  Four crystal classes are optically active yet not chiral
(non-enantiomorphic). Corresponding Bragg diffraction patterns calculated for
circularly polarized (helical) x-rays tuned to an atomic resonance prove that
angular anisotropy in the distribution of electrons create spots not indexed on
the chemical structure (defined by a space group derived from Thomson
scattering by perfect spheres of charge). Templeton-Templeton scattering, as it
is usually called, of helical x-rays is quantified in terms of a chiral
signature defined as the partial diffracted intensity hallmarked by x-ray
helicity. Our electric dipole - electric dipole (E1-E1) chiral signature for a
space group in the optically active crystal class D2d affords a complete
interpretation in terms of copper quadrupoles of diffraction data collected on
copper metaborate [E. N. Ovchinnikova et al., J. Synchrotron Rad. 28, 1455
(2021)]. An example of a chiral signature derived from a parity-odd resonance
event (E1-E2) is included in our study. It is firmly established that tuning
the energy of x-rays to an atomic resonance enhances the intensity of
inherently weak Templeton-Templeton scattering and renders space-group
forbidden Bragg spots element specific. Our chiral signature as a function of
rotation about the reflection vector (azimuthal-angle scan) is specific to
position multiplicity, Wyckoff letter and symmetry in a favourable space group.
