  We study the relationship between the electronic spectrum structure and the
configurational order of one-dimensional quasiperiodic systems. We take the
Fibonacci case as an specific example, but the ideas outlined here may be
useful to accurately describe the energy spectra of general quasiperiodic
systems of technological interest. Our main result concerns the {\em
minimization} of the information entropy as a characteristic feature associated
to quasiperiodic arrangements. This feature is shown to be related to the
ability of quasiperiodic systems to encode more information, in the Shannon
sense, than periodic ones. In the conclusion we comment on interesting
implications of these results on further developments on the issue of
quasiperiodic order.
