Consider the scales $r_{\alpha}=2^{-\alpha}$. For each $x\in M$ we associate the infinite tuple $T(x)\in\mathds{Z}_{2}^{\mathds{N}}$ defined by

$\displaystyle T_{\alpha}(x)\equiv\begin{cases}1\text{ if }|\mathcal{V}^{\delta}_{4r_{\alpha}}(x)-\mathcal{V}^{\delta}_{r_{\alpha}/4}(x)|\geq\delta\,\\ 0\text{ if }|\mathcal{V}^{\delta}_{4r_{\alpha}}(x)-\mathcal{V}^{\delta}_{r_{\alpha}/4}(x)|<\delta\,.\end{cases}$

We denote by $|T|(x)=\sum T_{\alpha}(x)$ the number of bad scales at $x\in M^{4}$.