  We generalize the Kuramoto model of globally coupled oscillators to
multifrequency communities. A situation when mean frequencies of two
subpopulations are close to resonance 2:1 is considered in detail. We derive
uniformly rotating solutions describing synchronization inside communities and
between them. Remarkably, cross-coupling between the frequency scales can
promote synchrony even when ensembles are separately asynchronous. We also show
that the transition to synchrony due to the cross-coupling is accompanied by a
huge multiplicity of distinct synchronous solutions what is directly related to
a multi-branch entrainment. On the other hand, for synchronous populations, the
cross-frequency coupling can destroy a phase-locking and lead to chaos of mean
fields.
