The human cortex exhibits a temporal hierarchy during task states as evidenced by intrinsic neural timescale. How the task-based intrinsic neural timescale is shaped by resting state's spatial topography especially the recently established core-periphery hierarchy (with the default-mode network (DMN) at the core and sensory networks at the periphery) remains an open issue. Using MEG data from the Human Connectome Project (HCP), we investigated the intrinsic neural timescales by measuring the autocorrelation window in short (ACW-50) and, introducing a novel variant, long (ACW-0) windows in various networks following core-periphery hierarchy. We demonstrate longer ACW-50 and ACW-0 in networks located at the core, i.e., DMN, frontoparietal network, and cingulum-operculum network, during both rest and task states. While networks at the periphery, i.e., auditory, visual, and somatomotor networks, exhibit shorter ACW-50 and ACW-0. Comparing both ACW scales during rest and task, i.e., rest-task difference revealed task-and network-specific effects. That is complemented by strong correlation of both ACW scales in rest with their counterpart during task states, following again the core-periphery hierarchy. Finally, we demonstrate that the longer window (ACW-0) exhibits better prediction in classifying a region's time window as belonging to either core or periphery. Overall, our findings provide fundamental insight into how the human cortex's temporal hierarchy of intrinsic neural timescales converges with spatial topography, the core-periphery hierarchy.Converging evidence shows an intrinsic temporal architecture in the brain 1,2,[11][12][13][14][15][3][4][5][6][7][8][9][10] . Lower-order sensory and higher-order cognitive regions/networks exhibit different temporal features during task states, that is, "temporal receptive fields" 13 or "temporal receptive windows" 1,2,12,[15][16][17][18][19][20][21][3][4][5][6][7][8][9]11 . Specifically, short segments like single words are processed mainly in lower-order regions like visual or auditory cortex while longer segments integrating different stimuli are processed in higher-order regions like default-mode network (DMN) and frontoparietal network (FPN) 1,2,12,15,16,[19][20][21][22][3][4][5][6][7][8][9]11 .Analogously, hierarchical organisation has also been observed on the spatial side. Converging evidence shows micro-and macro-scale hierarchical organization in the human cortex following what has been described as 'core-periphery' 8,9,[23][24][25][26][27][28] . A core-periphery (CP) architecture 29 can be characterized by a core that shares nodes with strong interconnections among each other; core-core connections ('dynamic core' or 'rich club'; 30-33 can be observed among regions included in the default-mode network (DMN), fronto-parietal network (FPN), and cingulum-operculum network (CON) 8,9,[23][24][25]28 . These networks constituting the core have been distinguished from those at the opposite end of the core-periphery gradient; that is, visual, auditory, and somatomotor n...