  We show that the set of balanced binary trees is closed by interval in the
Tamari lattice. We establish that the intervals [T, T'] where T and T' are
balanced binary trees are isomorphic as posets to a hypercube. We introduce
synchronous grammars that allow to generate tree-like structures and obtain
fixed-point functional equations to enumerate these. We also introduce
imbalance tree patterns and show that they can be used to describe some sets of
balanced binary trees that play a particular role in the Tamari lattice.
Finally, we investigate other families of binary trees that are also closed by
interval in the Tamari lattice.
