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In this paper, we present a method for estimating the local keys of an audio signal. We propose to address the problem of local key finding by investigating the possible combination and extension of different previous proposed global key estimation approaches. The specificity of our approach is that we introduce key dependency on the harmonic and the metric structures. In this work, we focus on the relationship between the chord progression and the local key progression in a piece of music. A contribution of our work is that we address the problem of finding a good analysis window length for local key estimation by introducing information related to the metric structure in our model. Key estimation is not performed on empirical-chosen segments length but on segments that are adapted to the analyzed piece and independent from the tempo. We evaluate and analyze our results on a new database composed of classical music pieces.