  Disorder in crystals is rarely random, and instead involves local
correlations whose presence and nature are hidden from conventional
crystallographic probes. This hidden order can sometimes be controlled, but its
importance for physical properties of materials is not well understood. Using
simple models for electronic and interatomic interactions, we show how crystals
with identical average structures but different types of hidden order can have
very different electronic and phononic band structures. Increasing the strength
of local correlations within hidden-order states can open band gaps and tune
mode (de)localisation -- both mechanisms allowing for fundamental changes in
physical properties without long-range symmetry breaking. Taken together, our
results demonstrate how control over hidden order offers a new mechanism for
tuning material properties, orthogonal to the conventional principles of
(ordered) structure/property relationships.
