Brain oscillatory activity has long been thought to have spatial properties, the details of which are unresolved. Here we examine spatial organizational rules for the human brain oscillatory activity as measured by blood oxygen level-dependent (BOLD) signal. Resting-state BOLD signal was transformed into frequency space (Welch's method) and averaged across subjects, and its spatial distribution was studied as a function of four frequency bands, spanning the full BOLD bandwidth. The brain showed anatomically constrained distribution of power for each frequency band. This result was replicated on a repository dataset of 195 subjects. Next, we examined larger-scale organization by parceling the neocortex into regions approximating Brodmann areas (BAs). This indicated that BAs of simple function/connectivity (unimodal), versus complex properties (transmodal), are dominated by low-frequency BOLD oscillations, and within the visual ventral stream we observe a graded shift of power to higher-frequency bands for BAs further removed from the primary visual cortex (increased complexity), linking BOLD frequency properties to hodology. Additionally, BOLD oscillation properties for the default mode network demonstrated that it is composed of distinct frequency-dependent regions. When the same analysis was performed on a visual-motor task, frequency-dependent global and voxelwise shifts in BOLD oscillations could be detected at brain sites mostly outside those identified with general linear modeling. Thus, analysis of BOLD oscillations in full bandwidth uncovers novel brain organizational rules, linking anatomical structures and functional networks to characteristic BOLD oscillations. The approach also identifies changes in brain intrinsic properties in relation to responses to external inputs.