Brain dynamics span multiple spatial and temporal scales, from fast spiking neurons to slow fluctuations over distributed areas. No single experimental method links data across scales. Here, we bridge this gap using The Virtual Brain connectome-based modelling platform to integrate multimodal data with biophysical models and support neurophysiological inference. Simulated cell populations were linked with subject-specific white-matter connectivity estimates and driven by electroencephalography-derived electric source activity. The models were fit to subject-specific resting-state functional magnetic resonance imaging data, and overfitting was excluded using 5-fold cross-validation. Further evaluation of the models show how balancing excitation with feedback inhibition generates an inverse relationship between α-rhythms and population firing on a faster time scale and resting-state network oscillations on a slower time scale. Lastly, large-scale interactions in the model lead to the emergence of scale-free power-law spectra. Our novel findings underscore the integrative role for computational modelling to complement empirical studies.