  For an abelian length category $\mathcal{A}$ with only finitely many
isoclasses of simple objects, we have the wall-chamber structure and the TF
equivalence in the dual real Grothendeick group
$K_0(\mathcal{A})_\mathbb{R}^*=\operatorname{Hom}_\mathbb{R}(K_0(\mathcal{A})_\mathbb{R},\mathbb{R})$,
which are defined by semistable subcategories and semistable torsion pairs in
$\mathcal{A}$ associated to elements $\theta \in
K_0(\mathcal{A})_\mathbb{R}^*$. In this paper, we introduce the $M$-TF
equivalence for each object $M \in \mathcal{A}$ as a systematic way to coarsen
the TF equivalence. We show that the set $\Sigma(M)$ of the closures of $M$-TF
equivalence classes is a finite complete fan in
$K_0(\mathcal{A})_\mathbb{R}^*$, and that $\Sigma(M)$ is the normal fan of the
Newton polytope $\mathrm{N}(M)$ in $K_0(\mathcal{A})_\mathbb{R}$.
