Long-context modeling is essential for symbolic music generation, since motif repetition and developmental variation can span thousands of musical events, yet practical workflows frequently rely on resource-limited hardware. We introduce Depth-Structured Music Recurrence (DSMR), a training-time design that learns from complete compositions end to end by streaming each piece left-to-right with stateful recurrent attention and distributing layer-wise memory horizons under a fixed recurrent-state budget. Our main instantiation, two-scale DSMR, assigns long history windows to lower layers and a uniform short window to the remaining layers. On the MAESTRO piano performance dataset, two-scale DSMR matches a full-memory recurrent reference in perplexity (5.96 vs. 5.98) while using approximately 59% less GPU memory and achieving roughly 36% higher throughput. Variant analyses further show strong layer substitutability under binary-horizon schedules: performance depends primarily on total allocated memory rather than which layers carry it.