(\Box B\) is \(\blacktriangle (B, B)\) and \(\blacktriangle A\) is \(\blacktriangle (\mathrm{T}, A))\) . In this way a dyadic formula reduces to a truthfunctional combination of monadic formulas, so it is monadically representable in the sense of Humbertsone (Bull. Austr. Math. Soc. 29:365–376, 1984). In §3 it is proved that the notion of \(\triangle (B, A)\) as above defined is not monadically representable. After seeing that alternative definitions of dyadic contingency in terms of non-necessity and impossibility lead to inconsistencies, the conclusion is that the only plausible definition of dyadic contingency is in terms of possibility. In the last section the author proposes a study of the interrelation between \(\triangle (A, B)\) and \(\blacktriangle (A, B)\) by making use of squares of opposition.