Semantics are one of the primary sources of top-down preattentive information. Modern deep object detectors excel at extracting such valuable semantic cues from complex visual scenes. However, the size of the visual input to be processed by these detectors can become a bottleneck, particularly in terms of time costs, affecting an artificial attention system's biological plausibility and real-time deployability. Inspired by classical exponential density roll-off topologies, we apply a new artificial foveation module to our novel attention prediction pipeline: the Semantic-based Bayesian Attention (SemBA) framework. We aim at reducing detection-related computational costs without compromising visual task accuracy, thereby making SemBA more biologically plausible. The proposed multi-scale pyramidal field-of-view retains maximum acuity at an innermost level, around a focal point, while gradually increasing distortion for outer levels to mimic peripheral uncertainty via downsampling. In this work we evaluate the performance of our novel Multi-Scale Fovea, incorporated into \textit{SemBA}, on target-present visual search. We also compare it against other artificial foveal systems, and conduct ablation studies with different deep object detection models to assess the impact of the new topology in terms of computational costs. We experimentally demonstrate that including the new Multi-Scale Fovea module effectively reduces inherent processing costs while improving SemBA's scanpath prediction accuracy. Remarkably, we show that SemBA closely approximates human consistency while retaining the actual human fovea's proportions.