The excellent performance of recent self-supervised learning methods on various downstream tasks has attracted great attention from academia and industry. Some recent research efforts have been devoted to self-supervised music representation learning. Nevertheless, most of them learn to represent equally-sized music clips in the waveform or a spectrogram. Despite being effective in some tasks, learning music representations in such a manner largely neglect the inherent part-whole hierarchies of music. Due to the hierarchical nature of the auditory cortex [24], understanding the bottom-up structure of music, i.e., how different parts constitute the whole at different levels, is essential for music understanding and representation learning. This work pursues hierarchical music representation learning and introduces the Music-PAW framework, which enables feature interactions of cropped music clips with part-whole hierarchies. From a technical perspective, we propose a transformer-based part-whole interaction module to progressively reason the structural relationships between part-whole music clips at adjacent levels. Besides, to create a multi-hierarchy representation space, we devise a hierarchical contrastive learning objective to align part-whole music representations in adjacent hierarchies. The merits of audio representation learning from part-whole hierarchies have been validated on various downstream tasks, including music classification (single-label and multi-label), cover song identification and acoustic scene classification.