  Chiral multiferroic langasites have attracted attention due to their
doubly-chiral magnetic ground state within an enantiomorphic crystal. We report
on a detailed resonant soft X-ray diffraction study of the multiferroic
Ba$_3$TaFe$_3$Si$_2$O$_{14}$ at the Fe $L_{2,3}$ and oxygen $K$ edges. Below
$T_N$ ($\approx27K$) we observe the satellite reflections $(0,0,\tau)$,
$(0,0,2\tau)$, $(0,0,3\tau)$ and $(0,0,1-3\tau)$ where $\tau \approx 0.140 \pm
0.001$. The dependence of the scattering intensity on X-ray polarization and
azimuthal angle indicate that the odd harmonics are dominated by the
out-of-plane ($\mathbf{\hat{c}}$-axis) magnetic dipole while the $(0,0,2\tau)$
originates from the electron density distortions accompanying magnetic order.
We observe dissimilar energy dependences of the diffraction intensity of the
purely magnetic odd-harmonic satellites at the Fe $L_3$ edge. Utilizing
first-principles calculations, we show that this is a consequence of the loss
of threefold crystal symmetry in the multiferroic phase.
