  In the present paper we study the variation of the dimensions $h_k$ of spaces
of symplectically harmonic cohomology classes (in the sense of Brylinski) on
closed symplectic manifolds. We give a description of such variation for all
6-dimensional nilmanifolds equipped with symplectic forms. In particular, it
turns out that certain 6-dimensional nilmanifolds possess families of
homogeneous symplectic forms $\omega_t$ for which numbers $h_k(M,\omega_t)$
vary with respect to t. This gives an affirmative answer to a question raised
by Boris Khesin and Dusa McDuff. Our result is in contrast with the case of
4-dimensional nilmanifolds which do not admit such variations by a remark of
Dong Yan.
