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This paper investigates how precise a model should be for a robust model-based NMF analysis of piano recordings. While inharmonicity is an essential feature of piano tones from a perceptual point of view, its explicit inclusion in sound models is not straightforward and may even damage the quality of the analysis. Here, we assess the quality of the analysis with a transcription task, and compare three different models for the spectra of the dictionary: one strictly harmonic, one following the theoretical inharmonicity law, and one with relaxed inharmonicity constraints. Experimental results show that both inharmonic models can indeed significantly enhance the results, but only in the case when a good initialization is provided.