The brain's diverse intrinsic timescales enable us to perceive stimuli with varying temporal persistency. This study aimed to uncover the cortical organizational schemes underlying these variations, revealing the neural architecture for processing a wide range of sensory experiences. We collected resting-state fMRI, task-fMRI, and diffusion-weighted imaging data from 47 individuals. Based on this data, we extracted six organizational schemes: (1) the structural Rich Club (RC) architecture, shown to synchronize the connectome; (2) the structural Diverse Club architecture, as an alternative to the RC based on the network's module structure; (3) the functional uni-to-multimodal gradient, reflected in a wide range of structural and functional features; and (4) the spatial posterior/lateral-to-anterior/medial gradient, established for hierarchical levels of cognitive control. Also, we explored the effects of (5) structural graph theoretical measures of centrality and (6) cytoarchitectural differences. Using Bayesian model comparison, we contrasted the impact of these organizational schemes on (1) intrinsic resting-state timescales and (2) inter-subject correlation (ISC) from a task involving hierarchically nested digit sequences. As expected, resting-state timescales were slower in structural network hubs, hierarchically higher areas defined by the functional and spatial gradients, and thicker cortical regions. ISC analysis demonstrated hints for the engagement of higher cortical areas with more temporally persistent stimuli. Finally, the model comparison identified the uni-to-multimodal gradient as the best organizational scheme for explaining the chronotopy in both task and rest. Future research should explore the microarchitectural features that shape this gradient, elucidating how our brain adapts and evolves across different modes of processing.