We consider first order logic over words and show FO+MOD[<] is contained in MAJ[<] with three variables.
It is known that for the classes FO[<], FO+MOD[<], FO+GROUP[<] three variables suffice. In the case of MOD[<] even two variables are sufficient.

As a consequence we know that if TC^ 0 neq NC^1 then for every regular language describable in MAJ[<] three variables are sufficient.