The dynamic organization of chromatin plays an essential role in the regulation of gene expression and in other fundamental cellular processes. The underlying physical basis of these activities lies in the sequential positioning, chemical composition, and intermolecular interactions of the nucleosomes—the familiar assemblies of ~ 150 DNA base pairs and eight histone proteins—found on chromatin fibers. Here we introduce a mesoscale model of short nucleosomal arrays and a computational framework that make it possible to incorporate detailed structural features of DNA and histones in simulations of short chromatin constructs. We explore the effects of nucleosome positioning and the presence or absence of cationic N-terminal histone tails on the ‘local’ inter-nucleosomal interactions and the global deformations of the simulated chains. The correspondence between the predicted and observed effects of nucleosome composition and numbers on the long-range communication between the ends of designed nucleosome arrays lends credence to the model and to the molecular insights gleaned from the simulated structures. We also extract effective nucleosome-nucleosome potentials from the simulations and implement the potentials in a larger-scale computational treatment of regularly repeating chromatin fibers. Our results reveal a remarkable effect of nucleosome spacing on chromatin flexibility, with small changes in DNA linker length significantly altering the interactions of nucleosomes and the dimensions of the fiber as a whole. In addition, we find that these changes in nucleosome positioning influence the statistical properties of long chromatin constructs. That is, simulated chromatin fibers with the same number of nucleosomes exhibit polymeric behaviors ranging from Gaussian to worm-like, depending upon nucleosome spacing. These findings suggest that the physical and mechanical properties of chromatin can span a wide range of behaviors, depending on nucleosome positioning, and that care must be taken in the choice of models used to interpret the experimental properties of long chromatin fibers.