Given a
∂
∂
¯
\partial \bar \partial
-manifold
X
X
with trivial canonical bundle and carrying a metric
ω
\omega
such that
∂
∂
¯
ω
=
0
\partial \bar \partial \omega =0
, we introduce the concept of small deformations of
X
X
polarised by the Aeppli cohomology class
[
ω
]
A
[\omega ]_A
of a strong Kähler with torsion metric
ω
\omega
. There is a correspondence between the manifolds polarised by
[
ω
]
A
[\omega ]_A
in the Kuranishi family of
X
X
and the Bott-Chern classes that are primitive in a sense that we define. We also investigate the existence of a primitive element in an arbitrary Bott-Chern primitive class and compare the metrics on the base space of the subfamily of manifolds polarised by
[
ω
]
A
[\omega ]_A
within the Kuranishi family.