Low-noise pulleys and methods of constructing low-noise pulleys are disclosed. In a first aspect, first and second pluralities of arms extending radially outward from the outer hub to the outer rim are angularly offset from each other about the axis of rotation to eliminate symmetry across the lateral midline of the pulley. In a second aspect, the radially outermost ends of a plurality of arms are arcuately spaced apart according to a pitch sequence describing a pseudo-random pattern of relative spacings so as to reduce or eliminate rotational symmetry of the pulley. In a third aspect, features of the first and second aspects are combined, and in one embodiment, first and second pluralities of arms are, respectively, approximately oppositely canted so as to vary the arcuate spacings of the laterally outermost ends of the arms.