An almost strong relation

Let \mu be a strong limit singular cardinal. We prove that if 2^{\mu} > \mu^+ then \binom{\mu^+}{\mu}\to \binom{\tau}{\mu}_{<{\rm cf}(\mu)} for every ordinal \tau<\mu^+. We obtain an optimal positive relation under 2^\mu = \mu^+, as after collapsing 2^\mu to \mu^+ this positive relation is preserved.