An out-of-tune singer or instrument can ruin the enjoyment of music. However, there is disagreement on how we perceive mistuning in natural music settings. To address this question, we presented listeners with in-tune and out-of-tune passages of two-part music and manipulated the two primary candidate acoustic cues: beats (fluctuations caused by interactions between nearby frequency components) and inharmonicity (non-integer harmonic frequency relationships) across seven experiments (Exp 1: N = 101; Exp 2: N = 63; Exp 3a: N = 87; Exp 3b: N = 28; Exp 3c: N = 69; Exp 4: N = 160; Exp 5: N = 105). Mistuning detection worsened markedly when removing either beating or inharmonicity cues, suggesting important contributions from both. The relative importance of the two cues varied reliably between listeners but was unaffected by musical experience. Finally, a general asymmetry in sensitivity to mistuning was discovered, with compressed pitch differences being more easily detected than stretched ones, thereby demonstrating a generalization of the previously found stretched-octave effect. Overall, the results reveal the acoustic underpinnings of the critical perceptual phenomenon of dissonance through mistuning in natural music.