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Adaptive feedback cancellers in hearing aids can produce unpleasant sounding distortion artifacts (entrainment) in response to periodic inputs, including music. Reliable objective metrics that predict user-perceived distortion could significantly reduce development costs for new hearing aids. The aim of this study was to gain insight into the ability of different objective metrics to predict subjective ratings of the sound quality of music processed by adaptive feedback cancellation. The metrics tested consisted of perceptual measures from established audio quality models (including Perceptual Evaluation of Audio Quality (PEAQ), PEMO-Q and .Rnonlin). Neural networks were used to map between the values of the perceptual measures and a subjective scale of perceived quality. Training data consisted of values of perceptual measures obtained from ten different excerpts of orchestral music processed by a simplified model of a hearing aid with an adaptive feedback canceller, and corresponding subjective quality ratings from 27 normal hearing subjects. An optimal combination of perceptual measures to use as inputs to a network input was found using an extended Fourier amplitude sensitivity test (EFAST). Our results suggest that the most salient inputs to a multivariate model of measured quality ratings consist of perceptual measures related to spectral noise loudness, modulation differences between clean and processed signals, and correlation-based measurement of nonlinear distortion. The intraclass correlation between mean subjective ratings and the output of a network combining these perceptual measures was high , which compares favorably to results from previous studies of perceptual quality metrics applied to audio signals with other forms of noise or distortion.