  High-order, beyond-pairwise interdependencies are at the core of biological,
economic, and social complex systems, and their adequate analysis is paramount
to understand, engineer, and control such systems. This paper presents a
framework to measure high-order interdependence that disentangles their effect
on each individual pattern exhibited by a multivariate system. The approach is
centred on the 'local O-information', a new measure that assesses the balance
between synergistic and redundant interdependencies at each pattern. To
illustrate the potential of this framework, we present a detailed analysis of
music scores from J.S. Bach, which reveals how high-order interdependence is
deeply connected with highly non-trivial aspects of the musical discourse. Our
results place the local O-information as a promising tool of wide
applicability, which opens new perspectives for analysing high-order
relationships in the patterns exhibited by complex systems.
