Let $u:B_{2}(p)\to\mathds{R}^{k}$ be a harmonic function and put $\omega^{\ell}=du^{1}\wedge\cdots\wedge du^{\ell}$. For $x\in B_{1}(p)$ and $\delta>0$, define the singular scale $s^{\delta}_{x}\geq 0$ to be the infimum of all radii $s$ such that for all $r$ with $s\leq r<\frac{1}{2}$ and all $1\leq\ell\leq k$ we have