Rhythms stretching across multiple interacting frequencies and spatial scales are ubiquitous in brain activity during complex cognitive tasks. Yet their functional significance is hotly debated between a structural epiphenomenon of brain activity and mechanisms implementing computations. Speech processing, with its temporal cadence and multi-scale of syntactic invariants (syllables, words), is a paradigmatic example where rhythms have been proposed to play a key role [1], with a speech-modulated hierarchical structure of intercoupled cortical oscillations correlating with successful comprehens