The synchronization between neural oscillations at different frequencies has been proposed as a core mechanism for the coordination and integration of neural systems at different spatiotemporal scales. Because neural oscillations of different frequencies can only fully synchronize when their "peak" frequencies form harmonic relationships (e.g., f 2 ϭ f 1 /2), the present study explored whether the transient occurrence of harmonic cross-frequency relationship between task-relevant rhythms underlies efficient cognitive processing. Continuous EEG recordings (51 human participants; 14 males) were obtained during an arithmetic task, rest and breath focus. In two separate experiments, we consistently show that the proportion of epochs displaying a 2:1 harmonic relationship between alpha (8 -14 Hz) and theta (4 -8 Hz) peak frequencies (i.e., alpha peak Ϸ 10.6 Hz; theta peak Ϸ 5.3 Hz), was significantly higher when cognitive demands increased. In addition, a higher incidence of 2:1 harmonic cross-frequency relationships was significantly associated with increased alpha-theta phase synchrony and improved arithmetic task performance, thereby underlining the functional relevance of this crossfrequency configuration. Notably, opposite dynamics were identified for a specific range of "nonharmonic" alpha-theta cross-frequency relationships (i.e., alpha peak /theta peak ϭ 1.1-1.6), which showed a higher incidence during rest compared with the arithmetic task. The observation that alpha and theta rhythms shifted into harmonic versus nonharmonic cross-frequency relationships depending on (cognitive) task demands is in line with the notion that the neural frequency architecture entails optimal frequency arrangements to facilitate cross-frequency "coupling" and "decoupling". Significance StatementNeural activity is known to oscillate within discrete frequency bands and the interplay between these brain rhythms is hypothesized to underlie cognitive functions. A recent theory posits that shifts in the peak frequencies of oscillatory rhythms form the principal mechanism by which cross-frequency coupling and decoupling is implemented in the brain. In line with this notion, we show that the occurrence of a cross-frequency arrangement that mathematically enables coupling between alpha and theta rhythms is more prominent during active cognitive processing (compared with rest and non-cognitively demanding tasks) and is associated with improved cognitive performance. Together, our results open new vistas for future research on cross-frequency dynamics in the brain and their functional role in cognitive processing.

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In the last years, secularized versions of Buddhist contemplative practices have become increasingly common in our society due to their putative health benefits. An important part of these practices consist of directing the attentional focus to a specific object (e.g. the sensation of breathing) while 'noticing' and 'letting pass' self-generated thoughts (i.e. mind-wandering episodes) (

Neural activity is known to oscillate within discrete frequency bands and the synchronization between these rhythms is hypothesized to underlie information integration in the brain. Since strict synchronization is only possible for harmonic frequencies, a recent theory proposes that the interaction between different brain rhythms is facilitated by transient harmonic frequency arrangements. In this line, it has been recently shown that the transient occurrence of 2:1 harmonic cross-frequency relationships between alpha and theta rhythms (i.e. f alpha ≈ 12 Hz; f theta ≈ 6 Hz) is enhanced during effortful cognition. In this study, we tested whether achieving a state of 'mental emptiness' during meditation is accompanied by a relative decrease in the occurrence of 2:1 harmonic cross-frequency relationships between alpha and theta rhythms. Continuous EEG recordings (19 electrodes) were obtained from 43 highly experienced meditators during meditation practice, rest and an arithmetic task. We show that the occurrence of transient alpha:theta 2:1 harmonic relationships increased linearly from a meditative to an active cognitive processing state (i.e. meditation < rest < arithmetic task). It is argued that transient EEG cross-frequency arrangements that prevent alpha:theta cross-frequency coupling could facilitate the experience of 'mental emptiness' by avoiding the interaction between the memory and executive components of cognition.

Ethics approval. The study was approved by the Singhealth Centralized Institutional Review Board and was conducted in accordance with the ethical standards of the 1964 Helsinki declaration and its later amendments.Consent. All participants provided written informed consent.