Transformer architectures have achieved state-of-the-art performance across natural language tasks, yet they fundamentally misrepresent the hierarchical nature of human language by processing text as flat token sequences. This results in quadratic computational cost, weak computational cost, weak compositional generalization, and inadequate discourse-level modeling. We propose Hierarchical Resolution Transformer (HRT), a novel wavelet-inspired neural architecture that processes language simultaneously across multiple resolutions, from characters to discourse-level units. HRT constructs a multi-resolution attention, enabling bottom-up composition and top-down contextualization. By employing exponential sequence reduction across scales, HRT achieves O(nlogn) complexity, offering significant efficiency improvements over standard transformers. We evaluated HRT on a diverse suite of benchmarks, including GLUE, SuperGLUE, Long Range Arena, and WikiText-103, and results demonstrated that HRT outperforms standard transformer baselines by an average of +3.8% on GLUE, +4.5% on SuperGLUE, and +6.1% on Long Range Arena, while reducing memory usage by 42% and inference latency by 37% compared to BERT and GPT style models of similar parameter count. Ablation studies confirm the effectiveness of cross-resolution attention and scale-specialized modules, showing that each contributes independently to both efficiency and accuracy. Our findings establish HRT as the first architecture to align computational structure with the hierarchical organization of human language, demonstrating that multi-scale, wavelet-inspired processing yields both theoretical efficiency gains and practical improvements in language understanding.