We present HAFM, a system that generates instrumental music audio to accompany input vocals. Given isolated singing voice, HAFM produces a coherent instrumental accompaniment that can be directly mixed with the input to create complete music. We propose three key innovations over prior work: (1) a dual-rate codec tokenization scheme using HuBERT semantic tokens at 50\,Hz for vocals and EnCodec acoustic tokens at 75\,Hz for instrumentals, enabling time-aligned yet rate-independent modeling; (2) a three-stage hierarchical autoregressive architecture (semantic to coarse acoustic to fine acoustic) with interleaved multi-codebook prediction and classifier-free guidance; and (3) modern Transformer design choices including QK-norm, GEGLU activations, RMSNorm, and T5-style relative position bias for improved training stability and sequence generalization. Experiments on MUSDB18 demonstrate that HAFM achieves a Fréchet Audio Distance (FAD) of 2.08 on isolated vocal inputs, outperforming retrieval baselines and matching prior state-of-the-art systems with fewer parameters. The source code is available at https://github.com/HackerHyper/HAFM.